%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM452+6 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 5 04:57:23 PM UTC 2026
% Result : Theorem 1.83s 1.89s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 17
% Syntax : Number of formulae : 104 ( 26 unt; 0 def)
% Number of atoms : 573 ( 141 equ)
% Maximal formula atoms : 102 ( 5 avg)
% Number of connectives : 725 ( 256 ~; 263 |; 171 &)
% ( 10 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 144 ( 0 sgn 77 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2171) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModRef) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
fof(m__2079,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2079) ).
fof(m__2046,hypothesis,
( aSet0(xS)
& ! [X1] :
( ( aElementOf0(X1,xS)
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
& ( ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) ) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
=> aElementOf0(X1,xS) ) )
& xS = cS2043 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(m__,conjecture,
( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
| aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
fof(c_0_17,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
fof(c_0_18,hypothesis,
! [X284,X286,X287,X288,X290,X291,X292,X293] :
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ( aInteger0(X284)
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aInteger0(esk26_1(X284))
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdtasdt0(xp,esk26_1(X284)) = sdtpldt0(X284,smndt0(sz10))
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aDivisorOf0(xp,sdtpldt0(X284,smndt0(sz10)))
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdteqdtlpzmzozddtrp0(X284,sz10,xp)
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aInteger0(X287)
| sdtasdt0(xp,X287) != sdtpldt0(X286,smndt0(sz10))
| ~ aInteger0(X286)
| aElementOf0(X286,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aDivisorOf0(xp,sdtpldt0(X286,smndt0(sz10)))
| ~ aInteger0(X286)
| aElementOf0(X286,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ sdteqdtlpzmzozddtrp0(X286,sz10,xp)
| ~ aInteger0(X286)
| aElementOf0(X286,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(sbsmnsldt0(xS))
& ( aInteger0(X288)
| ~ aElementOf0(X288,sbsmnsldt0(xS)) )
& ( aElementOf0(esk27_1(X288),xS)
| ~ aElementOf0(X288,sbsmnsldt0(xS)) )
& ( aElementOf0(X288,esk27_1(X288))
| ~ aElementOf0(X288,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X290)
| ~ aElementOf0(X291,xS)
| ~ aElementOf0(X290,X291)
| aElementOf0(X290,sbsmnsldt0(xS)) )
& ( aInteger0(X292)
| ~ aElementOf0(X292,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X292,sbsmnsldt0(xS))
| ~ aElementOf0(X292,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X292)
| aElementOf0(X292,sbsmnsldt0(xS))
| aElementOf0(X292,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X293,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X293,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])]) ).
fof(c_0_19,plain,
! [X145] :
( ( sdtpldt0(X145,smndt0(X145)) = sz00
| ~ aInteger0(X145) )
& ( sz00 = sdtpldt0(smndt0(X145),X145)
| ~ aInteger0(X145) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_20,hypothesis,
( aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_23,hypothesis,
( aDivisorOf0(xp,sz00)
| ~ aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_24,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X167,X168] :
( ~ aInteger0(X167)
| ~ aInteger0(X168)
| X168 = sz00
| sdteqdtlpzmzozddtrp0(X167,X167,X168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).
cnf(c_0_26,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,hypothesis,
( aDivisorOf0(xp,sz00)
| ~ sdteqdtlpzmzozddtrp0(sz10,sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22])]) ).
cnf(c_0_28,plain,
( X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,hypothesis,
( aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aDivisorOf0(xp,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_22])]) ).
cnf(c_0_32,hypothesis,
aDivisorOf0(xp,sz00),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_22])]),c_0_30]) ).
fof(c_0_33,plain,
! [X157,X158] :
( ~ aInteger0(X157)
| ~ aInteger0(X158)
| sdtasdt0(X157,X158) != sz00
| X157 = sz00
| X158 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
cnf(c_0_34,hypothesis,
( sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_35,hypothesis,
aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_36,hypothesis,
( aInteger0(esk26_1(X1))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_37,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,hypothesis,
sdtasdt0(xp,esk26_1(sz10)) = sdtpldt0(sz10,smndt0(sz10)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,hypothesis,
aInteger0(esk26_1(sz10)),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
fof(c_0_40,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(fof_simplification,[status(thm)],[m__2079]) ).
cnf(c_0_41,hypothesis,
( esk26_1(sz10) = sz00
| sdtpldt0(sz10,smndt0(sz10)) != sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_29])]),c_0_30]) ).
fof(c_0_42,hypothesis,
! [X254,X256,X257,X258,X259] :
( aSet0(sbsmnsldt0(xS))
& ( aInteger0(X254)
| ~ aElementOf0(X254,sbsmnsldt0(xS)) )
& ( aElementOf0(esk19_1(X254),xS)
| ~ aElementOf0(X254,sbsmnsldt0(xS)) )
& ( aElementOf0(X254,esk19_1(X254))
| ~ aElementOf0(X254,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X256)
| ~ aElementOf0(X257,xS)
| ~ aElementOf0(X256,X257)
| aElementOf0(X256,sbsmnsldt0(xS)) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ( aInteger0(X258)
| ~ aElementOf0(X258,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X258,sbsmnsldt0(xS))
| ~ aElementOf0(X258,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X258)
| aElementOf0(X258,sbsmnsldt0(xS))
| aElementOf0(X258,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X259,stldt0(sbsmnsldt0(xS)))
| X259 = sz10
| X259 = smndt0(sz10) )
& ( X259 != sz10
| aElementOf0(X259,stldt0(sbsmnsldt0(xS))) )
& ( X259 != smndt0(sz10)
| aElementOf0(X259,stldt0(sbsmnsldt0(xS))) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])])]) ).
fof(c_0_43,hypothesis,
! [X242,X244,X246,X247,X248,X249,X250,X252,X253] :
( aSet0(xS)
& ( aInteger0(esk16_1(X242))
| ~ aElementOf0(X242,xS) )
& ( esk16_1(X242) != sz00
| ~ aElementOf0(X242,xS) )
& ( isPrime0(esk16_1(X242))
| ~ aElementOf0(X242,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( aInteger0(X244)
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( aInteger0(esk17_2(X242,X244))
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( sdtasdt0(esk16_1(X242),esk17_2(X242,X244)) = sdtpldt0(X244,smndt0(sz00))
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( aDivisorOf0(esk16_1(X242),sdtpldt0(X244,smndt0(sz00)))
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( sdteqdtlpzmzozddtrp0(X244,sz00,esk16_1(X242))
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( ~ aInteger0(X247)
| sdtasdt0(esk16_1(X242),X247) != sdtpldt0(X246,smndt0(sz00))
| ~ aInteger0(X246)
| aElementOf0(X246,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( ~ aDivisorOf0(esk16_1(X242),sdtpldt0(X246,smndt0(sz00)))
| ~ aInteger0(X246)
| aElementOf0(X246,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X246,sz00,esk16_1(X242))
| ~ aInteger0(X246)
| aElementOf0(X246,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)) = X242
| ~ aElementOf0(X242,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( aInteger0(X250)
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( aInteger0(esk18_3(X248,X249,X250))
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( sdtasdt0(X249,esk18_3(X248,X249,X250)) = sdtpldt0(X250,smndt0(sz00))
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( aDivisorOf0(X249,sdtpldt0(X250,smndt0(sz00)))
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( sdteqdtlpzmzozddtrp0(X250,sz00,X249)
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( ~ aInteger0(X253)
| sdtasdt0(X249,X253) != sdtpldt0(X252,smndt0(sz00))
| ~ aInteger0(X252)
| aElementOf0(X252,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( ~ aDivisorOf0(X249,sdtpldt0(X252,smndt0(sz00)))
| ~ aInteger0(X252)
| aElementOf0(X252,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X252,sz00,X249)
| ~ aInteger0(X252)
| aElementOf0(X252,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,X249) != X248
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& xS = cS2043 ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2046])])])])])]) ).
cnf(c_0_44,hypothesis,
esk26_1(sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_21]),c_0_22])]) ).
cnf(c_0_45,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,hypothesis,
xS = cS2043,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,sz00),
inference(rw,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_48,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,hypothesis,
stldt0(sbsmnsldt0(cS2043)) = cS2076,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,hypothesis,
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| X1 != smndt0(sz10) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_51,plain,
! [X139,X140,X141] :
( ~ aInteger0(X139)
| ~ aInteger0(X140)
| ~ aInteger0(X141)
| sdtpldt0(X139,sdtpldt0(X140,X141)) = sdtpldt0(sdtpldt0(X139,X140),X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_52,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_47]),c_0_22])]) ).
cnf(c_0_53,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_46]),c_0_49]) ).
cnf(c_0_54,hypothesis,
aElementOf0(smndt0(sz10),cS2076),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_46]),c_0_49])]) ).
cnf(c_0_55,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(rw,[status(thm)],[c_0_47,c_0_52]) ).
cnf(c_0_57,hypothesis,
aInteger0(smndt0(sz10)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_58,plain,
! [X144] :
( ( sdtpldt0(X144,sz00) = X144
| ~ aInteger0(X144) )
& ( X144 = sdtpldt0(sz00,X144)
| ~ aInteger0(X144) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_59,hypothesis,
( sdtpldt0(sz10,sdtpldt0(smndt0(sz10),X1)) = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_22])]) ).
cnf(c_0_60,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_61,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_62,hypothesis,
sdtpldt0(sz10,sz00) = sdtpldt0(sz00,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_22])]) ).
fof(c_0_63,plain,
! [X135,X136] :
( ~ aInteger0(X135)
| ~ aInteger0(X136)
| aInteger0(sdtpldt0(X135,X136)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
fof(c_0_64,negated_conjecture,
~ ( ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
| aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_65,plain,
! [X156] :
( ( sdtasdt0(smndt0(sz10),X156) = smndt0(X156)
| ~ aInteger0(X156) )
& ( smndt0(X156) = sdtasdt0(X156,smndt0(sz10))
| ~ aInteger0(X156) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
cnf(c_0_66,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_22])]) ).
cnf(c_0_67,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_68,negated_conjecture,
! [X294,X295] :
( ( ~ aInteger0(X295)
| sdtasdt0(xp,X295) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aInteger0(X294)
| sdtasdt0(xp,X294) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| ~ aInteger0(X294)
| sdtasdt0(xp,X294) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| ~ aInteger0(X294)
| sdtasdt0(xp,X294) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X294)
| sdtasdt0(xp,X294) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& ( ~ aInteger0(X295)
| sdtasdt0(xp,X295) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
& ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
& ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
& ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
& ( ~ aInteger0(X295)
| sdtasdt0(xp,X295) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
& ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
& ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
& ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
& ( ~ aInteger0(X295)
| sdtasdt0(xp,X295) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
| ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
| ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])]) ).
cnf(c_0_69,hypothesis,
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X1)
| sdtasdt0(xp,X1) != sdtpldt0(X2,smndt0(sz10))
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_70,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_71,hypothesis,
sdtpldt0(sz10,sz00) = sz10,
inference(rw,[status(thm)],[c_0_62,c_0_66]) ).
cnf(c_0_72,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_73,hypothesis,
( aInteger0(sdtpldt0(sz00,X1))
| ~ aInteger0(sdtpldt0(smndt0(sz10),X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_59]),c_0_22])]) ).
cnf(c_0_74,negated_conjecture,
( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X1)
| sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(X1,smndt0(sz10)) != smndt0(xp)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_29])]),c_0_57])]) ).
cnf(c_0_76,hypothesis,
( sdtpldt0(sz10,sdtpldt0(sz00,X1)) = sdtpldt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_71]),c_0_72]),c_0_22])]) ).
cnf(c_0_77,hypothesis,
( aInteger0(sdtpldt0(sz00,X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_67]),c_0_57])]) ).
cnf(c_0_78,negated_conjecture,
( sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) != smndt0(xp)
| sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
| ~ aInteger0(sdtpldt0(sz10,smndt0(xp)))
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,hypothesis,
( aInteger0(sdtpldt0(sz10,X1))
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_76]),c_0_22])]),c_0_77]) ).
fof(c_0_80,plain,
! [X142,X143] :
( ~ aInteger0(X142)
| ~ aInteger0(X143)
| sdtpldt0(X142,X143) = sdtpldt0(X143,X142) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_81,negated_conjecture,
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),smndt0(sz10))) != smndt0(xp)
| sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_55]),c_0_57]),c_0_22])]),c_0_79]) ).
cnf(c_0_82,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( sdtpldt0(sz10,sdtpldt0(smndt0(sz10),smndt0(xp))) != smndt0(xp)
| sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_57])]) ).
cnf(c_0_84,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_85,plain,
! [X149,X150] :
( ~ aInteger0(X149)
| ~ aInteger0(X150)
| sdtasdt0(X149,X150) = sdtasdt0(X150,X149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_86,hypothesis,
( sdtpldt0(sz00,smndt0(smndt0(sz10))) = sz10
| ~ aInteger0(smndt0(smndt0(sz10))) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_21]),c_0_57])]),c_0_71]) ).
fof(c_0_87,plain,
! [X134] :
( ~ aInteger0(X134)
| aInteger0(smndt0(X134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_88,hypothesis,
( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_59]),c_0_84]) ).
cnf(c_0_89,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_90,hypothesis,
( smndt0(smndt0(sz10)) = sz10
| ~ aInteger0(smndt0(smndt0(sz10))) ),
inference(spm,[status(thm)],[c_0_84,c_0_86]) ).
cnf(c_0_91,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_92,hypothesis,
( sdtasdt0(X1,xp) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_29])]) ).
cnf(c_0_93,hypothesis,
smndt0(smndt0(sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_57])]) ).
cnf(c_0_94,hypothesis,
( sdtasdt0(X1,xp) != sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp))
| ~ aInteger0(sdtpldt0(sz10,xp))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_82]),c_0_57])]) ).
cnf(c_0_95,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_55]),c_0_67]) ).
cnf(c_0_96,hypothesis,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_93]),c_0_57])]) ).
cnf(c_0_97,hypothesis,
( sdtasdt0(X1,xp) != sdtpldt0(xp,sz00)
| ~ aInteger0(sdtpldt0(sz10,xp))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
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_94,c_0_95]),c_0_96]),c_0_29]),c_0_22]),c_0_57])]) ).
cnf(c_0_98,hypothesis,
( sdtasdt0(X1,xp) != sdtpldt0(xp,sz00)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_67]),c_0_29]),c_0_22])]) ).
fof(c_0_99,plain,
! [X151] :
( ( sdtasdt0(X151,sz10) = X151
| ~ aInteger0(X151) )
& ( X151 = sdtasdt0(sz10,X151)
| ~ aInteger0(X151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
cnf(c_0_100,hypothesis,
( sdtasdt0(X1,xp) != sdtpldt0(xp,sz00)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_91]),c_0_29])]) ).
cnf(c_0_101,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_102,hypothesis,
sdtpldt0(xp,sz00) != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_22]),c_0_29])]) ).
cnf(c_0_103,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_61]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM452+6 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 00:36:03 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.83/1.89 % Version : CSE_E---1.7
% 1.83/1.89 % Problem : theBenchmark.p
% 1.83/1.89 % SZS status Theorem for theBenchmark.p
% 1.83/1.89 % SZS output start CNFRefutation
% See solution above
% 1.83/1.89 % Total time : 1.373s
%------------------------------------------------------------------------------