%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM453+6 : 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 : n001.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 1.43s 0.76s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 79 ( 21 unt; 0 def)
% Number of atoms : 323 ( 102 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 345 ( 101 ~; 108 |; 113 &)
% ( 10 <=>; 13 =>; 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 : 85 ( 0 sgn 47 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2171,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(m__2079,hypothesis,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = smndt0(sz10)
| X1 = sz10 ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).
fof(m__2232,hypothesis,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(X1) )
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& ? [X1] :
( sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2232) ).
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(m__,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
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(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(c_0_11,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
fof(c_0_12,hypothesis,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = smndt0(sz10)
| X1 = sz10 ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(fof_simplification,[status(thm)],[m__2079]) ).
fof(c_0_13,hypothesis,
! [X161,X163,X164,X165,X167,X168,X169,X170] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ( aElementOf0(X170,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X170,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X169,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X169,sbsmnsldt0(xS))
| ~ aInteger0(X169) )
& ( ~ aElementOf0(X169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X169,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X169,stldt0(sbsmnsldt0(xS)))
| aInteger0(X169) )
& ( aElementOf0(X167,sbsmnsldt0(xS))
| ~ aElementOf0(X167,X168)
| ~ aElementOf0(X168,xS)
| ~ aInteger0(X167) )
& ( ~ aElementOf0(X165,sbsmnsldt0(xS))
| aElementOf0(X165,esk27_1(X165)) )
& ( ~ aElementOf0(X165,sbsmnsldt0(xS))
| aElementOf0(esk27_1(X165),xS) )
& ( ~ aElementOf0(X165,sbsmnsldt0(xS))
| aInteger0(X165) )
& aSet0(sbsmnsldt0(xS))
& ( aElementOf0(X163,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X163)
| ~ sdteqdtlpzmzozddtrp0(X163,sz10,xp) )
& ( aElementOf0(X163,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X163)
| ~ aDivisorOf0(xp,sdtpldt0(X163,smndt0(sz10))) )
& ( aElementOf0(X163,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X163)
| sdtasdt0(xp,X164) != sdtpldt0(X163,smndt0(sz10))
| ~ aInteger0(X164) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdteqdtlpzmzozddtrp0(X161,sz10,xp) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aDivisorOf0(xp,sdtpldt0(X161,smndt0(sz10))) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtasdt0(xp,esk26_1(X161)) = sdtpldt0(X161,smndt0(sz10)) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(esk26_1(X161)) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(X161) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
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_11])])])])])])]) ).
fof(c_0_14,hypothesis,
! [X131,X133,X134,X135,X136] :
( stldt0(sbsmnsldt0(xS)) = cS2076
& ( aElementOf0(X136,stldt0(sbsmnsldt0(xS)))
| X136 != smndt0(sz10) )
& ( aElementOf0(X136,stldt0(sbsmnsldt0(xS)))
| X136 != sz10 )
& ( X136 = smndt0(sz10)
| X136 = sz10
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( aElementOf0(X135,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X135,sbsmnsldt0(xS))
| ~ aInteger0(X135) )
& ( ~ aElementOf0(X135,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X135,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X135,stldt0(sbsmnsldt0(xS)))
| aInteger0(X135) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ( aElementOf0(X133,sbsmnsldt0(xS))
| ~ aElementOf0(X133,X134)
| ~ aElementOf0(X134,xS)
| ~ aInteger0(X133) )
& ( ~ aElementOf0(X131,sbsmnsldt0(xS))
| aElementOf0(X131,esk19_1(X131)) )
& ( ~ aElementOf0(X131,sbsmnsldt0(xS))
| aElementOf0(esk19_1(X131),xS) )
& ( ~ aElementOf0(X131,sbsmnsldt0(xS))
| aInteger0(X131) )
& aSet0(sbsmnsldt0(xS)) ),
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_12])])])])])])]) ).
cnf(c_0_15,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,hypothesis,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdtasdt0(xp,esk29_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(esk29_0)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdtasdt0(xp,esk28_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(esk28_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2232])]) ).
cnf(c_0_18,hypothesis,
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| X1 = smndt0(sz10)
| X1 = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,hypothesis,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,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])])])]) ).
cnf(c_0_22,hypothesis,
( ~ aElementOf0(X1,cS2076)
| X1 = sz10
| X1 = smndt0(sz10) ),
inference(rw,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_23,hypothesis,
aElementOf0(sdtpldt0(sz10,xp),cS2076),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_24,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_25,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_26,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,hypothesis,
( sdtpldt0(sz10,xp) = sz10
| smndt0(sz10) = sdtpldt0(sz10,xp) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_30,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,hypothesis,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sdtpldt0(sz10,xp),sz10) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_33,hypothesis,
aInteger0(sdtpldt0(sz10,xp)),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
fof(c_0_34,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(fof_nnf,[status(thm)],[c_0_30]) ).
cnf(c_0_35,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz10,xp) = sz10
| 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_31,c_0_32]),c_0_28]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_37,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_38,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sdtpldt0(sz10,xp),sz10) = sdtpldt0(sz00,smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,hypothesis,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz00,smndt0(xp)) = sz00 ),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
fof(c_0_41,plain,
! [X6] :
( aInteger0(smndt0(X6))
| ~ aInteger0(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
cnf(c_0_42,hypothesis,
( ~ aInteger0(smndt0(xp))
| smndt0(xp) = sz00
| sdtpldt0(sz10,xp) = sz10 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_44,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_46,hypothesis,
( smndt0(xp) = sz00
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_47,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_48,hypothesis,
( sdtpldt0(xp,sz00) = sz00
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_44])]) ).
cnf(c_0_49,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_50,hypothesis,
sdtasdt0(xp,esk28_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_51,hypothesis,
sdtpldt0(sz10,xp) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_44])]),c_0_49]) ).
fof(c_0_52,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_53,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,esk28_0),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_55,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_56,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(esk26_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_57,hypothesis,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_58,plain,
! [X14,X15] :
( sdtpldt0(X14,X15) = sdtpldt0(X15,X14)
| ~ aInteger0(X15)
| ~ aInteger0(X14) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_59,hypothesis,
sdtasdt0(xp,esk28_0) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_53]),c_0_28])]) ).
cnf(c_0_60,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(X1,smndt0(sz10)) != sz00
| esk26_1(X1) = sz00 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_44])]),c_0_49]),c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(sz10,xp) = sz10 ),
inference(spm,[status(thm)],[c_0_57,c_0_36]) ).
cnf(c_0_62,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz10,sdtpldt0(xp,X1)) = sdtpldt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_51]),c_0_44]),c_0_28])]) ).
cnf(c_0_63,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(rw,[status(thm)],[c_0_53,c_0_59]) ).
cnf(c_0_65,hypothesis,
aInteger0(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_66,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(X1,smndt0(sz10)) != sz00
| sdtpldt0(X1,smndt0(sz10)) = sdtasdt0(xp,sz00) ),
inference(spm,[status(thm)],[c_0_55,c_0_60]) ).
cnf(c_0_67,hypothesis,
aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(spm,[status(thm)],[c_0_20,c_0_61]) ).
cnf(c_0_68,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz10,sdtpldt0(X1,xp)) = sdtpldt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_44])]) ).
cnf(c_0_69,hypothesis,
( ~ aInteger0(X1)
| ~ aInteger0(smndt0(sz10))
| sdtpldt0(sz10,sdtpldt0(smndt0(sz10),X1)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_64]),c_0_28])]) ).
cnf(c_0_70,hypothesis,
esk28_0 = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_59]),c_0_65]),c_0_44])]),c_0_49]) ).
cnf(c_0_71,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_45]),c_0_67]),c_0_28])]) ).
cnf(c_0_72,hypothesis,
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_73,hypothesis,
( X1 != smndt0(sz10)
| aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_74,hypothesis,
( ~ aInteger0(smndt0(sz10))
| sdtpldt0(sz00,xp) = sz00 ),
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_68,c_0_69]),c_0_53]),c_0_70]),c_0_71]),c_0_44])]) ).
cnf(c_0_75,hypothesis,
( ~ aElementOf0(X1,cS2076)
| aInteger0(X1) ),
inference(rw,[status(thm)],[c_0_72,c_0_16]) ).
cnf(c_0_76,hypothesis,
aElementOf0(smndt0(sz10),cS2076),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_16])]) ).
cnf(c_0_77,hypothesis,
sdtpldt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]) ).
cnf(c_0_78,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_77]),c_0_44])]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM453+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:36:43 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.47 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
% 1.43/0.76 % Version: 3.5.1
% 1.43/0.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.43/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.43/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.43/0.76 % Starting new_bool_3 with 300s (1) cores
% 1.43/0.76 % Starting new_bool_1 with 300s (1) cores
% 1.43/0.76 % Starting sh5l with 300s (1) cores
% 1.43/0.76 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2004301 completed with status 0
% 1.43/0.76 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.43/0.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.43/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.43/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.43/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.43/0.76 % No SInE strategy applied
% 1.43/0.76 % Search class: FGHSF-FSLM31-MFFFFFNN
% 1.43/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.43/0.76 % Starting SubtermCWHack with 136s (1) cores
% 1.43/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.43/0.76 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.43/0.76 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 1.43/0.76 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 1.43/0.76 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 2004308 completed with status 0
% 1.43/0.76 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 1.43/0.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.43/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.43/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.43/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.43/0.76 % No SInE strategy applied
% 1.43/0.76 % Search class: FGHSF-FSLM31-MFFFFFNN
% 1.43/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.43/0.76 % Starting SubtermCWHack with 136s (1) cores
% 1.43/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.43/0.76 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.43/0.76 % Preprocessing time : 0.007 s
% 1.43/0.76 % Presaturation interreduction done
% 1.43/0.76
% 1.43/0.76 % Proof found!
% 1.43/0.76 % SZS status Theorem
% 1.43/0.76 % SZS output start CNFRefutation
% See solution above
% 1.43/0.76 % Parsed axioms : 48
% 1.43/0.76 % Removed by relevancy pruning/SinE : 0
% 1.43/0.76 % Initial clauses : 227
% 1.43/0.76 % Removed in clause preprocessing : 5
% 1.43/0.76 % Initial clauses in saturation : 222
% 1.43/0.76 % Processed clauses : 1361
% 1.43/0.76 % ...of these trivial : 21
% 1.43/0.76 % ...subsumed : 529
% 1.43/0.76 % ...remaining for further processing : 811
% 1.43/0.76 % Other redundant clauses eliminated : 45
% 1.43/0.76 % Clauses deleted for lack of memory : 0
% 1.43/0.76 % Backward-subsumed : 47
% 1.43/0.76 % Backward-rewritten : 142
% 1.43/0.76 % Generated clauses : 3933
% 1.43/0.76 % ...of the previous two non-redundant : 2978
% 1.43/0.76 % ...aggressively subsumed : 0
% 1.43/0.76 % Contextual simplify-reflections : 25
% 1.43/0.76 % Paramodulations : 3884
% 1.43/0.76 % Factorizations : 4
% 1.43/0.76 % NegExts : 0
% 1.43/0.76 % Equation resolutions : 45
% 1.43/0.76 % Disequality decompositions : 0
% 1.43/0.76 % Total rewrite steps : 4062
% 1.43/0.76 % ...of those cached : 4016
% 1.43/0.76 % Propositional unsat checks : 0
% 1.43/0.76 % Propositional check models : 0
% 1.43/0.76 % Propositional check unsatisfiable : 0
% 1.43/0.76 % Propositional clauses : 0
% 1.43/0.76 % Propositional clauses after purity: 0
% 1.43/0.76 % Propositional unsat core size : 0
% 1.43/0.76 % Propositional preprocessing time : 0.000
% 1.43/0.76 % Propositional encoding time : 0.000
% 1.43/0.76 % Propositional solver time : 0.000
% 1.43/0.76 % Success case prop preproc time : 0.000
% 1.43/0.76 % Success case prop encoding time : 0.000
% 1.43/0.76 % Success case prop solver time : 0.000
% 1.43/0.76 % Current number of processed clauses : 383
% 1.43/0.76 % Positive orientable unit clauses : 44
% 1.43/0.76 % Positive unorientable unit clauses: 0
% 1.43/0.76 % Negative unit clauses : 5
% 1.43/0.76 % Non-unit-clauses : 334
% 1.43/0.76 % Current number of unprocessed clauses: 1801
% 1.43/0.76 % ...number of literals in the above : 8602
% 1.43/0.76 % Current number of archived formulas : 0
% 1.43/0.76 % Current number of archived clauses : 393
% 1.43/0.76 % Clause-clause subsumption calls (NU) : 24431
% 1.43/0.76 % Rec. Clause-clause subsumption calls : 10287
% 1.43/0.76 % Non-unit clause-clause subsumptions : 562
% 1.43/0.76 % Unit Clause-clause subsumption calls : 740
% 1.43/0.76 % Rewrite failures with RHS unbound : 0
% 1.43/0.76 % BW rewrite match attempts : 16
% 1.43/0.76 % BW rewrite match successes : 15
% 1.43/0.76 % Condensation attempts : 0
% 1.43/0.76 % Condensation successes : 0
% 1.43/0.76 % Termbank termtop insertions : 86050
% 1.43/0.76 % Search garbage collected termcells : 3794
% 1.43/0.76
% 1.43/0.76 % -------------------------------------------------
% 1.43/0.76 % User time : 0.235 s
% 1.43/0.76 % System time : 0.013 s
% 1.43/0.76 % Total time : 0.248 s
% 1.43/0.76 % Maximum resident set size: 3716 pages
% 1.43/0.76
% 1.43/0.76 % -------------------------------------------------
% 1.43/0.76 % User time : 1.069 s
% 1.43/0.76 % System time : 0.061 s
% 1.43/0.76 % Total time : 1.130 s
% 1.43/0.76 % Maximum resident set size: 4864 pages
% 1.43/0.76 % E exiting
%------------------------------------------------------------------------------