TSTP Solution File: NUM454+1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM454+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.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 01:14:02 EDT 2024
% Result : Theorem 1.54s 0.74s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 27 unt; 0 def)
% Number of atoms : 310 ( 109 equ)
% Maximal formula atoms : 46 ( 3 avg)
% Number of connectives : 363 ( 138 ~; 146 |; 55 &)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 113 ( 0 sgn 65 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mArSeq,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(m__,conjecture,
( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
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/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(m__2232,hypothesis,
( aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2232) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(c_0_16,plain,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mArSeq]) ).
fof(c_0_17,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_18,plain,
! [X96,X97,X98,X99,X100,X101] :
( ( aSet0(X98)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aInteger0(X96)
| ~ aInteger0(X97)
| X97 = sz00 )
& ( aInteger0(X99)
| ~ aElementOf0(X99,X98)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aInteger0(X96)
| ~ aInteger0(X97)
| X97 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X99,X96,X97)
| ~ aElementOf0(X99,X98)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aInteger0(X96)
| ~ aInteger0(X97)
| X97 = sz00 )
& ( ~ aInteger0(X100)
| ~ sdteqdtlpzmzozddtrp0(X100,X96,X97)
| aElementOf0(X100,X98)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aInteger0(X96)
| ~ aInteger0(X97)
| X97 = sz00 )
& ( ~ aElementOf0(esk11_3(X96,X97,X101),X101)
| ~ aInteger0(esk11_3(X96,X97,X101))
| ~ sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97)
| ~ aSet0(X101)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aInteger0(X96)
| ~ aInteger0(X97)
| X97 = sz00 )
& ( aInteger0(esk11_3(X96,X97,X101))
| aElementOf0(esk11_3(X96,X97,X101),X101)
| ~ aSet0(X101)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aInteger0(X96)
| ~ aInteger0(X97)
| X97 = sz00 )
& ( sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97)
| aElementOf0(esk11_3(X96,X97,X101),X101)
| ~ aSet0(X101)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aInteger0(X96)
| ~ aInteger0(X97)
| X97 = sz00 ) ),
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_16])])])])])])]) ).
fof(c_0_19,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
fof(c_0_20,plain,
! [X17] :
( ( sdtpldt0(X17,smndt0(X17)) = sz00
| ~ aInteger0(X17) )
& ( sz00 = sdtpldt0(smndt0(X17),X17)
| ~ aInteger0(X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
fof(c_0_21,negated_conjecture,
( sdtpldt0(sz10,xp) = smndt0(sz10)
& sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( aInteger0(X1)
| X4 = sz00
| ~ aElementOf0(X1,X2)
| X2 != szAzrzSzezqlpdtcmdtrp0(X3,X4)
| ~ aInteger0(X3)
| ~ aInteger0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(fof_nnf,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X11,X12,X13] :
( ~ aInteger0(X11)
| ~ aInteger0(X12)
| ~ aInteger0(X13)
| sdtpldt0(X11,sdtpldt0(X12,X13)) = sdtpldt0(sdtpldt0(X11,X12),X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_25,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_28,plain,
( X1 = sz00
| aInteger0(X2)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X3) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_29,hypothesis,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[m__2232]) ).
cnf(c_0_30,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_34,hypothesis,
aInteger0(sdtpldt0(sz10,xp)),
inference(sr,[status(thm)],[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_27])]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_36,negated_conjecture,
( sdtpldt0(sdtpldt0(sz10,xp),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_32,c_0_33]),c_0_27]),c_0_34])]) ).
cnf(c_0_37,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_35,c_0_26]) ).
fof(c_0_38,plain,
! [X6] :
( ~ aInteger0(X6)
| aInteger0(smndt0(X6)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
fof(c_0_39,plain,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
inference(fof_simplification,[status(thm)],[mEquMod]) ).
cnf(c_0_40,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| ~ aElementOf0(X1,X4)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,negated_conjecture,
( sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtpldt0(sz00,smndt0(xp))
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_43,plain,
! [X36,X37,X38] :
( ( ~ sdteqdtlpzmzozddtrp0(X36,X37,X38)
| aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37)))
| ~ aInteger0(X36)
| ~ aInteger0(X37)
| ~ aInteger0(X38)
| X38 = sz00 )
& ( ~ aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37)))
| sdteqdtlpzmzozddtrp0(X36,X37,X38)
| ~ aInteger0(X36)
| ~ aInteger0(X37)
| ~ aInteger0(X38)
| X38 = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).
cnf(c_0_44,plain,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X3) ),
inference(er,[status(thm)],[c_0_40]) ).
fof(c_0_45,plain,
! [X16] :
( ( sdtpldt0(X16,sz00) = X16
| ~ aInteger0(X16) )
& ( X16 = sdtpldt0(sz00,X16)
| ~ aInteger0(X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_46,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtpldt0(sz00,smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_30])]) ).
cnf(c_0_47,plain,
( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,hypothesis,
sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_30]),c_0_27])]),c_0_31]) ).
cnf(c_0_49,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,negated_conjecture,
sdtpldt0(sz00,smndt0(xp)) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_46]),c_0_30])]) ).
fof(c_0_51,plain,
! [X28] :
( ( sdtasdt0(smndt0(sz10),X28) = smndt0(X28)
| ~ aInteger0(X28) )
& ( smndt0(X28) = sdtasdt0(X28,smndt0(sz10))
| ~ aInteger0(X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])])]) ).
fof(c_0_52,plain,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mDivisor]) ).
cnf(c_0_53,hypothesis,
aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp))),
inference(sr,[status(thm)],[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_48]),c_0_26]),c_0_30]),c_0_27]),c_0_34])]),c_0_31]) ).
cnf(c_0_54,negated_conjecture,
( smndt0(xp) = sdtpldt0(sz00,xp)
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_55,plain,
! [X18,X19,X20] :
( ~ aInteger0(X18)
| ~ aInteger0(X19)
| ~ aInteger0(X20)
| sdtasdt0(X18,sdtasdt0(X19,X20)) = sdtasdt0(sdtasdt0(X18,X19),X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_56,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_57,plain,
! [X31,X32,X34,X35] :
( ( aInteger0(X32)
| ~ aDivisorOf0(X32,X31)
| ~ aInteger0(X31) )
& ( X32 != sz00
| ~ aDivisorOf0(X32,X31)
| ~ aInteger0(X31) )
& ( aInteger0(esk1_2(X31,X32))
| ~ aDivisorOf0(X32,X31)
| ~ aInteger0(X31) )
& ( sdtasdt0(X32,esk1_2(X31,X32)) = X31
| ~ aDivisorOf0(X32,X31)
| ~ aInteger0(X31) )
& ( ~ aInteger0(X34)
| X34 = sz00
| ~ aInteger0(X35)
| sdtasdt0(X34,X35) != X31
| aDivisorOf0(X34,X31)
| ~ aInteger0(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)],[c_0_52])])])])])])]) ).
cnf(c_0_58,hypothesis,
aDivisorOf0(xp,sdtpldt0(sz00,xp)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_46]),c_0_50]) ).
cnf(c_0_59,negated_conjecture,
smndt0(xp) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_42]),c_0_30])]) ).
cnf(c_0_60,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
( sdtasdt0(sdtpldt0(sz10,xp),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(rw,[status(thm)],[c_0_56,c_0_26]) ).
cnf(c_0_62,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,hypothesis,
aDivisorOf0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_49]),c_0_30])]) ).
cnf(c_0_64,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz00,xp)) = sdtpldt0(sz00,xp),
inference(rw,[status(thm)],[c_0_50,c_0_59]) ).
cnf(c_0_65,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_66,plain,
! [X24,X25,X26] :
( ( sdtasdt0(X24,sdtpldt0(X25,X26)) = sdtpldt0(sdtasdt0(X24,X25),sdtasdt0(X24,X26))
| ~ aInteger0(X24)
| ~ aInteger0(X25)
| ~ aInteger0(X26) )
& ( sdtasdt0(sdtpldt0(X24,X25),X26) = sdtpldt0(sdtasdt0(X24,X26),sdtasdt0(X25,X26))
| ~ aInteger0(X24)
| ~ aInteger0(X25)
| ~ aInteger0(X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])])]) ).
cnf(c_0_67,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_68,plain,
! [X21,X22] :
( ~ aInteger0(X21)
| ~ aInteger0(X22)
| sdtasdt0(X21,X22) = sdtasdt0(X22,X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_69,plain,
( sdtasdt0(sdtpldt0(sz10,xp),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_34])]) ).
cnf(c_0_70,hypothesis,
sdtasdt0(xp,esk1_2(xp,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_30])]) ).
cnf(c_0_71,negated_conjecture,
sdtpldt0(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_49]),c_0_30])]) ).
cnf(c_0_72,hypothesis,
aInteger0(esk1_2(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_63]),c_0_30])]) ).
cnf(c_0_73,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_74,plain,
( sdtasdt0(X1,sdtpldt0(sz10,xp)) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(rw,[status(thm)],[c_0_67,c_0_26]) ).
cnf(c_0_75,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_76,hypothesis,
sdtasdt0(sdtpldt0(sz10,xp),xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_59]),c_0_71]),c_0_70]),c_0_72]),c_0_30])]) ).
cnf(c_0_77,negated_conjecture,
sdtpldt0(sdtpldt0(sz00,xp),xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_59]),c_0_30])]) ).
fof(c_0_78,plain,
! [X29,X30] :
( ~ aInteger0(X29)
| ~ aInteger0(X30)
| sdtasdt0(X29,X30) != sz00
| X29 = sz00
| X30 = sz00 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])])]) ).
cnf(c_0_79,plain,
( sdtpldt0(sdtasdt0(X1,X2),smndt0(X1)) = sdtasdt0(X1,sdtpldt0(X2,sdtpldt0(sz10,xp)))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_34])]) ).
cnf(c_0_80,hypothesis,
sdtasdt0(xp,sdtpldt0(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_30]),c_0_34])]) ).
cnf(c_0_81,negated_conjecture,
sdtpldt0(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_49]),c_0_30])]) ).
cnf(c_0_82,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_83,hypothesis,
sdtasdt0(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_59]),c_0_71]),c_0_81]),c_0_46]),c_0_59]),c_0_71]),c_0_71]),c_0_34]),c_0_30])]) ).
cnf(c_0_84,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_30])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM454+1 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n010.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 : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 05:32:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 1.54/0.74 # Version: 3.1.0
% 1.54/0.74 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.54/0.74 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.54/0.74 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.54/0.74 # Starting new_bool_3 with 300s (1) cores
% 1.54/0.74 # Starting new_bool_1 with 300s (1) cores
% 1.54/0.74 # Starting sh5l with 300s (1) cores
% 1.54/0.74 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 31598 completed with status 0
% 1.54/0.74 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.54/0.74 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.54/0.74 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.54/0.74 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.54/0.74 # No SInE strategy applied
% 1.54/0.74 # Search class: FGHSF-FSLM31-SFFFFFNN
% 1.54/0.74 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.54/0.74 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 666s (1) cores
% 1.54/0.74 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.54/0.74 # Starting new_bool_3 with 194s (1) cores
% 1.54/0.74 # Starting new_bool_1 with 188s (1) cores
% 1.54/0.74 # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 1.54/0.74 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 31603 completed with status 0
% 1.54/0.74 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.54/0.74 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.54/0.74 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.54/0.74 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.54/0.74 # No SInE strategy applied
% 1.54/0.74 # Search class: FGHSF-FSLM31-SFFFFFNN
% 1.54/0.74 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.54/0.74 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 666s (1) cores
% 1.54/0.74 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.54/0.74 # Preprocessing time : 0.005 s
% 1.54/0.74 # Presaturation interreduction done
% 1.54/0.74
% 1.54/0.74 # Proof found!
% 1.54/0.74 # SZS status Theorem
% 1.54/0.74 # SZS output start CNFRefutation
% See solution above
% 1.54/0.74 # Parsed axioms : 49
% 1.54/0.74 # Removed by relevancy pruning/SinE : 0
% 1.54/0.74 # Initial clauses : 126
% 1.54/0.74 # Removed in clause preprocessing : 5
% 1.54/0.74 # Initial clauses in saturation : 121
% 1.54/0.74 # Processed clauses : 1558
% 1.54/0.74 # ...of these trivial : 30
% 1.54/0.74 # ...subsumed : 851
% 1.54/0.74 # ...remaining for further processing : 677
% 1.54/0.74 # Other redundant clauses eliminated : 33
% 1.54/0.74 # Clauses deleted for lack of memory : 0
% 1.54/0.74 # Backward-subsumed : 13
% 1.54/0.74 # Backward-rewritten : 68
% 1.54/0.74 # Generated clauses : 8951
% 1.54/0.74 # ...of the previous two non-redundant : 6649
% 1.54/0.74 # ...aggressively subsumed : 0
% 1.54/0.74 # Contextual simplify-reflections : 79
% 1.54/0.74 # Paramodulations : 8918
% 1.54/0.74 # Factorizations : 0
% 1.54/0.74 # NegExts : 0
% 1.54/0.74 # Equation resolutions : 33
% 1.54/0.74 # Disequality decompositions : 0
% 1.54/0.74 # Total rewrite steps : 15970
% 1.54/0.74 # ...of those cached : 15884
% 1.54/0.74 # Propositional unsat checks : 0
% 1.54/0.74 # Propositional check models : 0
% 1.54/0.74 # Propositional check unsatisfiable : 0
% 1.54/0.74 # Propositional clauses : 0
% 1.54/0.74 # Propositional clauses after purity: 0
% 1.54/0.74 # Propositional unsat core size : 0
% 1.54/0.74 # Propositional preprocessing time : 0.000
% 1.54/0.74 # Propositional encoding time : 0.000
% 1.54/0.74 # Propositional solver time : 0.000
% 1.54/0.74 # Success case prop preproc time : 0.000
% 1.54/0.74 # Success case prop encoding time : 0.000
% 1.54/0.74 # Success case prop solver time : 0.000
% 1.54/0.74 # Current number of processed clauses : 445
% 1.54/0.74 # Positive orientable unit clauses : 67
% 1.54/0.74 # Positive unorientable unit clauses: 0
% 1.54/0.74 # Negative unit clauses : 10
% 1.54/0.74 # Non-unit-clauses : 368
% 1.54/0.74 # Current number of unprocessed clauses: 5152
% 1.54/0.74 # ...number of literals in the above : 21341
% 1.54/0.74 # Current number of archived formulas : 0
% 1.54/0.74 # Current number of archived clauses : 200
% 1.54/0.74 # Clause-clause subsumption calls (NU) : 33241
% 1.54/0.74 # Rec. Clause-clause subsumption calls : 19653
% 1.54/0.74 # Non-unit clause-clause subsumptions : 920
% 1.54/0.74 # Unit Clause-clause subsumption calls : 1296
% 1.54/0.74 # Rewrite failures with RHS unbound : 0
% 1.54/0.74 # BW rewrite match attempts : 33
% 1.54/0.74 # BW rewrite match successes : 31
% 1.54/0.74 # Condensation attempts : 0
% 1.54/0.74 # Condensation successes : 0
% 1.54/0.74 # Termbank termtop insertions : 163973
% 1.54/0.74 # Search garbage collected termcells : 2357
% 1.54/0.74
% 1.54/0.74 # -------------------------------------------------
% 1.54/0.74 # User time : 0.224 s
% 1.54/0.74 # System time : 0.014 s
% 1.54/0.74 # Total time : 0.238 s
% 1.54/0.74 # Maximum resident set size: 2072 pages
% 1.54/0.74
% 1.54/0.74 # -------------------------------------------------
% 1.54/0.74 # User time : 1.131 s
% 1.54/0.74 # System time : 0.029 s
% 1.54/0.74 # Total time : 1.160 s
% 1.54/0.74 # Maximum resident set size: 1752 pages
% 1.54/0.74 % E---3.1 exiting
% 1.54/0.74 % E exiting
%------------------------------------------------------------------------------