TSTP Solution File: NUM453+6 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : NUM453+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:07:12 EDT 2023
% Result : Theorem 0.96s 0.63s
% Output : CNFRefutation 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 88 ( 34 unt; 0 def)
% Number of atoms : 326 ( 105 equ)
% Maximal formula atoms : 44 ( 3 avg)
% Number of connectives : 333 ( 95 ~; 100 |; 114 &)
% ( 10 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn; 51 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',m__2171) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',mEquModRef) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',mIntOne) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',mZeroDiv) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',mAddNeg) ).
fof(m__2079,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',m__2079) ).
fof(m__,conjecture,
( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',m__) ).
fof(m__2232,hypothesis,
( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',m__2232) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',mAddAsso) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',mAddComm) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',mAddZero) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p',mIntNeg) ).
fof(c_0_12,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
fof(c_0_13,hypothesis,
! [X47,X49,X50,X51,X53,X54,X55,X56] :
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ( aInteger0(X47)
| ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aInteger0(esk11_1(X47))
| ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdtasdt0(xp,esk11_1(X47)) = sdtpldt0(X47,smndt0(sz10))
| ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aDivisorOf0(xp,sdtpldt0(X47,smndt0(sz10)))
| ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdteqdtlpzmzozddtrp0(X47,sz10,xp)
| ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aInteger0(X50)
| sdtasdt0(xp,X50) != sdtpldt0(X49,smndt0(sz10))
| ~ aInteger0(X49)
| aElementOf0(X49,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aDivisorOf0(xp,sdtpldt0(X49,smndt0(sz10)))
| ~ aInteger0(X49)
| aElementOf0(X49,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ sdteqdtlpzmzozddtrp0(X49,sz10,xp)
| ~ aInteger0(X49)
| aElementOf0(X49,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(sbsmnsldt0(xS))
& ( aInteger0(X51)
| ~ aElementOf0(X51,sbsmnsldt0(xS)) )
& ( aElementOf0(esk12_1(X51),xS)
| ~ aElementOf0(X51,sbsmnsldt0(xS)) )
& ( aElementOf0(X51,esk12_1(X51))
| ~ aElementOf0(X51,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X53)
| ~ aElementOf0(X54,xS)
| ~ aElementOf0(X53,X54)
| aElementOf0(X53,sbsmnsldt0(xS)) )
& ( aInteger0(X55)
| ~ aElementOf0(X55,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X55,sbsmnsldt0(xS))
| ~ aElementOf0(X55,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X55)
| aElementOf0(X55,sbsmnsldt0(xS))
| aElementOf0(X55,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X56,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X56,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(distribute,[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_12])])])])])]) ).
fof(c_0_14,plain,
! [X85,X86] :
( ~ aInteger0(X85)
| ~ aInteger0(X86)
| X86 = sz00
| sdteqdtlpzmzozddtrp0(X85,X85,X86) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).
cnf(c_0_15,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
( X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_18,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X80,X81] :
( ~ aInteger0(X80)
| ~ aInteger0(X81)
| sdtasdt0(X80,X81) != sz00
| X80 = sz00
| X81 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
cnf(c_0_21,hypothesis,
( sdtasdt0(xp,esk11_1(X1)) = sdtpldt0(X1,smndt0(sz10))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,hypothesis,
aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_23,hypothesis,
( aInteger0(esk11_1(X1))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,hypothesis,
sdtasdt0(xp,esk11_1(sz10)) = sdtpldt0(sz10,smndt0(sz10)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,hypothesis,
aInteger0(esk11_1(sz10)),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
fof(c_0_27,plain,
! [X110] :
( ( sdtpldt0(X110,smndt0(X110)) = sz00
| ~ aInteger0(X110) )
& ( sz00 = sdtpldt0(smndt0(X110),X110)
| ~ aInteger0(X110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
fof(c_0_28,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(fof_simplification,[status(thm)],[m__2079]) ).
cnf(c_0_29,hypothesis,
( esk11_1(sz10) = sz00
| sdtpldt0(sz10,smndt0(sz10)) != sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_18])]),c_0_19]) ).
cnf(c_0_30,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_31,hypothesis,
! [X17,X19,X20,X21,X22] :
( aSet0(sbsmnsldt0(xS))
& ( aInteger0(X17)
| ~ aElementOf0(X17,sbsmnsldt0(xS)) )
& ( aElementOf0(esk4_1(X17),xS)
| ~ aElementOf0(X17,sbsmnsldt0(xS)) )
& ( aElementOf0(X17,esk4_1(X17))
| ~ aElementOf0(X17,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X19)
| ~ aElementOf0(X20,xS)
| ~ aElementOf0(X19,X20)
| aElementOf0(X19,sbsmnsldt0(xS)) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ( aInteger0(X21)
| ~ aElementOf0(X21,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X21,sbsmnsldt0(xS))
| ~ aElementOf0(X21,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X21)
| aElementOf0(X21,sbsmnsldt0(xS))
| aElementOf0(X21,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X22,stldt0(sbsmnsldt0(xS)))
| X22 = sz10
| X22 = smndt0(sz10) )
& ( X22 != sz10
| aElementOf0(X22,stldt0(sbsmnsldt0(xS))) )
& ( X22 != smndt0(sz10)
| aElementOf0(X22,stldt0(sbsmnsldt0(xS))) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(distribute,[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_28])])])])])]) ).
fof(c_0_32,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_33,hypothesis,
esk11_1(sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_17])]) ).
cnf(c_0_34,hypothesis,
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| X1 != smndt0(sz10) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_36,hypothesis,
( aInteger0(esk13_0)
& sdtasdt0(xp,esk13_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& aInteger0(esk14_0)
& sdtasdt0(xp,esk14_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2232])]) ).
fof(c_0_37,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(fof_nnf,[status(thm)],[c_0_32]) ).
cnf(c_0_38,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,sz00),
inference(rw,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_39,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,hypothesis,
( aElementOf0(X1,cS2076)
| X1 != smndt0(sz10) ),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,hypothesis,
sdtasdt0(xp,esk14_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_43,plain,
! [X105,X106,X107] :
( ~ aInteger0(X105)
| ~ aInteger0(X106)
| ~ aInteger0(X107)
| sdtpldt0(X105,sdtpldt0(X106,X107)) = sdtpldt0(sdtpldt0(X105,X106),X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_44,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_38]),c_0_17])]) ).
cnf(c_0_45,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_46,hypothesis,
aElementOf0(smndt0(sz10),cS2076),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,esk14_0)
| sdtpldt0(sz10,xp) = sz10 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(rw,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_50,hypothesis,
aInteger0(smndt0(sz10)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_51,plain,
! [X108,X109] :
( ~ aInteger0(X108)
| ~ aInteger0(X109)
| sdtpldt0(X108,X109) = sdtpldt0(X109,X108) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_52,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtasdt0(xp,esk14_0) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_47]),c_0_17])]) ).
cnf(c_0_53,hypothesis,
aInteger0(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_54,hypothesis,
sdtasdt0(xp,esk13_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_55,hypothesis,
( sdtpldt0(sz10,sdtpldt0(smndt0(sz10),X1)) = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_17])]) ).
cnf(c_0_56,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| esk14_0 = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_52]),c_0_53]),c_0_18])]),c_0_19]) ).
cnf(c_0_58,hypothesis,
sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))) = sdtasdt0(xp,esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_48]),c_0_18]),c_0_17])]),c_0_50])]) ).
cnf(c_0_59,hypothesis,
( sdtpldt0(sz10,sdtpldt0(X1,smndt0(sz10))) = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_50])]) ).
cnf(c_0_60,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_61,hypothesis,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_62,plain,
! [X78] :
( ( sdtpldt0(X78,sz00) = X78
| ~ aInteger0(X78) )
& ( X78 = sdtpldt0(sz00,X78)
| ~ aInteger0(X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_63,hypothesis,
( sdtasdt0(xp,esk13_0) = sz00
| esk14_0 = sz00 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_57]),c_0_38]),c_0_44]) ).
cnf(c_0_64,hypothesis,
sdtasdt0(xp,esk13_0) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_18])]) ).
cnf(c_0_65,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_66,hypothesis,
aInteger0(sdtpldt0(sz10,smndt0(xp))),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_68,hypothesis,
( sdtpldt0(sz00,xp) = sz00
| esk14_0 = sz00 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,hypothesis,
sdtpldt0(sz10,sz00) = sdtpldt0(sz00,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_65]),c_0_17])]) ).
cnf(c_0_71,hypothesis,
sdtpldt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))) = sdtasdt0(xp,esk14_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_56]),c_0_66]),c_0_50])]) ).
cnf(c_0_72,hypothesis,
esk14_0 = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_18])]),c_0_19]) ).
cnf(c_0_73,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_17])]) ).
cnf(c_0_74,hypothesis,
sdtpldt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))) = sz00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_44]) ).
cnf(c_0_75,hypothesis,
sdtpldt0(sz10,sz00) = sz10,
inference(rw,[status(thm)],[c_0_70,c_0_73]) ).
cnf(c_0_76,hypothesis,
sdtpldt0(sz00,sdtpldt0(sz10,smndt0(xp))) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_74]),c_0_75]),c_0_66])]) ).
cnf(c_0_77,hypothesis,
sdtpldt0(sz10,smndt0(xp)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_76]),c_0_66])]) ).
cnf(c_0_78,hypothesis,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(rw,[status(thm)],[c_0_74,c_0_77]) ).
cnf(c_0_79,hypothesis,
( sdtpldt0(smndt0(sz10),sdtpldt0(sz10,X1)) = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_78]),c_0_17]),c_0_50])]) ).
fof(c_0_80,plain,
! [X114] :
( ~ aInteger0(X114)
| aInteger0(smndt0(X114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_81,hypothesis,
( sdtpldt0(sz00,smndt0(xp)) = sz00
| ~ aInteger0(smndt0(xp)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_77]),c_0_78]) ).
cnf(c_0_82,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_83,hypothesis,
sdtpldt0(sz00,smndt0(xp)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_18])]) ).
cnf(c_0_84,hypothesis,
( smndt0(xp) = sz00
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_67,c_0_83]) ).
cnf(c_0_85,hypothesis,
smndt0(xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_82]),c_0_18])]) ).
cnf(c_0_86,hypothesis,
sdtpldt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_85]),c_0_18])]) ).
cnf(c_0_87,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_86]),c_0_18])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM453+6 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 2400
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Oct 2 14:06:00 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.50 Running first-order model finding
% 0.21/0.50 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/tmp/tmp.ZJfc3hI7ur/E---3.1_6965.p
% 0.96/0.63 # Version: 3.1pre001
% 0.96/0.63 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.96/0.63 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.96/0.63 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.96/0.63 # Starting new_bool_3 with 300s (1) cores
% 0.96/0.63 # Starting new_bool_1 with 300s (1) cores
% 0.96/0.63 # Starting sh5l with 300s (1) cores
% 0.96/0.63 # new_bool_1 with pid 7125 completed with status 0
% 0.96/0.63 # Result found by new_bool_1
% 0.96/0.63 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.96/0.63 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.96/0.63 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.96/0.63 # Starting new_bool_3 with 300s (1) cores
% 0.96/0.63 # Starting new_bool_1 with 300s (1) cores
% 0.96/0.63 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.96/0.63 # Search class: FGHSF-FSLM31-MFFFFFNN
% 0.96/0.63 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.96/0.63 # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 163s (1) cores
% 0.96/0.63 # G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with pid 7127 completed with status 0
% 0.96/0.63 # Result found by G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S
% 0.96/0.63 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.96/0.63 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.96/0.63 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.96/0.63 # Starting new_bool_3 with 300s (1) cores
% 0.96/0.63 # Starting new_bool_1 with 300s (1) cores
% 0.96/0.63 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.96/0.63 # Search class: FGHSF-FSLM31-MFFFFFNN
% 0.96/0.63 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.96/0.63 # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 163s (1) cores
% 0.96/0.63 # Preprocessing time : 0.008 s
% 0.96/0.63 # Presaturation interreduction done
% 0.96/0.63
% 0.96/0.63 # Proof found!
% 0.96/0.63 # SZS status Theorem
% 0.96/0.63 # SZS output start CNFRefutation
% See solution above
% 0.96/0.63 # Parsed axioms : 48
% 0.96/0.63 # Removed by relevancy pruning/SinE : 4
% 0.96/0.63 # Initial clauses : 207
% 0.96/0.63 # Removed in clause preprocessing : 5
% 0.96/0.63 # Initial clauses in saturation : 202
% 0.96/0.63 # Processed clauses : 663
% 0.96/0.63 # ...of these trivial : 25
% 0.96/0.63 # ...subsumed : 101
% 0.96/0.63 # ...remaining for further processing : 537
% 0.96/0.63 # Other redundant clauses eliminated : 2
% 0.96/0.63 # Clauses deleted for lack of memory : 0
% 0.96/0.63 # Backward-subsumed : 6
% 0.96/0.63 # Backward-rewritten : 79
% 0.96/0.63 # Generated clauses : 1460
% 0.96/0.63 # ...of the previous two non-redundant : 1239
% 0.96/0.63 # ...aggressively subsumed : 0
% 0.96/0.63 # Contextual simplify-reflections : 0
% 0.96/0.63 # Paramodulations : 1429
% 0.96/0.63 # Factorizations : 1
% 0.96/0.63 # NegExts : 0
% 0.96/0.63 # Equation resolutions : 30
% 0.96/0.63 # Total rewrite steps : 1723
% 0.96/0.63 # Propositional unsat checks : 0
% 0.96/0.63 # Propositional check models : 0
% 0.96/0.63 # Propositional check unsatisfiable : 0
% 0.96/0.63 # Propositional clauses : 0
% 0.96/0.63 # Propositional clauses after purity: 0
% 0.96/0.63 # Propositional unsat core size : 0
% 0.96/0.63 # Propositional preprocessing time : 0.000
% 0.96/0.63 # Propositional encoding time : 0.000
% 0.96/0.63 # Propositional solver time : 0.000
% 0.96/0.63 # Success case prop preproc time : 0.000
% 0.96/0.63 # Success case prop encoding time : 0.000
% 0.96/0.63 # Success case prop solver time : 0.000
% 0.96/0.63 # Current number of processed clauses : 268
% 0.96/0.63 # Positive orientable unit clauses : 67
% 0.96/0.63 # Positive unorientable unit clauses: 0
% 0.96/0.63 # Negative unit clauses : 4
% 0.96/0.63 # Non-unit-clauses : 197
% 0.96/0.63 # Current number of unprocessed clauses: 914
% 0.96/0.63 # ...number of literals in the above : 3976
% 0.96/0.63 # Current number of archived formulas : 0
% 0.96/0.63 # Current number of archived clauses : 269
% 0.96/0.63 # Clause-clause subsumption calls (NU) : 9883
% 0.96/0.63 # Rec. Clause-clause subsumption calls : 2991
% 0.96/0.63 # Non-unit clause-clause subsumptions : 97
% 0.96/0.63 # Unit Clause-clause subsumption calls : 378
% 0.96/0.63 # Rewrite failures with RHS unbound : 0
% 0.96/0.63 # BW rewrite match attempts : 28
% 0.96/0.63 # BW rewrite match successes : 22
% 0.96/0.63 # Condensation attempts : 0
% 0.96/0.63 # Condensation successes : 0
% 0.96/0.63 # Termbank termtop insertions : 40156
% 0.96/0.63
% 0.96/0.63 # -------------------------------------------------
% 0.96/0.63 # User time : 0.101 s
% 0.96/0.63 # System time : 0.013 s
% 0.96/0.63 # Total time : 0.114 s
% 0.96/0.63 # Maximum resident set size: 2344 pages
% 0.96/0.63
% 0.96/0.63 # -------------------------------------------------
% 0.96/0.63 # User time : 0.106 s
% 0.96/0.63 # System time : 0.016 s
% 0.96/0.63 # Total time : 0.122 s
% 0.96/0.63 # Maximum resident set size: 1756 pages
% 0.96/0.63 % E---3.1 exiting
%------------------------------------------------------------------------------