%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM431+3 : 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 : n004.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 04:57:19 PM UTC 2026
% Result : Theorem 9.15s 6.21s
% Output : CNFRefutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 23
% Syntax : Number of formulae : 174 ( 86 unt; 0 def)
% Number of atoms : 393 ( 149 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 365 ( 146 ~; 144 |; 56 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 64 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',mEquModSym) ).
fof(m__853,hypothesis,
( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xb,smndt0(xc)) )
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__853) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(m__818,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00
& aInteger0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> 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(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
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/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(m__876,hypothesis,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__876) ).
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(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
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(m__899,hypothesis,
( aInteger0(xm)
& sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__899) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__,conjecture,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_23,plain,
! [X78,X79,X80] :
( ~ aInteger0(X78)
| ~ aInteger0(X79)
| ~ aInteger0(X80)
| X80 = sz00
| ~ sdteqdtlpzmzozddtrp0(X78,X79,X80)
| sdteqdtlpzmzozddtrp0(X79,X78,X80) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModSym])]) ).
fof(c_0_24,hypothesis,
( aInteger0(esk2_0)
& sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb))
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aInteger0(esk3_0)
& sdtasdt0(xq,esk3_0) = sdtpldt0(xb,smndt0(xc))
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__853])]) ).
fof(c_0_25,plain,
! [X73,X74,X75] :
( ( ~ sdteqdtlpzmzozddtrp0(X73,X74,X75)
| aDivisorOf0(X75,sdtpldt0(X73,smndt0(X74)))
| ~ aInteger0(X73)
| ~ aInteger0(X74)
| ~ aInteger0(X75)
| X75 = sz00 )
& ( ~ aDivisorOf0(X75,sdtpldt0(X73,smndt0(X74)))
| sdteqdtlpzmzozddtrp0(X73,X74,X75)
| ~ aInteger0(X73)
| ~ aInteger0(X74)
| ~ aInteger0(X75)
| X75 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_26,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,hypothesis,
sdteqdtlpzmzozddtrp0(xb,xc,xq),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_29,hypothesis,
aInteger0(xc),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_30,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_31,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__818]) ).
fof(c_0_32,plain,
! [X68,X69,X71,X72] :
( ( aInteger0(X69)
| ~ aDivisorOf0(X69,X68)
| ~ aInteger0(X68) )
& ( X69 != sz00
| ~ aDivisorOf0(X69,X68)
| ~ aInteger0(X68) )
& ( aInteger0(esk1_2(X68,X69))
| ~ aDivisorOf0(X69,X68)
| ~ aInteger0(X68) )
& ( sdtasdt0(X69,esk1_2(X68,X69)) = X68
| ~ aDivisorOf0(X69,X68)
| ~ aInteger0(X68) )
& ( ~ aInteger0(X71)
| X71 = sz00
| ~ aInteger0(X72)
| sdtasdt0(X71,X72) != X68
| aDivisorOf0(X71,X68)
| ~ aInteger0(X68) ) ),
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)],[mDivisor])])])])])]) ).
cnf(c_0_33,plain,
( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,hypothesis,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
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_26,c_0_27]),c_0_28]),c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_35,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,hypothesis,
aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb))),
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_33,c_0_34]),c_0_28]),c_0_30]),c_0_29])]),c_0_31]) ).
fof(c_0_37,plain,
! [X44,X45] :
( ~ aInteger0(X44)
| ~ aInteger0(X45)
| aInteger0(sdtpldt0(X44,X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_38,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,hypothesis,
( sdtasdt0(xq,esk1_2(sdtpldt0(xc,smndt0(xb)),xq)) = sdtpldt0(xc,smndt0(xb))
| ~ aInteger0(sdtpldt0(xc,smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_41,plain,
! [X43] :
( ~ aInteger0(X43)
| aInteger0(smndt0(X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_42,hypothesis,
( aInteger0(esk1_2(sdtpldt0(xc,smndt0(xb)),xq))
| ~ aInteger0(sdtpldt0(xc,smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
fof(c_0_43,plain,
! [X55,X56,X57] :
( ~ aInteger0(X55)
| ~ aInteger0(X56)
| ~ aInteger0(X57)
| sdtasdt0(X55,sdtasdt0(X56,X57)) = sdtasdt0(sdtasdt0(X55,X56),X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_44,hypothesis,
( sdtasdt0(xq,esk1_2(sdtpldt0(xc,smndt0(xb)),xq)) = sdtpldt0(xc,smndt0(xb))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_29])]) ).
cnf(c_0_45,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,hypothesis,
( aInteger0(esk1_2(sdtpldt0(xc,smndt0(xb)),xq))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_40]),c_0_29])]) ).
cnf(c_0_47,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,hypothesis,
sdtasdt0(xq,esk1_2(sdtpldt0(xc,smndt0(xb)),xq)) = sdtpldt0(xc,smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_30])]) ).
cnf(c_0_49,hypothesis,
aInteger0(esk1_2(sdtpldt0(xc,smndt0(xb)),xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_45]),c_0_30])]) ).
fof(c_0_50,plain,
! [X64] :
( ( sdtasdt0(X64,sz00) = sz00
| ~ aInteger0(X64) )
& ( sz00 = sdtasdt0(sz00,X64)
| ~ aInteger0(X64) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(c_0_51,plain,
! [X46,X47] :
( ~ aInteger0(X46)
| ~ aInteger0(X47)
| aInteger0(sdtasdt0(X46,X47)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_52,hypothesis,
( sdtasdt0(xq,sdtasdt0(esk1_2(sdtpldt0(xc,smndt0(xb)),xq),X1)) = sdtasdt0(sdtpldt0(xc,smndt0(xb)),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_28])]) ).
cnf(c_0_53,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_55,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,hypothesis,
sdtasdt0(sdtpldt0(xc,smndt0(xb)),sz00) = sdtasdt0(xq,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_49])]) ).
cnf(c_0_57,hypothesis,
aInteger0(sdtpldt0(xc,smndt0(xb))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_48]),c_0_49]),c_0_28])]) ).
fof(c_0_58,plain,
! [X58,X59] :
( ~ aInteger0(X58)
| ~ aInteger0(X59)
| sdtasdt0(X58,X59) = sdtasdt0(X59,X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_59,hypothesis,
sdtasdt0(xq,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_56]),c_0_57])]) ).
fof(c_0_60,plain,
! [X61,X62,X63] :
( ( sdtasdt0(X61,sdtpldt0(X62,X63)) = sdtpldt0(sdtasdt0(X61,X62),sdtasdt0(X61,X63))
| ~ aInteger0(X61)
| ~ aInteger0(X62)
| ~ aInteger0(X63) )
& ( sdtasdt0(sdtpldt0(X61,X62),X63) = sdtpldt0(sdtasdt0(X61,X63),sdtasdt0(X62,X63))
| ~ aInteger0(X61)
| ~ aInteger0(X62)
| ~ aInteger0(X63) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
cnf(c_0_61,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_62,hypothesis,
sdtasdt0(sdtpldt0(xc,smndt0(xb)),sz00) = sz00,
inference(rw,[status(thm)],[c_0_56,c_0_59]) ).
cnf(c_0_63,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_60]) ).
cnf(c_0_64,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_65,hypothesis,
sdtasdt0(sz00,sdtpldt0(xc,smndt0(xb))) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_54]),c_0_57])]) ).
cnf(c_0_66,plain,
( sdtpldt0(sdtasdt0(sz00,X1),sz00) = sdtasdt0(sz00,sdtpldt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_54])]) ).
fof(c_0_67,plain,
! [X53] :
( ( sdtpldt0(X53,sz00) = X53
| ~ aInteger0(X53) )
& ( X53 = sdtpldt0(sz00,X53)
| ~ aInteger0(X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_68,hypothesis,
( sdtpldt0(sdtasdt0(sz00,xc),sz00) = sz00
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_29])]) ).
fof(c_0_69,plain,
! [X60] :
( ( sdtasdt0(X60,sz10) = X60
| ~ aInteger0(X60) )
& ( X60 = sdtasdt0(sz10,X60)
| ~ aInteger0(X60) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
cnf(c_0_70,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_71,hypothesis,
sdtpldt0(sdtasdt0(sz00,xc),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_45]),c_0_30])]) ).
cnf(c_0_72,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_60]) ).
cnf(c_0_73,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_74,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_75,hypothesis,
( sdtasdt0(sz00,xc) = sz00
| ~ aInteger0(sdtasdt0(sz00,xc)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,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_72,c_0_73]),c_0_74])]) ).
cnf(c_0_77,hypothesis,
sdtasdt0(sz00,xc) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_55]),c_0_29]),c_0_54])]) ).
cnf(c_0_78,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),xc) = sdtpldt0(sz00,xc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_29]),c_0_54])]) ).
cnf(c_0_79,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_80,hypothesis,
sdtpldt0(sz00,xc) = sdtasdt0(sz10,xc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_74])]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_82,hypothesis,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__876]) ).
cnf(c_0_83,plain,
( aInteger0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_47]),c_0_55]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(sz10,xc) = xc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_29])]) ).
fof(c_0_85,plain,
! [X65] :
( ( sdtasdt0(smndt0(sz10),X65) = smndt0(X65)
| ~ aInteger0(X65) )
& ( smndt0(X65) = sdtasdt0(X65,smndt0(sz10))
| ~ aInteger0(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
fof(c_0_86,plain,
! [X54] :
( ( sdtpldt0(X54,smndt0(X54)) = sz00
| ~ aInteger0(X54) )
& ( sz00 = sdtpldt0(smndt0(X54),X54)
| ~ aInteger0(X54) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_87,hypothesis,
aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_88,hypothesis,
sdtasdt0(xq,esk2_0) = sdtasdt0(xq,xn),
inference(rw,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,hypothesis,
aInteger0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_90,plain,
! [X48,X49,X50] :
( ~ aInteger0(X48)
| ~ aInteger0(X49)
| ~ aInteger0(X50)
| sdtpldt0(X48,sdtpldt0(X49,X50)) = sdtpldt0(sdtpldt0(X48,X49),X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_91,hypothesis,
( aInteger0(sdtasdt0(X1,xc))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_29]),c_0_74])]) ).
cnf(c_0_92,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,hypothesis,
sdtasdt0(xq,esk3_0) = sdtpldt0(xb,smndt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_94,hypothesis,
sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)),
inference(split_conjunct,[status(thm)],[m__899]) ).
cnf(c_0_95,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_96,hypothesis,
aDivisorOf0(xq,sdtasdt0(xq,xn)),
inference(rw,[status(thm)],[c_0_87,c_0_82]) ).
cnf(c_0_97,hypothesis,
aInteger0(sdtasdt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_88]),c_0_89]),c_0_28])]) ).
cnf(c_0_98,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_99,hypothesis,
( aInteger0(smndt0(xc))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_29])]) ).
cnf(c_0_100,hypothesis,
sdtasdt0(xq,esk3_0) = sdtasdt0(xq,xm),
inference(rw,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_101,hypothesis,
aInteger0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_102,plain,
( sdtpldt0(X1,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz10,X2),X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).
fof(c_0_103,plain,
! [X51,X52] :
( ~ aInteger0(X51)
| ~ aInteger0(X52)
| sdtpldt0(X51,X52) = sdtpldt0(X52,X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_104,plain,
( smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_95]),c_0_54])]) ).
cnf(c_0_105,hypothesis,
sdtasdt0(xq,esk1_2(sdtasdt0(xq,xn),xq)) = sdtasdt0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_96]),c_0_97])]) ).
cnf(c_0_106,hypothesis,
aInteger0(esk1_2(sdtasdt0(xq,xn),xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_96]),c_0_97])]) ).
cnf(c_0_107,hypothesis,
( sdtpldt0(xb,sdtpldt0(smndt0(xc),X1)) = sdtpldt0(sdtasdt0(xq,xm),X1)
| ~ aInteger0(smndt0(xc))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_94]),c_0_30])]) ).
cnf(c_0_108,hypothesis,
aInteger0(smndt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_45]),c_0_74])]) ).
cnf(c_0_109,hypothesis,
( sdtpldt0(sdtasdt0(xq,X1),sdtasdt0(xq,xm)) = sdtasdt0(xq,sdtpldt0(X1,esk3_0))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_100]),c_0_101]),c_0_28])]) ).
cnf(c_0_110,hypothesis,
sdtasdt0(sdtpldt0(sz10,sz00),xc) = sdtpldt0(xc,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_77]),c_0_29]),c_0_54])]) ).
cnf(c_0_111,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_112,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),xc) = xc,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_80]),c_0_84]) ).
cnf(c_0_113,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_45]),c_0_54])]) ).
cnf(c_0_114,hypothesis,
( sdtasdt0(xq,sdtasdt0(esk1_2(sdtasdt0(xq,xn),xq),X1)) = sdtasdt0(sdtasdt0(xq,xn),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_105]),c_0_106]),c_0_28])]) ).
cnf(c_0_115,hypothesis,
( sdtpldt0(xb,sdtpldt0(smndt0(xc),X1)) = sdtpldt0(sdtasdt0(xq,xm),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108])]) ).
cnf(c_0_116,hypothesis,
sdtpldt0(sz00,sdtasdt0(xq,xm)) = sdtasdt0(xq,sdtpldt0(sz00,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_59]),c_0_54])]) ).
cnf(c_0_117,hypothesis,
aInteger0(sdtasdt0(xq,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_100]),c_0_101]),c_0_28])]) ).
cnf(c_0_118,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_95]),c_0_45]) ).
cnf(c_0_119,hypothesis,
sdtpldt0(xc,sz00) = xc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_54]),c_0_74])]) ).
cnf(c_0_120,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_113]),c_0_54])]) ).
cnf(c_0_121,hypothesis,
sdtasdt0(sdtasdt0(xq,xn),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_53]),c_0_59]),c_0_54]),c_0_106])]) ).
cnf(c_0_122,hypothesis,
sdtpldt0(sdtasdt0(xq,xm),xc) = sdtpldt0(xb,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_95]),c_0_29])]) ).
cnf(c_0_123,hypothesis,
sdtasdt0(xq,sdtpldt0(sz00,esk3_0)) = sdtasdt0(xq,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_116]),c_0_117])]) ).
cnf(c_0_124,hypothesis,
sdtpldt0(smndt0(xc),xc) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_54]),c_0_29])]) ).
cnf(c_0_125,hypothesis,
sdtasdt0(sz00,sdtasdt0(xq,xn)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_121]),c_0_54]),c_0_97])]) ).
cnf(c_0_126,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_127,hypothesis,
sdtpldt0(xc,sdtasdt0(xq,xm)) = sdtpldt0(xb,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_122]),c_0_29]),c_0_117])]) ).
cnf(c_0_128,hypothesis,
sdtpldt0(sz00,sdtasdt0(xq,xm)) = sdtasdt0(xq,xm),
inference(rw,[status(thm)],[c_0_116,c_0_123]) ).
cnf(c_0_129,hypothesis,
sdtpldt0(smndt0(smndt0(xc)),sz00) = xc,
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_118,c_0_124]),c_0_80]),c_0_84]),c_0_29]),c_0_108])]) ).
cnf(c_0_130,hypothesis,
( sdtpldt0(sdtasdt0(sz00,xa),sz00) = sz00
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_82]),c_0_125]),c_0_126])]) ).
cnf(c_0_131,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_98]),c_0_54])]),c_0_40]) ).
cnf(c_0_132,hypothesis,
sdtpldt0(smndt0(xc),sdtpldt0(xb,sz00)) = sdtasdt0(xq,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_127]),c_0_128]),c_0_117]),c_0_29])]) ).
cnf(c_0_133,hypothesis,
( smndt0(smndt0(xc)) = xc
| ~ aInteger0(smndt0(smndt0(xc))) ),
inference(spm,[status(thm)],[c_0_70,c_0_129]) ).
cnf(c_0_134,hypothesis,
sdtpldt0(sdtasdt0(sz00,xa),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_45]),c_0_30])]) ).
cnf(c_0_135,hypothesis,
sdtpldt0(smndt0(xc),xb) = sdtasdt0(xq,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_30]),c_0_108])]) ).
cnf(c_0_136,hypothesis,
smndt0(smndt0(xc)) = xc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_45]),c_0_108])]) ).
cnf(c_0_137,hypothesis,
( sdtasdt0(sz00,xa) = sz00
| ~ aInteger0(sdtasdt0(sz00,xa)) ),
inference(spm,[status(thm)],[c_0_70,c_0_134]) ).
cnf(c_0_138,hypothesis,
sdtpldt0(xb,sz00) = sdtpldt0(sz00,xb),
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_118,c_0_135]),c_0_136]),c_0_127]),c_0_30]),c_0_108])]) ).
cnf(c_0_139,hypothesis,
sdtasdt0(sz00,xa) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_55]),c_0_126]),c_0_54])]) ).
cnf(c_0_140,plain,
( aInteger0(sdtasdt0(sdtpldt0(X1,X2),X3))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_72]),c_0_55]),c_0_55]) ).
cnf(c_0_141,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_138]),c_0_30])]) ).
cnf(c_0_142,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),xa) = sdtpldt0(sz00,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_139]),c_0_126]),c_0_54])]) ).
cnf(c_0_143,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm)) = sdtasdt0(xq,sdtpldt0(esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_88]),c_0_89])]) ).
cnf(c_0_144,hypothesis,
aInteger0(xm),
inference(split_conjunct,[status(thm)],[m__899]) ).
cnf(c_0_145,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__876]) ).
cnf(c_0_146,hypothesis,
( aInteger0(sdtasdt0(xb,X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_30]),c_0_54])]) ).
cnf(c_0_147,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_148,hypothesis,
sdtpldt0(sz00,xa) = sdtasdt0(sz10,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_79]),c_0_74])]) ).
cnf(c_0_149,hypothesis,
sdtasdt0(xq,sdtpldt0(esk2_0,esk3_0)) = sdtasdt0(xq,sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_143]),c_0_144]),c_0_145]),c_0_28])]) ).
cnf(c_0_150,hypothesis,
( aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_30])]) ).
cnf(c_0_151,hypothesis,
sdtasdt0(sz10,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_148]),c_0_126])]) ).
cnf(c_0_152,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),sdtasdt0(xq,xm)) = sdtasdt0(xq,sdtpldt0(xn,xm)),
inference(rw,[status(thm)],[c_0_143,c_0_149]) ).
cnf(c_0_153,hypothesis,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_82]),c_0_126])]) ).
cnf(c_0_154,hypothesis,
aInteger0(smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_45]),c_0_74])]) ).
cnf(c_0_155,hypothesis,
sdtpldt0(xb,sz00) = xb,
inference(rw,[status(thm)],[c_0_138,c_0_141]) ).
cnf(c_0_156,hypothesis,
sdtasdt0(sdtpldt0(sz10,sz00),xa) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_139]),c_0_126]),c_0_54])]) ).
cnf(c_0_157,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),xa) = xa,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_148]),c_0_151]) ).
cnf(c_0_158,hypothesis,
( sdtpldt0(sdtasdt0(xq,xn),sdtpldt0(sdtasdt0(xq,xm),X1)) = sdtpldt0(sdtasdt0(xq,sdtpldt0(xn,xm)),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_152]),c_0_117]),c_0_97])]) ).
cnf(c_0_159,hypothesis,
sdtpldt0(sdtasdt0(xq,xm),xc) = xb,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_138]),c_0_141]) ).
cnf(c_0_160,hypothesis,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_154])]) ).
cnf(c_0_161,hypothesis,
sdtpldt0(smndt0(xb),xb) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_155]),c_0_120]),c_0_54]),c_0_30])]) ).
cnf(c_0_162,hypothesis,
sdtpldt0(xa,sz00) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_111]),c_0_157]),c_0_54]),c_0_74])]) ).
cnf(c_0_163,hypothesis,
sdtpldt0(sdtasdt0(xq,sdtpldt0(xn,xm)),xc) = sdtpldt0(sdtasdt0(xq,xn),xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_29])]) ).
cnf(c_0_164,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),xb) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_162]),c_0_30])]) ).
cnf(c_0_165,hypothesis,
sdtpldt0(sdtasdt0(xq,sdtpldt0(xn,xm)),xc) = xa,
inference(rw,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_166,hypothesis,
aInteger0(sdtasdt0(xq,sdtpldt0(xn,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_152]),c_0_117]),c_0_97])]) ).
cnf(c_0_167,plain,
( sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_79]),c_0_54])]) ).
cnf(c_0_168,hypothesis,
sdtpldt0(xc,sdtasdt0(xq,sdtpldt0(xn,xm))) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_165]),c_0_29]),c_0_166])]) ).
cnf(c_0_169,hypothesis,
sdtpldt0(sz00,sdtasdt0(xq,sdtpldt0(xn,xm))) = sdtasdt0(xq,sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_152]),c_0_117]),c_0_97])]) ).
fof(c_0_170,negated_conjecture,
sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_171,hypothesis,
sdtpldt0(smndt0(xc),xa) = sdtasdt0(xq,sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_168]),c_0_169]),c_0_166]),c_0_29])]) ).
cnf(c_0_172,negated_conjecture,
sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_173,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_171]),c_0_126]),c_0_108])]),c_0_172]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM431+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.17/0.33 % Computer : n004.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 00:32:47 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 9.15/6.21 % Version : CSE_E---1.7
% 9.15/6.21 % Problem : theBenchmark.p
% 9.15/6.21 % SZS status Theorem for theBenchmark.p
% 9.15/6.21 % SZS output start CNFRefutation
% See solution above
% 9.15/6.25 % Total time : 4.368s
%------------------------------------------------------------------------------