%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM454+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:08 PM UTC 2026
% Result : Theorem 0.22s 20.66s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 90 ( 29 unt; 0 def)
% Number of atoms : 314 ( 108 equ)
% Maximal formula atoms : 46 ( 3 avg)
% Number of connectives : 363 ( 139 ~; 143 |; 56 &)
% ( 8 <=>; 17 =>; 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 : 112 ( 0 sgn 69 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> 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(mArSeq,axiom,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sdteqdtlpzmzozddtrp0(X4,X1,X2)
& aInteger0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(m__2171,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(m__2232,hypothesis,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2232) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> 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(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(c_0_17,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_18,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_19,plain,
! [X17] :
( ( ~ aInteger0(X17)
| sz00 = sdtpldt0(smndt0(X17),X17) )
& ( ~ aInteger0(X17)
| sdtpldt0(X17,smndt0(X17)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
fof(c_0_20,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10)
& sdtpldt0(sz10,xp) = smndt0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X6] :
( aInteger0(smndt0(X6))
| ~ aInteger0(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
fof(c_0_22,plain,
! [X11,X12,X13] :
( sdtpldt0(X11,sdtpldt0(X12,X13)) = sdtpldt0(sdtpldt0(X11,X12),X13)
| ~ aInteger0(X13)
| ~ aInteger0(X12)
| ~ aInteger0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_23,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_26,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sdteqdtlpzmzozddtrp0(X4,X1,X2)
& aInteger0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mArSeq]) ).
cnf(c_0_28,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_30,negated_conjecture,
aInteger0(sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_25])]) ).
cnf(c_0_31,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_32,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
fof(c_0_33,plain,
! [X96,X97,X98,X99,X100,X101] :
( ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aSet0(X101)
| aElementOf0(esk11_3(X96,X97,X101),X101)
| sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aSet0(X101)
| aElementOf0(esk11_3(X96,X97,X101),X101)
| aInteger0(esk11_3(X96,X97,X101)) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aSet0(X101)
| ~ sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97)
| ~ aInteger0(esk11_3(X96,X97,X101))
| ~ aElementOf0(esk11_3(X96,X97,X101),X101) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| aElementOf0(X100,X98)
| ~ sdteqdtlpzmzozddtrp0(X100,X96,X97)
| ~ aInteger0(X100) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aElementOf0(X99,X98)
| sdteqdtlpzmzozddtrp0(X99,X96,X97) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aElementOf0(X99,X98)
| aInteger0(X99) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| aSet0(X98) ) ),
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_27])])])])])])]) ).
cnf(c_0_34,negated_conjecture,
( ~ aInteger0(X1)
| sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,X1)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]),c_0_30])]) ).
cnf(c_0_35,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_31,c_0_24]) ).
fof(c_0_36,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
inference(fof_nnf,[status(thm)],[c_0_32]) ).
fof(c_0_37,plain,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
inference(fof_simplification,[status(thm)],[mEquMod]) ).
cnf(c_0_38,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aElementOf0(X1,X4)
| X3 = sz00
| sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtpldt0(sz00,smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_41,plain,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[mDivisor]) ).
fof(c_0_42,plain,
! [X36,X37,X38] :
( ( X38 = sz00
| ~ aInteger0(X38)
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| sdteqdtlpzmzozddtrp0(X36,X37,X38)
| ~ aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37))) )
& ( X38 = sz00
| ~ aInteger0(X38)
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37)))
| ~ sdteqdtlpzmzozddtrp0(X36,X37,X38) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
cnf(c_0_43,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_44,hypothesis,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[m__2232]) ).
cnf(c_0_45,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_46,plain,
! [X16] :
( ( ~ aInteger0(X16)
| X16 = sdtpldt0(sz00,X16) )
& ( ~ aInteger0(X16)
| sdtpldt0(X16,sz00) = X16 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_47,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_39,c_0_26]),c_0_40])]) ).
fof(c_0_48,plain,
! [X31,X32,X34,X35] :
( ( ~ aInteger0(X31)
| aDivisorOf0(X34,X31)
| sdtasdt0(X34,X35) != X31
| ~ aInteger0(X35)
| X34 = sz00
| ~ aInteger0(X34) )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| sdtasdt0(X32,esk1_2(X31,X32)) = X31 )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| aInteger0(esk1_2(X31,X32)) )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| X32 != sz00 )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| aInteger0(X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])])])])]) ).
cnf(c_0_49,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,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_43,c_0_44]),c_0_40]),c_0_25])]),c_0_45]) ).
cnf(c_0_51,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
sdtpldt0(sz00,smndt0(xp)) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_47]),c_0_40])]) ).
cnf(c_0_53,plain,
( ~ aInteger0(X1)
| ~ aDivisorOf0(X2,X1)
| aInteger0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,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_49,c_0_50]),c_0_24]),c_0_40]),c_0_25]),c_0_30])]),c_0_45]) ).
fof(c_0_55,plain,
! [X7,X8] :
( aInteger0(sdtpldt0(X7,X8))
| ~ aInteger0(X8)
| ~ aInteger0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])])]) ).
fof(c_0_56,plain,
! [X28] :
( ( ~ aInteger0(X28)
| smndt0(X28) = sdtasdt0(X28,smndt0(sz10)) )
& ( ~ aInteger0(X28)
| sdtasdt0(smndt0(sz10),X28) = smndt0(X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])])]) ).
cnf(c_0_57,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| smndt0(xp) = sdtpldt0(sz00,xp) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,hypothesis,
( ~ aInteger0(sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)))
| aInteger0(esk1_2(sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)),xp)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_60,plain,
! [X18,X19,X20] :
( sdtasdt0(X18,sdtasdt0(X19,X20)) = sdtasdt0(sdtasdt0(X18,X19),X20)
| ~ aInteger0(X20)
| ~ aInteger0(X19)
| ~ aInteger0(X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_61,plain,
( ~ aInteger0(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,hypothesis,
aDivisorOf0(xp,sdtpldt0(sz00,xp)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_47]),c_0_52]) ).
cnf(c_0_63,negated_conjecture,
smndt0(xp) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_26]),c_0_40])]) ).
cnf(c_0_64,hypothesis,
aInteger0(esk1_2(sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)),xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_30])]) ).
cnf(c_0_65,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
( ~ aInteger0(X1)
| sdtasdt0(sdtpldt0(sz10,xp),X1) = smndt0(X1) ),
inference(rw,[status(thm)],[c_0_61,c_0_24]) ).
cnf(c_0_67,plain,
( ~ aInteger0(X2)
| ~ aDivisorOf0(X1,X2)
| sdtasdt0(X1,esk1_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_68,hypothesis,
aDivisorOf0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_51]),c_0_40])]) ).
cnf(c_0_69,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz00,xp)) = sdtpldt0(sz00,xp),
inference(rw,[status(thm)],[c_0_52,c_0_63]) ).
cnf(c_0_70,hypothesis,
aInteger0(esk1_2(sdtpldt0(sz00,xp),xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_34]),c_0_40])]) ).
fof(c_0_71,plain,
! [X24,X25,X26] :
( ( ~ aInteger0(X26)
| ~ aInteger0(X25)
| ~ aInteger0(X24)
| sdtasdt0(sdtpldt0(X24,X25),X26) = sdtpldt0(sdtasdt0(X24,X26),sdtasdt0(X25,X26)) )
& ( ~ aInteger0(X26)
| ~ aInteger0(X25)
| ~ aInteger0(X24)
| sdtasdt0(X24,sdtpldt0(X25,X26)) = sdtpldt0(sdtasdt0(X24,X25),sdtasdt0(X24,X26)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])])]) ).
cnf(c_0_72,plain,
( ~ aInteger0(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_73,plain,
! [X21,X22] :
( sdtasdt0(X21,X22) = sdtasdt0(X22,X21)
| ~ aInteger0(X22)
| ~ aInteger0(X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_74,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(sdtpldt0(sz10,xp),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_30])]) ).
cnf(c_0_75,hypothesis,
sdtasdt0(xp,esk1_2(xp,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_40])]) ).
cnf(c_0_76,negated_conjecture,
sdtpldt0(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_51]),c_0_40])]) ).
cnf(c_0_77,hypothesis,
aInteger0(esk1_2(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_51]),c_0_40])]) ).
cnf(c_0_78,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_79,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sdtpldt0(sz10,xp)) = smndt0(X1) ),
inference(rw,[status(thm)],[c_0_72,c_0_24]) ).
cnf(c_0_80,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_81,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_74,c_0_75]),c_0_63]),c_0_76]),c_0_75]),c_0_77]),c_0_40])]) ).
cnf(c_0_82,negated_conjecture,
sdtpldt0(sdtpldt0(sz00,xp),xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_63]),c_0_40])]) ).
fof(c_0_83,plain,
! [X29,X30] :
( X30 = sz00
| X29 = sz00
| sdtasdt0(X29,X30) != sz00
| ~ aInteger0(X30)
| ~ aInteger0(X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])])]) ).
cnf(c_0_84,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtasdt0(X1,X2),smndt0(X1)) = sdtasdt0(X1,sdtpldt0(X2,sdtpldt0(sz10,xp))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_30])]) ).
cnf(c_0_85,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_80,c_0_81]),c_0_40]),c_0_30])]) ).
cnf(c_0_86,negated_conjecture,
sdtpldt0(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_51]),c_0_40])]) ).
cnf(c_0_87,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_88,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_84,c_0_85]),c_0_63]),c_0_76]),c_0_86]),c_0_47]),c_0_63]),c_0_76]),c_0_76]),c_0_30]),c_0_40])]) ).
cnf(c_0_89,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_40])]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM454+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/20.47 % Computer : n010.cluster.edu
% 0.18/20.47 % Model : x86_64 x86_64
% 0.18/20.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/20.47 % Memory : 8046.5625MB
% 0.18/20.47 % OS : Linux 6.8.0-71-generic
% 0.18/20.47 % CPULimit : 300
% 0.18/20.47 % WCLimit : 300
% 0.18/20.47 % DateTime : Mon Sep 21 02:32:03 UTC 2026
% 0.18/20.48 % CPUTime :
% 0.18/20.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/20.52 Running first-order theorem proving
% 0.22/20.52 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
% 0.22/20.66 % Version: 3.5.1
% 0.22/20.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/20.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/20.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/20.66 % Starting new_bool_3 with 300s (1) cores
% 0.22/20.66 % Starting new_bool_1 with 300s (1) cores
% 0.22/20.66 % Starting sh5l with 300s (1) cores
% 0.22/20.66 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4045310 completed with status 0
% 0.22/20.66 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.22/20.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/20.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/20.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/20.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/20.66 % No SInE strategy applied
% 0.22/20.66 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.22/20.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/20.66 % Starting SubtermCWHack with 136s (1) cores
% 0.22/20.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/20.66 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 0.22/20.66 % Starting new_bool_3 with 194s (1) cores
% 0.22/20.66 % Starting new_bool_1 with 188s (1) cores
% 0.22/20.66 % new_bool_3 with pid 4045320 completed with status 0
% 0.22/20.66 % Result found by new_bool_3
% 0.22/20.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/20.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/20.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/20.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/20.66 % No SInE strategy applied
% 0.22/20.66 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.22/20.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/20.66 % Starting SubtermCWHack with 136s (1) cores
% 0.22/20.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.22/20.66 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 0.22/20.66 % Starting new_bool_3 with 194s (1) cores
% 0.22/20.66 % Preprocessing time : 0.002 s
% 0.22/20.66 % Presaturation interreduction done
% 0.22/20.66
% 0.22/20.66 % Proof found!
% 0.22/20.66 % SZS status Theorem
% 0.22/20.66 % SZS output start CNFRefutation
% See solution above
% 0.22/20.66 % Parsed axioms : 49
% 0.22/20.66 % Removed by relevancy pruning/SinE : 0
% 0.22/20.66 % Initial clauses : 126
% 0.22/20.66 % Removed in clause preprocessing : 5
% 0.22/20.66 % Initial clauses in saturation : 121
% 0.22/20.66 % Processed clauses : 1657
% 0.22/20.66 % ...of these trivial : 47
% 0.22/20.66 % ...subsumed : 908
% 0.22/20.66 % ...remaining for further processing : 702
% 0.22/20.66 % Other redundant clauses eliminated : 34
% 0.22/20.66 % Clauses deleted for lack of memory : 0
% 0.22/20.66 % Backward-subsumed : 15
% 0.22/20.66 % Backward-rewritten : 95
% 0.22/20.66 % Generated clauses : 9043
% 0.22/20.66 % ...of the previous two non-redundant : 6596
% 0.22/20.66 % ...aggressively subsumed : 0
% 0.22/20.66 % Contextual simplify-reflections : 80
% 0.22/20.66 % Paramodulations : 9009
% 0.22/20.66 % Factorizations : 0
% 0.22/20.66 % NegExts : 0
% 0.22/20.66 % Equation resolutions : 34
% 0.22/20.66 % Disequality decompositions : 0
% 0.22/20.66 % Total rewrite steps : 17985
% 0.22/20.66 % ...of those cached : 17878
% 0.22/20.66 % Propositional unsat checks : 0
% 0.22/20.66 % Propositional check models : 0
% 0.22/20.66 % Propositional check unsatisfiable : 0
% 0.22/20.66 % Propositional clauses : 0
% 0.22/20.66 % Propositional clauses after purity: 0
% 0.22/20.66 % Propositional unsat core size : 0
% 0.22/20.66 % Propositional preprocessing time : 0.000
% 0.22/20.66 % Propositional encoding time : 0.000
% 0.22/20.66 % Propositional solver time : 0.000
% 0.22/20.66 % Success case prop preproc time : 0.000
% 0.22/20.66 % Success case prop encoding time : 0.000
% 0.22/20.66 % Success case prop solver time : 0.000
% 0.22/20.66 % Current number of processed clauses : 441
% 0.22/20.66 % Positive orientable unit clauses : 71
% 0.22/20.66 % Positive unorientable unit clauses: 0
% 0.22/20.66 % Negative unit clauses : 6
% 0.22/20.66 % Non-unit-clauses : 364
% 0.22/20.66 % Current number of unprocessed clauses: 5108
% 0.22/20.66 % ...number of literals in the above : 21174
% 0.22/20.66 % Current number of archived formulas : 0
% 0.22/20.66 % Current number of archived clauses : 229
% 0.22/20.66 % Clause-clause subsumption calls (NU) : 37684
% 0.22/20.66 % Rec. Clause-clause subsumption calls : 20910
% 0.22/20.66 % Non-unit clause-clause subsumptions : 975
% 0.22/20.66 % Unit Clause-clause subsumption calls : 792
% 0.22/20.66 % Rewrite failures with RHS unbound : 0
% 0.22/20.66 % BW rewrite match attempts : 102
% 0.22/20.66 % BW rewrite match successes : 42
% 0.22/20.66 % Condensation attempts : 0
% 0.22/20.66 % Condensation successes : 0
% 0.22/20.66 % Termbank termtop insertions : 167762
% 0.22/20.66 % Search garbage collected termcells : 2357
% 0.22/20.66
% 0.22/20.66 % -------------------------------------------------
% 0.22/20.66 % User time : 0.104 s
% 0.22/20.66 % System time : 0.010 s
% 0.22/20.66 % Total time : 0.114 s
% 0.22/20.66 % Maximum resident set size: 3948 pages
% 0.22/20.66
% 0.22/20.66 % -------------------------------------------------
% 0.22/20.66 % User time : 0.502 s
% 0.22/20.66 % System time : 0.042 s
% 0.22/20.66 % Total time : 0.543 s
% 0.22/20.66 % Maximum resident set size: 4864 pages
% 0.22/20.66 % E exiting
%------------------------------------------------------------------------------