%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM454+6 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.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 4.86s 3.48s
% Output : CNFRefutation 4.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 22
% Syntax : Number of formulae : 161 ( 58 unt; 0 def)
% Number of atoms : 538 ( 175 equ)
% Maximal formula atoms : 46 ( 3 avg)
% Number of connectives : 594 ( 217 ~; 229 |; 116 &)
% ( 6 <=>; 26 =>; 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 : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 189 ( 0 sgn 90 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& 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/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__2232,hypothesis,
( ? [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/sandbox/benchmark/theBenchmark.p',m__2232) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(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(mArSeq,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(mEquModTrn,axiom,
! [X1,X2,X3,X4] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00
& aInteger0(X4) )
=> ( ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
& sdteqdtlpzmzozddtrp0(X2,X4,X3) )
=> sdteqdtlpzmzozddtrp0(X1,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModTrn) ).
fof(mEquModSym,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(c_0_22,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_23,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_24,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])]) ).
fof(c_0_25,negated_conjecture,
( sdtpldt0(sz10,xp) = smndt0(sz10)
& sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_22]) ).
fof(c_0_26,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_23])])])])])]) ).
cnf(c_0_27,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
fof(c_0_31,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_32,negated_conjecture,
( sdtpldt0(sz10,sdtpldt0(xp,X1)) = sdtpldt0(smndt0(sz10),X1)
| ~ aInteger0(X1) ),
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_30])]) ).
cnf(c_0_33,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_34,hypothesis,
( aInteger0(esk28_0)
& sdtasdt0(xp,esk28_0) = 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))
& aInteger0(esk29_0)
& sdtasdt0(xp,esk29_0) = 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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2232])]) ).
fof(c_0_35,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_36,negated_conjecture,
( sdtpldt0(sz10,sdtpldt0(X1,xp)) = sdtpldt0(smndt0(sz10),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29])]) ).
cnf(c_0_37,hypothesis,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sz10,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_28]),c_0_30])]) ).
cnf(c_0_40,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_41,hypothesis,
aElementOf0(smndt0(sz10),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(rw,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_42,negated_conjecture,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_30])]) ).
cnf(c_0_43,hypothesis,
aInteger0(smndt0(sz10)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_44,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_45,negated_conjecture,
( 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_27,c_0_42]),c_0_43]),c_0_30])]) ).
cnf(c_0_46,negated_conjecture,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(rw,[status(thm)],[c_0_39,c_0_42]) ).
cnf(c_0_47,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,negated_conjecture,
sdtpldt0(sz10,sz00) = sdtpldt0(sz00,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_30])]) ).
cnf(c_0_50,negated_conjecture,
( sdtpldt0(smndt0(sz10),smndt0(xp)) = sdtpldt0(sz10,sz00)
| ~ aInteger0(smndt0(xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_47]),c_0_29])]) ).
cnf(c_0_51,negated_conjecture,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_30])]) ).
cnf(c_0_52,negated_conjecture,
( sdtpldt0(smndt0(sz10),smndt0(xp)) = sz10
| ~ aInteger0(smndt0(xp)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_49]),c_0_51]) ).
cnf(c_0_53,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( sdtpldt0(sz00,smndt0(xp)) = sdtpldt0(sz10,sz10)
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_45,c_0_52]) ).
fof(c_0_55,plain,
! [X134] :
( ~ aInteger0(X134)
| aInteger0(smndt0(X134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_56,plain,
! [X219,X220,X221,X222,X223,X224] :
( ( aSet0(X221)
| X221 != szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( aInteger0(X222)
| ~ aElementOf0(X222,X221)
| X221 != szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X222,X219,X220)
| ~ aElementOf0(X222,X221)
| X221 != szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( ~ aInteger0(X223)
| ~ sdteqdtlpzmzozddtrp0(X223,X219,X220)
| aElementOf0(X223,X221)
| X221 != szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( ~ aElementOf0(esk11_3(X219,X220,X224),X224)
| ~ aInteger0(esk11_3(X219,X220,X224))
| ~ sdteqdtlpzmzozddtrp0(esk11_3(X219,X220,X224),X219,X220)
| ~ aSet0(X224)
| X224 = szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( aInteger0(esk11_3(X219,X220,X224))
| aElementOf0(esk11_3(X219,X220,X224),X224)
| ~ aSet0(X224)
| X224 = szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( sdteqdtlpzmzozddtrp0(esk11_3(X219,X220,X224),X219,X220)
| aElementOf0(esk11_3(X219,X220,X224),X224)
| ~ aSet0(X224)
| X224 = szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 ) ),
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)],[mArSeq])])])])])]) ).
fof(c_0_57,plain,
! [X172,X173,X174,X175] :
( ~ aInteger0(X172)
| ~ aInteger0(X173)
| ~ aInteger0(X174)
| X174 = sz00
| ~ aInteger0(X175)
| ~ sdteqdtlpzmzozddtrp0(X172,X173,X174)
| ~ sdteqdtlpzmzozddtrp0(X173,X175,X174)
| sdteqdtlpzmzozddtrp0(X172,X175,X174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModTrn])]) ).
cnf(c_0_58,hypothesis,
sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_59,plain,
! [X169,X170,X171] :
( ~ aInteger0(X169)
| ~ aInteger0(X170)
| ~ aInteger0(X171)
| X171 = sz00
| ~ sdteqdtlpzmzozddtrp0(X169,X170,X171)
| sdteqdtlpzmzozddtrp0(X170,X169,X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModSym])]) ).
cnf(c_0_60,negated_conjecture,
( sdtpldt0(sz10,sz10) = smndt0(xp)
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,plain,
( aElementOf0(X1,X4)
| X3 = sz00
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X1,X4,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ sdteqdtlpzmzozddtrp0(X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,hypothesis,
sdteqdtlpzmzozddtrp0(smndt0(sz10),sz10,xp),
inference(rw,[status(thm)],[c_0_58,c_0_28]) ).
cnf(c_0_65,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_66,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,negated_conjecture,
sdtpldt0(sz10,sz10) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_29])]) ).
fof(c_0_68,plain,
! [X135,X136] :
( ~ aInteger0(X135)
| ~ aInteger0(X136)
| aInteger0(sdtpldt0(X135,X136)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_69,hypothesis,
( sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_70,plain,
( X1 = sz00
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X3)
| ~ aInteger0(X2) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_71,hypothesis,
( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| ~ sdteqdtlpzmzozddtrp0(X1,smndt0(sz10),xp)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_30]),c_0_29])]),c_0_65]),c_0_43])]) ).
cnf(c_0_72,hypothesis,
sdteqdtlpzmzozddtrp0(sz10,smndt0(sz10),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_64]),c_0_29]),c_0_30])]),c_0_65]),c_0_43])]) ).
cnf(c_0_73,hypothesis,
( aInteger0(esk26_1(X1))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_74,negated_conjecture,
( sdtpldt0(sz10,sdtpldt0(sz10,X1)) = sdtpldt0(smndt0(xp),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_67]),c_0_30])]) ).
cnf(c_0_75,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_76,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,hypothesis,
sdtasdt0(xp,esk28_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_78,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_79,hypothesis,
( sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10))
| ~ sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_29]),c_0_30])]),c_0_65]) ).
cnf(c_0_80,hypothesis,
sdteqdtlpzmzozddtrp0(sz10,sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_30])]) ).
cnf(c_0_81,hypothesis,
( aInteger0(esk26_1(X1))
| ~ sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_70]),c_0_29]),c_0_30])]),c_0_65]) ).
cnf(c_0_82,negated_conjecture,
sdtpldt0(smndt0(xp),sz10) = smndt0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_67]),c_0_75]),c_0_30])]) ).
cnf(c_0_83,negated_conjecture,
aInteger0(smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_67]),c_0_30])]) ).
cnf(c_0_84,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_85,hypothesis,
sdtpldt0(smndt0(sz10),smndt0(sz10)) = sdtasdt0(xp,esk28_0),
inference(rw,[status(thm)],[c_0_77,c_0_28]) ).
fof(c_0_86,plain,
! [X146,X147,X148] :
( ~ aInteger0(X146)
| ~ aInteger0(X147)
| ~ aInteger0(X148)
| sdtasdt0(X146,sdtasdt0(X147,X148)) = sdtasdt0(sdtasdt0(X146,X147),X148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_87,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_88,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_89,hypothesis,
sdtasdt0(xp,esk26_1(sz10)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_42]),c_0_30])]) ).
cnf(c_0_90,hypothesis,
aInteger0(esk26_1(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_80]),c_0_30])]) ).
cnf(c_0_91,negated_conjecture,
( sdtpldt0(smndt0(xp),sdtpldt0(sz10,X1)) = sdtpldt0(smndt0(sz10),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_82]),c_0_30]),c_0_83])]) ).
cnf(c_0_92,negated_conjecture,
sdtpldt0(smndt0(xp),sz00) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_48]),c_0_67]),c_0_84]),c_0_30])]) ).
cnf(c_0_93,negated_conjecture,
sdtasdt0(xp,esk28_0) = 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_36,c_0_45]),c_0_85]),c_0_43]),c_0_29])]) ).
cnf(c_0_94,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_95,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_96,hypothesis,
esk26_1(sz10) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]),c_0_29])]),c_0_65]) ).
cnf(c_0_97,negated_conjecture,
sdtpldt0(sz00,xp) = smndt0(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_91,c_0_47]),c_0_92]),c_0_85]),c_0_93]),c_0_43]),c_0_30])]) ).
cnf(c_0_98,negated_conjecture,
( sdtpldt0(sz00,smndt0(smndt0(sz10))) = sz10
| ~ aInteger0(smndt0(smndt0(sz10))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_47]),c_0_43])]),c_0_49]),c_0_51]) ).
fof(c_0_99,plain,
! [X152,X153,X154] :
( ( sdtasdt0(X152,sdtpldt0(X153,X154)) = sdtpldt0(sdtasdt0(X152,X153),sdtasdt0(X152,X154))
| ~ aInteger0(X152)
| ~ aInteger0(X153)
| ~ aInteger0(X154) )
& ( sdtasdt0(sdtpldt0(X152,X153),X154) = sdtpldt0(sdtasdt0(X152,X154),sdtasdt0(X153,X154))
| ~ aInteger0(X152)
| ~ aInteger0(X153)
| ~ aInteger0(X154) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
fof(c_0_100,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_101,plain,
( sdtasdt0(smndt0(sz10),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_43])]) ).
cnf(c_0_102,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(rw,[status(thm)],[c_0_89,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
smndt0(xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_97]),c_0_29])]) ).
cnf(c_0_104,negated_conjecture,
( smndt0(smndt0(sz10)) = sz10
| ~ aInteger0(smndt0(smndt0(sz10))) ),
inference(spm,[status(thm)],[c_0_53,c_0_98]) ).
fof(c_0_105,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_106,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_107,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_108,hypothesis,
sdtasdt0(smndt0(sz10),sz00) = 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_101,c_0_102]),c_0_103]),c_0_102]),c_0_84]),c_0_29])]) ).
cnf(c_0_109,negated_conjecture,
smndt0(smndt0(sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_61]),c_0_43])]) ).
cnf(c_0_110,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
fof(c_0_111,plain,
! [X137,X138] :
( ~ aInteger0(X137)
| ~ aInteger0(X138)
| aInteger0(sdtasdt0(X137,X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
fof(c_0_112,plain,
! [X155] :
( ( sdtasdt0(X155,sz00) = sz00
| ~ aInteger0(X155) )
& ( sz00 = sdtasdt0(sz00,X155)
| ~ aInteger0(X155) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
cnf(c_0_113,plain,
( sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_30])]) ).
cnf(c_0_114,hypothesis,
sdtasdt0(sz10,sz00) = 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_101,c_0_108]),c_0_108]),c_0_109]),c_0_84]),c_0_43])]) ).
cnf(c_0_115,hypothesis,
sdtasdt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_102]),c_0_84]),c_0_29])]) ).
cnf(c_0_116,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_117,hypothesis,
( sdtasdt0(xp,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,sdtasdt0(xp,X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_102]),c_0_84]),c_0_29])]) ).
cnf(c_0_118,hypothesis,
sdtasdt0(xp,esk29_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_119,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_120,plain,
( sdtasdt0(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_113,c_0_53]),c_0_114]),c_0_84])]) ).
cnf(c_0_121,hypothesis,
( sdtasdt0(sz00,sdtasdt0(xp,X1)) = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_115]),c_0_29]),c_0_84])]) ).
cnf(c_0_122,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_123,plain,
( aInteger0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_106]),c_0_116]),c_0_116]) ).
cnf(c_0_124,hypothesis,
( sdtpldt0(sz00,sdtasdt0(xp,X1)) = sdtasdt0(xp,X1)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_117,c_0_53]) ).
cnf(c_0_125,hypothesis,
sdtasdt0(xp,esk29_0) = sdtasdt0(xp,esk28_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_75]),c_0_85]) ).
cnf(c_0_126,negated_conjecture,
sdtpldt0(xp,sz00) = xp,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_103]),c_0_103]) ).
cnf(c_0_127,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_119]),c_0_84])]) ).
cnf(c_0_128,plain,
( sdtasdt0(X1,sz10) = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_120]),c_0_30])]) ).
cnf(c_0_129,hypothesis,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_115]),c_0_30]),c_0_29])]) ).
cnf(c_0_130,negated_conjecture,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_97,c_0_103]) ).
cnf(c_0_131,hypothesis,
( aInteger0(sdtpldt0(sz00,sdtasdt0(xp,X1)))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_117]),c_0_84]),c_0_29])]) ).
cnf(c_0_132,hypothesis,
( sdtpldt0(sz00,sdtasdt0(X1,xp)) = sdtasdt0(X1,xp)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_110]),c_0_29])]) ).
cnf(c_0_133,hypothesis,
sdtasdt0(xp,esk29_0) = sdtpldt0(sz00,xp),
inference(rw,[status(thm)],[c_0_125,c_0_93]) ).
cnf(c_0_134,negated_conjecture,
( sdtpldt0(xp,sdtpldt0(sz00,X1)) = sdtpldt0(xp,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_126]),c_0_84]),c_0_29])]) ).
cnf(c_0_135,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_136,plain,
( sdtasdt0(sz00,sdtpldt0(sz00,X1)) = sz00
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]),c_0_30])]) ).
cnf(c_0_137,negated_conjecture,
sdtpldt0(sz00,sdtasdt0(xp,xp)) = sdtasdt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_130]),c_0_29])]) ).
cnf(c_0_138,hypothesis,
aInteger0(sdtasdt0(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_29])]) ).
cnf(c_0_139,hypothesis,
sdtasdt0(xp,esk29_0) = xp,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_97]),c_0_103]) ).
cnf(c_0_140,hypothesis,
aInteger0(esk29_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_141,negated_conjecture,
( sdtpldt0(xp,sdtpldt0(X1,sz00)) = sdtpldt0(xp,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_33]),c_0_84])]) ).
cnf(c_0_142,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_33,c_0_27]),c_0_76]) ).
cnf(c_0_143,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_122]),c_0_30])]) ).
cnf(c_0_144,negated_conjecture,
sdtpldt0(sz00,sdtasdt0(xp,sz10)) = sdtasdt0(xp,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_51]),c_0_30])]) ).
cnf(c_0_145,negated_conjecture,
sdtpldt0(smndt0(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_36,c_0_74]),c_0_46]),c_0_30]),c_0_29])]) ).
cnf(c_0_146,plain,
( sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_107]),c_0_30])]) ).
cnf(c_0_147,negated_conjecture,
sdtasdt0(sz00,sdtasdt0(xp,xp)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138])]) ).
cnf(c_0_148,hypothesis,
sdtasdt0(smndt0(sz10),xp) = 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_101,c_0_139]),c_0_103]),c_0_139]),c_0_140]),c_0_29])]) ).
cnf(c_0_149,plain,
( sdtasdt0(sdtpldt0(X1,X2),sz10) = sdtpldt0(sdtasdt0(X1,sz10),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_122]),c_0_30])]) ).
cnf(c_0_150,negated_conjecture,
( sdtpldt0(X1,xp) = sdtpldt0(xp,X1)
| ~ 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_141,c_0_142]),c_0_97]),c_0_103]),c_0_29]),c_0_84])]) ).
cnf(c_0_151,hypothesis,
sdtasdt0(xp,sz10) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_143]),c_0_102]),c_0_97]),c_0_103]),c_0_144]),c_0_30]),c_0_84]),c_0_29])]) ).
cnf(c_0_152,negated_conjecture,
sdtpldt0(xp,smndt0(xp)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_145]),c_0_29]),c_0_83])]) ).
cnf(c_0_153,plain,
( sdtasdt0(X1,X2) = sz00
| X3 = sz00
| sdtasdt0(X1,sdtasdt0(X2,X3)) != sz00
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_94]),c_0_116]) ).
cnf(c_0_154,negated_conjecture,
sdtasdt0(sz10,sdtasdt0(xp,xp)) = sdtasdt0(xp,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_146,c_0_147]),c_0_137]),c_0_51]),c_0_138]),c_0_84])]) ).
cnf(c_0_155,hypothesis,
sdtasdt0(sz10,xp) = 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_101,c_0_148]),c_0_148]),c_0_109]),c_0_29]),c_0_43])]) ).
cnf(c_0_156,plain,
( sdtasdt0(sdtpldt0(X1,X1),X2) = sdtasdt0(X1,sdtpldt0(X2,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_135]) ).
cnf(c_0_157,negated_conjecture,
( sdtasdt0(sdtpldt0(X1,xp),sz10) = sdtpldt0(xp,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151]),c_0_29])]) ).
cnf(c_0_158,negated_conjecture,
sdtpldt0(xp,xp) = sz00,
inference(rw,[status(thm)],[c_0_152,c_0_103]) ).
cnf(c_0_159,negated_conjecture,
sdtasdt0(xp,xp) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_155]),c_0_29]),c_0_30])]),c_0_65]) ).
cnf(c_0_160,negated_conjecture,
$false,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158]),c_0_67]),c_0_103]),c_0_30]),c_0_29])]),c_0_159]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM454+6 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n021.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 00:36:10 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 4.86/3.48 % Version : CSE_E---1.7
% 4.86/3.48 % Problem : theBenchmark.p
% 4.86/3.48 % SZS status Theorem for theBenchmark.p
% 4.86/3.48 % SZS output start CNFRefutation
% See solution above
% 4.96/3.50 % Total time : 2.373s
%------------------------------------------------------------------------------