%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM454+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 0.40s 0.68s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 89 ( 37 unt; 0 def)
% Number of atoms : 294 ( 97 equ)
% Maximal formula atoms : 44 ( 3 avg)
% Number of connectives : 301 ( 96 ~; 92 |; 92 &)
% ( 4 <=>; 17 =>; 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 : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
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/sandbox2/benchmark/theBenchmark.p',m__2171) ).
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/sandbox2/benchmark/theBenchmark.p',m__2232) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
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/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
fof(c_0_15,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_16,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_17,plain,
! [X81] :
( ( ~ aInteger0(X81)
| sz00 = sdtpldt0(smndt0(X81),X81) )
& ( ~ aInteger0(X81)
| sdtpldt0(X81,smndt0(X81)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
fof(c_0_18,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10)
& sdtpldt0(sz10,xp) = smndt0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X116] :
( aInteger0(smndt0(X116))
| ~ aInteger0(X116) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
fof(c_0_20,plain,
! [X108,X109,X110] :
( sdtpldt0(X108,sdtpldt0(X109,X110)) = sdtpldt0(sdtpldt0(X108,X109),X110)
| ~ aInteger0(X110)
| ~ aInteger0(X109)
| ~ aInteger0(X108) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_21,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_24,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_27,negated_conjecture,
aInteger0(sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23])]) ).
fof(c_0_28,plain,
! [X80] :
( ( ~ aInteger0(X80)
| X80 = sdtpldt0(sz00,X80) )
& ( ~ aInteger0(X80)
| sdtpldt0(X80,sz00) = X80 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_29,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_25,c_0_26]),c_0_23]),c_0_27])]) ).
cnf(c_0_30,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_31,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]) ).
cnf(c_0_32,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz00,sdtpldt0(sz10,xp)),
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_29,c_0_30]),c_0_22]),c_0_22]),c_0_27]),c_0_23])]) ).
fof(c_0_34,hypothesis,
! [X47,X49,X50,X51,X53,X54,X55,X56] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ( aElementOf0(X56,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X56,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X55,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X55,sbsmnsldt0(xS))
| ~ aInteger0(X55) )
& ( ~ aElementOf0(X55,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X55,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X55,stldt0(sbsmnsldt0(xS)))
| aInteger0(X55) )
& ( aElementOf0(X53,sbsmnsldt0(xS))
| ~ aElementOf0(X53,X54)
| ~ aElementOf0(X54,xS)
| ~ aInteger0(X53) )
& ( ~ aElementOf0(X51,sbsmnsldt0(xS))
| aElementOf0(X51,esk12_1(X51)) )
& ( ~ aElementOf0(X51,sbsmnsldt0(xS))
| aElementOf0(esk12_1(X51),xS) )
& ( ~ aElementOf0(X51,sbsmnsldt0(xS))
| aInteger0(X51) )
& aSet0(sbsmnsldt0(xS))
& ( aElementOf0(X49,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X49)
| ~ sdteqdtlpzmzozddtrp0(X49,sz10,xp) )
& ( aElementOf0(X49,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X49)
| ~ aDivisorOf0(xp,sdtpldt0(X49,smndt0(sz10))) )
& ( aElementOf0(X49,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X49)
| sdtasdt0(xp,X50) != sdtpldt0(X49,smndt0(sz10))
| ~ aInteger0(X50) )
& ( ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdteqdtlpzmzozddtrp0(X47,sz10,xp) )
& ( ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aDivisorOf0(xp,sdtpldt0(X47,smndt0(sz10))) )
& ( ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtasdt0(xp,esk11_1(X47)) = sdtpldt0(X47,smndt0(sz10)) )
& ( ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(esk11_1(X47)) )
& ( ~ aElementOf0(X47,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(X47) )
& 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_31])])])])])])]) ).
cnf(c_0_35,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz10,xp)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_27])]) ).
fof(c_0_36,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,esk14_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(esk14_0)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdtasdt0(xp,esk13_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2232])]) ).
fof(c_0_37,plain,
! [X118,X119] :
( aInteger0(sdtasdt0(X118,X119))
| ~ aInteger0(X119)
| ~ aInteger0(X118) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])])]) ).
cnf(c_0_38,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtasdt0(xp,esk11_1(X1)) = sdtpldt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_33,c_0_35]) ).
cnf(c_0_40,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_41,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_42,plain,
! [X111,X112] :
( sdtpldt0(X111,X112) = sdtpldt0(X112,X111)
| ~ aInteger0(X112)
| ~ aInteger0(X111) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_43,hypothesis,
sdtasdt0(xp,esk13_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtasdt0(xp,esk11_1(X1)) = sdtpldt0(X1,sdtpldt0(sz10,xp)) ),
inference(rw,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_46,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(xp,sz00)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_39]),c_0_40]),c_0_41]),c_0_23])]) ).
cnf(c_0_48,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,hypothesis,
sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtasdt0(xp,esk13_0),
inference(rw,[status(thm)],[c_0_43,c_0_22]) ).
cnf(c_0_50,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(sdtpldt0(X1,sdtpldt0(sz10,xp))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_41])]),c_0_46]) ).
cnf(c_0_51,hypothesis,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_52,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(sz00,xp)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_40]),c_0_41])]) ).
cnf(c_0_53,hypothesis,
sdtasdt0(xp,esk13_0) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_29]),c_0_41])]) ).
cnf(c_0_54,hypothesis,
aInteger0(sdtpldt0(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_29]),c_0_51]),c_0_41])]) ).
cnf(c_0_55,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_56,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz00,xp)) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_52]),c_0_49]),c_0_53]),c_0_54])]) ).
cnf(c_0_57,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_58,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_55,c_0_22]) ).
cnf(c_0_59,negated_conjecture,
sdtpldt0(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_41])]) ).
cnf(c_0_60,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz00,smndt0(xp)) = xp ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_58]),c_0_49]),c_0_53]),c_0_59]) ).
cnf(c_0_61,hypothesis,
sdtasdt0(xp,esk14_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_62,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| smndt0(xp) = xp ),
inference(spm,[status(thm)],[c_0_57,c_0_60]) ).
cnf(c_0_63,hypothesis,
sdtasdt0(xp,esk14_0) = sdtasdt0(xp,esk13_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_58]),c_0_22]),c_0_49]) ).
cnf(c_0_64,negated_conjecture,
smndt0(xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_24]),c_0_41])]) ).
fof(c_0_65,plain,
! [X120,X121,X122] :
( sdtasdt0(X120,sdtasdt0(X121,X122)) = sdtasdt0(sdtasdt0(X120,X121),X122)
| ~ aInteger0(X122)
| ~ aInteger0(X121)
| ~ aInteger0(X120) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_66,hypothesis,
sdtasdt0(xp,esk14_0) = sdtpldt0(sz00,xp),
inference(rw,[status(thm)],[c_0_63,c_0_53]) ).
cnf(c_0_67,negated_conjecture,
sdtpldt0(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_64]),c_0_41])]) ).
cnf(c_0_68,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_69,hypothesis,
sdtasdt0(xp,esk14_0) = xp,
inference(rw,[status(thm)],[c_0_66,c_0_59]) ).
cnf(c_0_70,hypothesis,
aInteger0(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_71,plain,
! [X151] :
( ( ~ aInteger0(X151)
| X151 = sdtasdt0(sz10,X151) )
& ( ~ aInteger0(X151)
| sdtasdt0(X151,sz10) = X151 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])])]) ).
cnf(c_0_72,hypothesis,
sdtpldt0(sz10,sdtpldt0(xp,sdtpldt0(sz10,xp))) = sdtasdt0(xp,esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_25]),c_0_27]),c_0_41]),c_0_23])]) ).
cnf(c_0_73,negated_conjecture,
( ~ aInteger0(X1)
| sdtpldt0(xp,sdtpldt0(xp,X1)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_67]),c_0_41])]) ).
fof(c_0_74,plain,
! [X113,X114,X115] :
( ( ~ aInteger0(X115)
| ~ aInteger0(X114)
| ~ aInteger0(X113)
| sdtasdt0(sdtpldt0(X113,X114),X115) = sdtpldt0(sdtasdt0(X113,X115),sdtasdt0(X114,X115)) )
& ( ~ aInteger0(X115)
| ~ aInteger0(X114)
| ~ aInteger0(X113)
| sdtasdt0(X113,sdtpldt0(X114,X115)) = sdtpldt0(sdtasdt0(X113,X114),sdtasdt0(X113,X115)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])])]) ).
cnf(c_0_75,hypothesis,
( ~ aInteger0(X1)
| sdtasdt0(xp,sdtasdt0(esk14_0,X1)) = sdtasdt0(xp,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_41])]) ).
cnf(c_0_76,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_77,hypothesis,
sdtpldt0(sz10,sdtpldt0(xp,sdtpldt0(sz10,xp))) = xp,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_53]),c_0_59]) ).
cnf(c_0_78,negated_conjecture,
( ~ aInteger0(X1)
| sdtpldt0(xp,sdtpldt0(X1,xp)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_48]),c_0_41])]) ).
cnf(c_0_79,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_74]) ).
cnf(c_0_80,hypothesis,
sdtasdt0(xp,sz10) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_69]),c_0_23]),c_0_70])]) ).
cnf(c_0_81,hypothesis,
sdtpldt0(sz10,sdtpldt0(sz00,sz10)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_23])]) ).
fof(c_0_82,plain,
! [X83,X84] :
( X84 = sz00
| X83 = sz00
| sdtasdt0(X83,X84) != sz00
| ~ aInteger0(X84)
| ~ aInteger0(X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])])]) ).
cnf(c_0_83,hypothesis,
( ~ aInteger0(X1)
| sdtasdt0(xp,sdtpldt0(X1,sz10)) = sdtpldt0(sdtasdt0(xp,X1),xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_23]),c_0_41])]) ).
cnf(c_0_84,hypothesis,
sdtpldt0(sz10,sz10) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_57]),c_0_23])]) ).
cnf(c_0_85,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_86,hypothesis,
sdtasdt0(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_80]),c_0_67]),c_0_23])]) ).
cnf(c_0_87,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_88,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_41])]),c_0_87]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM454+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n018.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 02:33:13 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.68 % Version: 3.5.1
% 0.40/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.40/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.40/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.40/0.68 % Starting new_bool_1 with 300s (1) cores
% 0.40/0.68 % Starting sh5l with 300s (1) cores
% 0.40/0.68 % new_bool_3 with pid 775050 completed with status 0
% 0.40/0.68 % Result found by new_bool_3
% 0.40/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.40/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.40/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.40/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.40/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.40/0.68 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.40/0.68 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.40/0.68 % Starting SubtermCWHack with 28s (1) cores
% 0.40/0.68 % SubtermCWHack with pid 775054 completed with status 0
% 0.40/0.68 % Result found by SubtermCWHack
% 0.40/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.40/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.40/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.40/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.40/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.40/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.40/0.68 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.40/0.68 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.40/0.68 % Starting SubtermCWHack with 28s (1) cores
% 0.40/0.68 % Preprocessing time : 0.005 s
% 0.40/0.68
% 0.40/0.68 % Proof found!
% 0.40/0.68 % SZS status Theorem
% 0.40/0.68 % SZS output start CNFRefutation
% See solution above
% 0.40/0.68 % Parsed axioms : 49
% 0.40/0.68 % Removed by relevancy pruning/SinE : 4
% 0.40/0.68 % Initial clauses : 210
% 0.40/0.68 % Removed in clause preprocessing : 5
% 0.40/0.68 % Initial clauses in saturation : 205
% 0.40/0.68 % Processed clauses : 725
% 0.40/0.68 % ...of these trivial : 20
% 0.40/0.68 % ...subsumed : 292
% 0.40/0.68 % ...remaining for further processing : 413
% 0.40/0.68 % Other redundant clauses eliminated : 34
% 0.40/0.68 % Clauses deleted for lack of memory : 0
% 0.40/0.68 % Backward-subsumed : 8
% 0.40/0.68 % Backward-rewritten : 36
% 0.40/0.68 % Generated clauses : 2677
% 0.40/0.68 % ...of the previous two non-redundant : 1877
% 0.40/0.68 % ...aggressively subsumed : 0
% 0.40/0.68 % Contextual simplify-reflections : 16
% 0.40/0.68 % Paramodulations : 2642
% 0.40/0.68 % Factorizations : 1
% 0.40/0.68 % NegExts : 0
% 0.40/0.68 % Equation resolutions : 34
% 0.40/0.68 % Disequality decompositions : 0
% 0.40/0.68 % Total rewrite steps : 3425
% 0.40/0.68 % ...of those cached : 3353
% 0.40/0.68 % Propositional unsat checks : 0
% 0.40/0.68 % Propositional check models : 0
% 0.40/0.68 % Propositional check unsatisfiable : 0
% 0.40/0.68 % Propositional clauses : 0
% 0.40/0.68 % Propositional clauses after purity: 0
% 0.40/0.68 % Propositional unsat core size : 0
% 0.40/0.68 % Propositional preprocessing time : 0.000
% 0.40/0.68 % Propositional encoding time : 0.000
% 0.40/0.68 % Propositional solver time : 0.000
% 0.40/0.68 % Success case prop preproc time : 0.000
% 0.40/0.68 % Success case prop encoding time : 0.000
% 0.40/0.68 % Success case prop solver time : 0.000
% 0.40/0.68 % Current number of processed clauses : 346
% 0.40/0.68 % Positive orientable unit clauses : 63
% 0.40/0.68 % Positive unorientable unit clauses: 0
% 0.40/0.68 % Negative unit clauses : 3
% 0.40/0.68 % Non-unit-clauses : 280
% 0.40/0.68 % Current number of unprocessed clauses: 1268
% 0.40/0.68 % ...number of literals in the above : 5219
% 0.40/0.68 % Current number of archived formulas : 0
% 0.40/0.68 % Current number of archived clauses : 44
% 0.40/0.68 % Clause-clause subsumption calls (NU) : 8155
% 0.40/0.68 % Rec. Clause-clause subsumption calls : 5168
% 0.40/0.68 % Non-unit clause-clause subsumptions : 303
% 0.40/0.68 % Unit Clause-clause subsumption calls : 456
% 0.40/0.68 % Rewrite failures with RHS unbound : 0
% 0.40/0.68 % BW rewrite match attempts : 18
% 0.40/0.68 % BW rewrite match successes : 18
% 0.40/0.68 % Condensation attempts : 0
% 0.40/0.68 % Condensation successes : 0
% 0.40/0.68 % Termbank termtop insertions : 57251
% 0.40/0.68 % Search garbage collected termcells : 3301
% 0.40/0.68
% 0.40/0.68 % -------------------------------------------------
% 0.40/0.68 % User time : 0.115 s
% 0.40/0.68 % System time : 0.008 s
% 0.40/0.68 % Total time : 0.123 s
% 0.40/0.68 % Maximum resident set size: 4228 pages
% 0.40/0.68
% 0.40/0.68 % -------------------------------------------------
% 0.40/0.68 % User time : 0.123 s
% 0.40/0.68 % System time : 0.013 s
% 0.40/0.68 % Total time : 0.136 s
% 0.40/0.68 % Maximum resident set size: 5120 pages
% 0.40/0.68 % E exiting
%------------------------------------------------------------------------------