%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM428+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 : n003.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 04:57:18 PM UTC 2026
% Result : Theorem 6.75s 4.74s
% Output : CNFRefutation 6.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 19
% Syntax : Number of formulae : 184 ( 76 unt; 0 def)
% Number of atoms : 449 ( 160 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 446 ( 181 ~; 180 |; 65 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 61 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(m__,conjecture,
( ( ? [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) )
=> ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xc)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sdteqdtlpzmzozddtrp0(xa,xc,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(m__818,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00
& aInteger0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
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(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(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(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(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(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(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(c_0_19,plain,
! [X49,X50,X51] :
( ~ aInteger0(X49)
| ~ aInteger0(X50)
| ~ aInteger0(X51)
| sdtpldt0(X49,sdtpldt0(X50,X51)) = sdtpldt0(sdtpldt0(X49,X50),X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_20,plain,
! [X55] :
( ( sdtpldt0(X55,smndt0(X55)) = sz00
| ~ aInteger0(X55) )
& ( sz00 = sdtpldt0(smndt0(X55),X55)
| ~ aInteger0(X55) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
fof(c_0_21,plain,
! [X44] :
( ~ aInteger0(X44)
| aInteger0(smndt0(X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_22,negated_conjecture,
~ ( ( ? [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) )
=> ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xc)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sdteqdtlpzmzozddtrp0(xa,xc,xq) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_23,plain,
! [X54] :
( ( sdtpldt0(X54,sz00) = X54
| ~ aInteger0(X54) )
& ( X54 = sdtpldt0(sz00,X54)
| ~ aInteger0(X54) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_24,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,negated_conjecture,
! [X84] :
( 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)
& ( ~ aInteger0(X84)
| sdtasdt0(xq,X84) != sdtpldt0(xa,smndt0(xc)) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
& ~ sdteqdtlpzmzozddtrp0(xa,xc,xq) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
fof(c_0_28,plain,
! [X45,X46] :
( ~ aInteger0(X45)
| ~ aInteger0(X46)
| aInteger0(sdtpldt0(X45,X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_29,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_31,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_32,negated_conjecture,
sdtasdt0(xq,esk3_0) = sdtpldt0(xb,smndt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_34,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,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_24,c_0_29]),c_0_30])]) ).
cnf(c_0_36,negated_conjecture,
( sdtpldt0(smndt0(xb),sdtasdt0(xq,esk3_0)) = sdtpldt0(sz00,smndt0(xc))
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,hypothesis,
aInteger0(xc),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_38,negated_conjecture,
( aInteger0(sdtasdt0(xq,esk3_0))
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_33])]) ).
cnf(c_0_39,negated_conjecture,
( sdtpldt0(sz00,sdtasdt0(xq,esk3_0)) = sdtasdt0(xq,esk3_0)
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_32]),c_0_33])]) ).
cnf(c_0_40,negated_conjecture,
sdtpldt0(smndt0(xb),sdtasdt0(xq,esk3_0)) = sdtpldt0(sz00,smndt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_26]),c_0_37])]) ).
cnf(c_0_41,negated_conjecture,
aInteger0(sdtasdt0(xq,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_26]),c_0_37])]) ).
cnf(c_0_42,negated_conjecture,
sdtpldt0(sz00,sdtasdt0(xq,esk3_0)) = sdtasdt0(xq,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_26]),c_0_37])]) ).
cnf(c_0_43,negated_conjecture,
( sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(sz00,smndt0(xc))) = sdtasdt0(xq,esk3_0)
| ~ aInteger0(smndt0(xb)) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_44,negated_conjecture,
sdtpldt0(smndt0(smndt0(xb)),sdtpldt0(sz00,smndt0(xc))) = sdtasdt0(xq,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_26]),c_0_33])]) ).
fof(c_0_45,plain,
! [X52,X53] :
( ~ aInteger0(X52)
| ~ aInteger0(X53)
| sdtpldt0(X52,X53) = sdtpldt0(X53,X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_46,negated_conjecture,
( sdtpldt0(smndt0(smndt0(xb)),smndt0(xc)) = sdtasdt0(xq,esk3_0)
| ~ aInteger0(smndt0(xc)) ),
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_47,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_48,negated_conjecture,
sdtpldt0(smndt0(smndt0(xb)),smndt0(xc)) = sdtasdt0(xq,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_26]),c_0_37])]) ).
cnf(c_0_49,negated_conjecture,
( sdtpldt0(smndt0(xc),smndt0(smndt0(xb))) = sdtasdt0(xq,esk3_0)
| ~ aInteger0(smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(xc)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,negated_conjecture,
( sdtpldt0(smndt0(xc),smndt0(smndt0(xb))) = sdtasdt0(xq,esk3_0)
| ~ aInteger0(smndt0(smndt0(xb))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_26]),c_0_37])]) ).
cnf(c_0_51,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_52,negated_conjecture,
( sdtpldt0(smndt0(xc),smndt0(smndt0(xb))) = sdtasdt0(xq,esk3_0)
| ~ aInteger0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_53,plain,
( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_51]),c_0_26]) ).
cnf(c_0_54,negated_conjecture,
sdtpldt0(smndt0(xc),smndt0(smndt0(xb))) = sdtasdt0(xq,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_26]),c_0_33])]) ).
cnf(c_0_55,negated_conjecture,
( sdtpldt0(sz00,smndt0(smndt0(xb))) = sdtpldt0(xc,sdtasdt0(xq,esk3_0))
| ~ aInteger0(smndt0(smndt0(xb))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_37])]) ).
cnf(c_0_56,negated_conjecture,
( sdtpldt0(smndt0(smndt0(xc)),sdtasdt0(xq,esk3_0)) = sdtpldt0(sz00,smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(xc)) ),
inference(spm,[status(thm)],[c_0_31,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
( sdtpldt0(sz00,smndt0(smndt0(xb))) = sdtpldt0(xc,sdtasdt0(xq,esk3_0))
| ~ aInteger0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_55,c_0_26]) ).
cnf(c_0_58,negated_conjecture,
( sdtpldt0(smndt0(smndt0(xc)),sdtasdt0(xq,esk3_0)) = sdtpldt0(sz00,smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(smndt0(xb))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_26]),c_0_37])]) ).
cnf(c_0_59,negated_conjecture,
sdtpldt0(sz00,smndt0(smndt0(xb))) = sdtpldt0(xc,sdtasdt0(xq,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_26]),c_0_33])]) ).
cnf(c_0_60,negated_conjecture,
( sdtpldt0(smndt0(smndt0(xc)),sdtasdt0(xq,esk3_0)) = sdtpldt0(sz00,smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_58,c_0_26]) ).
cnf(c_0_61,negated_conjecture,
( smndt0(smndt0(xb)) = sdtpldt0(xc,sdtasdt0(xq,esk3_0))
| ~ aInteger0(smndt0(smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_29,c_0_59]) ).
cnf(c_0_62,negated_conjecture,
sdtpldt0(smndt0(smndt0(xc)),sdtasdt0(xq,esk3_0)) = sdtpldt0(sz00,smndt0(smndt0(xb))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_26]),c_0_33])]) ).
fof(c_0_63,plain,
! [X79,X80,X81] :
( ~ aInteger0(X79)
| ~ aInteger0(X80)
| ~ aInteger0(X81)
| X81 = sz00
| ~ sdteqdtlpzmzozddtrp0(X79,X80,X81)
| sdteqdtlpzmzozddtrp0(X80,X79,X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModSym])]) ).
cnf(c_0_64,negated_conjecture,
( smndt0(smndt0(xb)) = sdtpldt0(xc,sdtasdt0(xq,esk3_0))
| ~ aInteger0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_61,c_0_26]) ).
cnf(c_0_65,negated_conjecture,
( aInteger0(sdtpldt0(sz00,smndt0(smndt0(xb))))
| ~ aInteger0(smndt0(smndt0(xc))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_62]),c_0_41])]) ).
fof(c_0_66,plain,
! [X74,X75,X76] :
( ( ~ sdteqdtlpzmzozddtrp0(X74,X75,X76)
| aDivisorOf0(X76,sdtpldt0(X74,smndt0(X75)))
| ~ aInteger0(X74)
| ~ aInteger0(X75)
| ~ aInteger0(X76)
| X76 = sz00 )
& ( ~ aDivisorOf0(X76,sdtpldt0(X74,smndt0(X75)))
| sdteqdtlpzmzozddtrp0(X74,X75,X76)
| ~ aInteger0(X74)
| ~ aInteger0(X75)
| ~ aInteger0(X76)
| X76 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_67,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,negated_conjecture,
sdteqdtlpzmzozddtrp0(xb,xc,xq),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_69,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_70,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_71,negated_conjecture,
smndt0(smndt0(xb)) = sdtpldt0(xc,sdtasdt0(xq,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_26]),c_0_33])]) ).
cnf(c_0_72,negated_conjecture,
( aInteger0(sdtpldt0(sz00,smndt0(smndt0(xb))))
| ~ aInteger0(smndt0(xc)) ),
inference(spm,[status(thm)],[c_0_65,c_0_26]) ).
fof(c_0_73,plain,
! [X69,X70,X72,X73] :
( ( aInteger0(X70)
| ~ aDivisorOf0(X70,X69)
| ~ aInteger0(X69) )
& ( X70 != sz00
| ~ aDivisorOf0(X70,X69)
| ~ aInteger0(X69) )
& ( aInteger0(esk1_2(X69,X70))
| ~ aDivisorOf0(X70,X69)
| ~ aInteger0(X69) )
& ( sdtasdt0(X70,esk1_2(X69,X70)) = X69
| ~ aDivisorOf0(X70,X69)
| ~ aInteger0(X69) )
& ( ~ aInteger0(X72)
| X72 = sz00
| ~ aInteger0(X73)
| sdtasdt0(X72,X73) != X69
| aDivisorOf0(X72,X69)
| ~ aInteger0(X69) ) ),
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_74,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_66]) ).
cnf(c_0_75,negated_conjecture,
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_67,c_0_68]),c_0_69]),c_0_37]),c_0_33])]),c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( sdtpldt0(smndt0(xb),sdtpldt0(xc,sdtasdt0(xq,esk3_0))) = sz00
| ~ aInteger0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_51,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
aInteger0(sdtpldt0(sz00,smndt0(smndt0(xb)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_26]),c_0_37])]) ).
cnf(c_0_78,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_79,negated_conjecture,
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_74,c_0_75]),c_0_69]),c_0_33]),c_0_37])]),c_0_70]) ).
cnf(c_0_80,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_81,negated_conjecture,
sdtpldt0(smndt0(xb),sdtpldt0(xc,sdtasdt0(xq,esk3_0))) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_26]),c_0_33])]) ).
cnf(c_0_82,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(xc,sdtasdt0(xq,esk3_0))) = sdtpldt0(xc,sdtasdt0(xq,esk3_0)),
inference(rw,[status(thm)],[c_0_59,c_0_71]) ).
cnf(c_0_83,negated_conjecture,
aInteger0(sdtpldt0(xc,sdtasdt0(xq,esk3_0))),
inference(rw,[status(thm)],[c_0_77,c_0_59]) ).
cnf(c_0_84,negated_conjecture,
( sdtasdt0(xq,esk1_2(sdtpldt0(xc,smndt0(xb)),xq)) = sdtpldt0(xc,smndt0(xb))
| ~ aInteger0(sdtpldt0(xc,smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,negated_conjecture,
( aInteger0(esk1_2(sdtpldt0(xc,smndt0(xb)),xq))
| ~ aInteger0(sdtpldt0(xc,smndt0(xb))) ),
inference(spm,[status(thm)],[c_0_80,c_0_79]) ).
cnf(c_0_86,negated_conjecture,
( sdtpldt0(sdtasdt0(xq,esk3_0),smndt0(smndt0(xc))) = sdtpldt0(sz00,smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(smndt0(xc))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_62]),c_0_41])]) ).
cnf(c_0_87,negated_conjecture,
sdtpldt0(xc,sdtasdt0(xq,esk3_0)) = sdtpldt0(xb,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_81]),c_0_82]),c_0_83]),c_0_33])]) ).
fof(c_0_88,plain,
! [X56,X57,X58] :
( ~ aInteger0(X56)
| ~ aInteger0(X57)
| ~ aInteger0(X58)
| sdtasdt0(X56,sdtasdt0(X57,X58)) = sdtasdt0(sdtasdt0(X56,X57),X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_89,negated_conjecture,
( 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_84,c_0_34]),c_0_37])]) ).
cnf(c_0_90,negated_conjecture,
( 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_85,c_0_34]),c_0_37])]) ).
cnf(c_0_91,negated_conjecture,
( sdtpldt0(sdtasdt0(xq,esk3_0),smndt0(smndt0(xc))) = sdtpldt0(sz00,smndt0(smndt0(xb)))
| ~ aInteger0(smndt0(xc)) ),
inference(spm,[status(thm)],[c_0_86,c_0_26]) ).
cnf(c_0_92,negated_conjecture,
sdtpldt0(smndt0(xb),sdtpldt0(xb,sz00)) = sz00,
inference(rw,[status(thm)],[c_0_81,c_0_87]) ).
cnf(c_0_93,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_94,negated_conjecture,
aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_95,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_96,negated_conjecture,
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_89,c_0_26]),c_0_33])]) ).
cnf(c_0_97,negated_conjecture,
aInteger0(esk1_2(sdtpldt0(xc,smndt0(xb)),xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_26]),c_0_33])]) ).
fof(c_0_98,plain,
! [X65] :
( ( sdtasdt0(X65,sz00) = sz00
| ~ aInteger0(X65) )
& ( sz00 = sdtasdt0(sz00,X65)
| ~ aInteger0(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(c_0_99,plain,
! [X47,X48] :
( ~ aInteger0(X47)
| ~ aInteger0(X48)
| aInteger0(sdtasdt0(X47,X48)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_100,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk3_0),smndt0(smndt0(xc))) = sdtpldt0(sz00,smndt0(smndt0(xb))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_26]),c_0_37])]) ).
cnf(c_0_101,negated_conjecture,
sdtpldt0(smndt0(xb),xb) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_33])]) ).
cnf(c_0_102,negated_conjecture,
aDivisorOf0(xq,sdtasdt0(xq,esk3_0)),
inference(rw,[status(thm)],[c_0_94,c_0_32]) ).
cnf(c_0_103,negated_conjecture,
( 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_95,c_0_96]),c_0_97]),c_0_69])]) ).
cnf(c_0_104,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_105,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_106,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_47,c_0_24]),c_0_34]) ).
cnf(c_0_107,negated_conjecture,
sdtpldt0(smndt0(xc),sdtpldt0(xc,sdtasdt0(xq,esk3_0))) = sdtasdt0(xq,esk3_0),
inference(rw,[status(thm)],[c_0_54,c_0_71]) ).
fof(c_0_108,plain,
! [X62,X63,X64] :
( ( sdtasdt0(X62,sdtpldt0(X63,X64)) = sdtpldt0(sdtasdt0(X62,X63),sdtasdt0(X62,X64))
| ~ aInteger0(X62)
| ~ aInteger0(X63)
| ~ aInteger0(X64) )
& ( sdtasdt0(sdtpldt0(X62,X63),X64) = sdtpldt0(sdtasdt0(X62,X64),sdtasdt0(X63,X64))
| ~ aInteger0(X62)
| ~ aInteger0(X63)
| ~ aInteger0(X64) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
cnf(c_0_109,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk3_0),smndt0(smndt0(xc))) = sdtpldt0(xc,sdtasdt0(xq,esk3_0)),
inference(rw,[status(thm)],[c_0_100,c_0_59]) ).
cnf(c_0_110,negated_conjecture,
sdtpldt0(xb,sz00) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_101]),c_0_33])]) ).
cnf(c_0_111,negated_conjecture,
sdtasdt0(xq,esk1_2(sdtasdt0(xq,esk3_0),xq)) = sdtasdt0(xq,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_102]),c_0_41])]) ).
cnf(c_0_112,negated_conjecture,
aInteger0(esk1_2(sdtasdt0(xq,esk3_0),xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_102]),c_0_41])]) ).
cnf(c_0_113,negated_conjecture,
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_103,c_0_104]),c_0_30]),c_0_97])]) ).
cnf(c_0_114,negated_conjecture,
aInteger0(sdtpldt0(xc,smndt0(xb))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_96]),c_0_97]),c_0_69])]) ).
cnf(c_0_115,plain,
( smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_25]),c_0_30])]) ).
cnf(c_0_116,negated_conjecture,
( sdtpldt0(sdtasdt0(xq,esk3_0),sdtpldt0(smndt0(xc),xc)) = sdtasdt0(xq,esk3_0)
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_41]),c_0_37])]) ).
cnf(c_0_117,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_108]) ).
cnf(c_0_118,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk3_0),smndt0(smndt0(xc))) = sdtpldt0(xb,sz00),
inference(rw,[status(thm)],[c_0_109,c_0_87]) ).
cnf(c_0_119,negated_conjecture,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_110]),c_0_33])]) ).
cnf(c_0_120,negated_conjecture,
( sdtasdt0(xq,sdtasdt0(esk1_2(sdtasdt0(xq,esk3_0),xq),X1)) = sdtasdt0(sdtasdt0(xq,esk3_0),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_111]),c_0_112]),c_0_69])]) ).
cnf(c_0_121,negated_conjecture,
sdtasdt0(xq,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_113]),c_0_114])]) ).
cnf(c_0_122,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_26]),c_0_30])]) ).
cnf(c_0_123,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk3_0),sdtpldt0(smndt0(xc),xc)) = sdtasdt0(xq,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_26]),c_0_37])]) ).
cnf(c_0_124,plain,
( sdtpldt0(sdtasdt0(X1,sz00),sz00) = sdtasdt0(sdtpldt0(X1,X2),sz00)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_104]),c_0_30])]) ).
cnf(c_0_125,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk3_0),smndt0(smndt0(xc))) = xb,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_110]),c_0_119]) ).
cnf(c_0_126,negated_conjecture,
sdtasdt0(sdtasdt0(xq,esk3_0),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_104]),c_0_121]),c_0_30]),c_0_112])]) ).
cnf(c_0_127,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_122]),c_0_30])]) ).
cnf(c_0_128,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk3_0),sz00) = sdtasdt0(xq,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_25]),c_0_37])]) ).
fof(c_0_129,plain,
! [X61] :
( ( sdtasdt0(X61,sz10) = X61
| ~ aInteger0(X61) )
& ( X61 = sdtasdt0(sz10,X61)
| ~ aInteger0(X61) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
cnf(c_0_130,negated_conjecture,
( sdtasdt0(xb,sz00) = sz00
| ~ aInteger0(smndt0(smndt0(xc))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]),c_0_127]),c_0_41])]) ).
cnf(c_0_131,negated_conjecture,
sdtpldt0(smndt0(sdtasdt0(xq,esk3_0)),sdtasdt0(xq,esk3_0)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_128]),c_0_127]),c_0_30]),c_0_41])]) ).
cnf(c_0_132,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_108]) ).
cnf(c_0_133,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_134,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_135,negated_conjecture,
( sdtasdt0(xb,sz00) = sz00
| ~ aInteger0(smndt0(xc)) ),
inference(spm,[status(thm)],[c_0_130,c_0_26]) ).
cnf(c_0_136,negated_conjecture,
( sdtpldt0(sz00,sdtpldt0(smndt0(xc),xc)) = sz00
| ~ aInteger0(sdtpldt0(smndt0(xc),xc)) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_123]),c_0_41])]),c_0_131]) ).
cnf(c_0_137,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_132,c_0_133]),c_0_134])]) ).
cnf(c_0_138,negated_conjecture,
sdtasdt0(xb,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_26]),c_0_37])]) ).
cnf(c_0_139,negated_conjecture,
( sdtpldt0(sz00,sdtpldt0(smndt0(xc),xc)) = sz00
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_34]),c_0_37])]) ).
cnf(c_0_140,negated_conjecture,
sdtasdt0(xb,sdtpldt0(sz00,sz10)) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_119]),c_0_30]),c_0_33])]) ).
cnf(c_0_141,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(smndt0(xc),xc)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_26]),c_0_37])]) ).
cnf(c_0_142,negated_conjecture,
( sdtpldt0(sdtpldt0(xc,sdtasdt0(xq,esk3_0)),smndt0(xb)) = sz00
| ~ aInteger0(smndt0(xb)) ),
inference(spm,[status(thm)],[c_0_25,c_0_71]) ).
cnf(c_0_143,plain,
( aInteger0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_95]),c_0_105]) ).
cnf(c_0_144,negated_conjecture,
sdtasdt0(xb,sz10) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_29]),c_0_134])]) ).
fof(c_0_145,plain,
! [X66] :
( ( sdtasdt0(smndt0(sz10),X66) = smndt0(X66)
| ~ aInteger0(X66) )
& ( smndt0(X66) = sdtasdt0(X66,smndt0(sz10))
| ~ aInteger0(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
cnf(c_0_146,negated_conjecture,
( sdtpldt0(smndt0(xc),xc) = sz00
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_141]),c_0_37])]) ).
cnf(c_0_147,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X2,sdtpldt0(X1,X3))
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_148,negated_conjecture,
sdtpldt0(sdtpldt0(xc,sdtasdt0(xq,esk3_0)),smndt0(xb)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_26]),c_0_33])]) ).
cnf(c_0_149,negated_conjecture,
( aInteger0(sdtasdt0(X1,xb))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_134]),c_0_33])]) ).
cnf(c_0_150,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_151,negated_conjecture,
sdtpldt0(smndt0(xc),xc) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_26]),c_0_37])]) ).
cnf(c_0_152,negated_conjecture,
( sdtpldt0(sdtasdt0(xq,esk3_0),sdtpldt0(xc,smndt0(xb))) = sz00
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_37]),c_0_41])]) ).
cnf(c_0_153,negated_conjecture,
( aInteger0(smndt0(xb))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_33])]) ).
cnf(c_0_154,negated_conjecture,
sdtpldt0(xc,sz00) = sdtpldt0(sz00,xc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_151]),c_0_37])]) ).
cnf(c_0_155,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk3_0),sdtpldt0(xc,smndt0(xb))) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_26]),c_0_33])]) ).
cnf(c_0_156,negated_conjecture,
aInteger0(smndt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_26]),c_0_134])]) ).
cnf(c_0_157,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_34,c_0_117]),c_0_105]),c_0_105]) ).
cnf(c_0_158,negated_conjecture,
sdtpldt0(sz00,xc) = xc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_154]),c_0_37])]) ).
cnf(c_0_159,plain,
( sdtpldt0(X1,sdtpldt0(sz00,X2)) = sdtpldt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_93]),c_0_30])]) ).
cnf(c_0_160,negated_conjecture,
sdtpldt0(xc,sdtpldt0(sz00,smndt0(xc))) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_155]),c_0_40]),c_0_41]),c_0_37])]),c_0_156])]) ).
cnf(c_0_161,negated_conjecture,
( aInteger0(sdtasdt0(xc,X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_37]),c_0_30])]) ).
cnf(c_0_162,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_163,negated_conjecture,
( sdtpldt0(xc,smndt0(xc)) = sz00
| ~ aInteger0(smndt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_37])]) ).
cnf(c_0_164,negated_conjecture,
( aInteger0(smndt0(xc))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_37])]) ).
cnf(c_0_165,negated_conjecture,
sdtpldt0(xc,smndt0(xc)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_26]),c_0_37])]) ).
cnf(c_0_166,negated_conjecture,
aInteger0(smndt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_26]),c_0_134])]) ).
cnf(c_0_167,negated_conjecture,
sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_168,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__818]) ).
cnf(c_0_169,negated_conjecture,
sdtpldt0(smndt0(xc),sz00) = sdtpldt0(sz00,smndt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_165]),c_0_37])]),c_0_166])]) ).
cnf(c_0_170,negated_conjecture,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,esk2_0),X1)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_167]),c_0_168])]) ).
cnf(c_0_171,negated_conjecture,
sdtpldt0(sz00,smndt0(xc)) = smndt0(xc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_169]),c_0_166])]) ).
cnf(c_0_172,negated_conjecture,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,esk2_0),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_156])]) ).
cnf(c_0_173,negated_conjecture,
sdtpldt0(smndt0(xb),sdtasdt0(xq,esk3_0)) = smndt0(xc),
inference(rw,[status(thm)],[c_0_40,c_0_171]) ).
cnf(c_0_174,negated_conjecture,
sdtpldt0(sdtasdt0(xq,esk2_0),sdtasdt0(xq,esk3_0)) = sdtpldt0(xa,smndt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_41])]) ).
cnf(c_0_175,negated_conjecture,
aInteger0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_176,negated_conjecture,
aInteger0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_177,negated_conjecture,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_178,negated_conjecture,
sdtpldt0(xa,smndt0(xc)) = sdtasdt0(xq,sdtpldt0(esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_174]),c_0_175]),c_0_176]),c_0_69])]) ).
cnf(c_0_179,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_180,negated_conjecture,
~ aDivisorOf0(xq,sdtasdt0(xq,sdtpldt0(esk2_0,esk3_0))),
inference(rw,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_181,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_179]),c_0_105]) ).
cnf(c_0_182,negated_conjecture,
~ aInteger0(sdtpldt0(esk2_0,esk3_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_69])]),c_0_70]) ).
cnf(c_0_183,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_34]),c_0_175]),c_0_176])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM428+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.09/0.28 % Computer : n003.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue May 5 00:32:56 EDT 2026
% 0.09/0.28 % CPUTime :
% 0.09/0.28 % start to proof: theBenchmark
% 6.75/4.74 % Version : CSE_E---1.7
% 6.75/4.74 % Problem : theBenchmark.p
% 6.75/4.74 % SZS status Theorem for theBenchmark.p
% 6.75/4.74 % SZS output start CNFRefutation
% See solution above
% 6.75/4.77 % Total time : 3.365s
%------------------------------------------------------------------------------