%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM479+1 : 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 : n010.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 04:57:29 PM UTC 2026
% Result : Theorem 4.82s 3.53s
% Output : CNFRefutation 4.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 19 unt; 0 def)
% Number of atoms : 185 ( 64 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 228 ( 97 ~; 98 |; 20 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 33 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(m__1553,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1553) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__1524_04,hypothesis,
( xl != sz00
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524_04) ).
fof(m__1524,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_12,plain,
! [X139,X140,X141] :
( ( aNaturalNumber0(X141)
| X141 != sdtsldt0(X140,X139)
| X139 = sz00
| ~ doDivides0(X139,X140)
| ~ aNaturalNumber0(X139)
| ~ aNaturalNumber0(X140) )
& ( X140 = sdtasdt0(X139,X141)
| X141 != sdtsldt0(X140,X139)
| X139 = sz00
| ~ doDivides0(X139,X140)
| ~ aNaturalNumber0(X139)
| ~ aNaturalNumber0(X140) )
& ( ~ aNaturalNumber0(X141)
| X140 != sdtasdt0(X139,X141)
| X141 = sdtsldt0(X140,X139)
| X139 = sz00
| ~ doDivides0(X139,X140)
| ~ aNaturalNumber0(X139)
| ~ aNaturalNumber0(X140) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
fof(c_0_13,plain,
! [X102,X103,X104] :
( ( sdtasdt0(X102,X103) != sdtasdt0(X102,X104)
| X103 = X104
| ~ aNaturalNumber0(X103)
| ~ aNaturalNumber0(X104)
| X102 = sz00
| ~ aNaturalNumber0(X102) )
& ( sdtasdt0(X103,X102) != sdtasdt0(X104,X102)
| X103 = X104
| ~ aNaturalNumber0(X103)
| ~ aNaturalNumber0(X104)
| X102 = sz00
| ~ aNaturalNumber0(X102) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_14,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1553]) ).
fof(c_0_18,plain,
! [X94] :
( ( sdtasdt0(X94,sz10) = X94
| ~ aNaturalNumber0(X94) )
& ( X94 = sdtasdt0(sz10,X94)
| ~ aNaturalNumber0(X94) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_19,plain,
! [X135,X136,X138] :
( ( aNaturalNumber0(esk2_2(X135,X136))
| ~ doDivides0(X135,X136)
| ~ aNaturalNumber0(X135)
| ~ aNaturalNumber0(X136) )
& ( X136 = sdtasdt0(X135,esk2_2(X135,X136))
| ~ doDivides0(X135,X136)
| ~ aNaturalNumber0(X135)
| ~ aNaturalNumber0(X136) )
& ( ~ aNaturalNumber0(X138)
| X136 != sdtasdt0(X135,X138)
| doDivides0(X135,X136)
| ~ aNaturalNumber0(X135)
| ~ aNaturalNumber0(X136) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_20,plain,
! [X81,X82] :
( ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82)
| aNaturalNumber0(sdtasdt0(X81,X82)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_21,plain,
! [X91,X92,X93] :
( ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93)
| sdtasdt0(sdtasdt0(X91,X92),X93) = sdtasdt0(X91,sdtasdt0(X92,X93)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_22,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[m__1524_04]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1524]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1524]) ).
cnf(c_0_26,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[m__1524_04]) ).
cnf(c_0_27,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_28,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_29,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_31,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_32,plain,
! [X89,X90] :
( ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X90)
| sdtasdt0(X89,X90) = sdtasdt0(X90,X89) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_33,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_34,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_35,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_36,hypothesis,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_37,hypothesis,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_24]),c_0_25])]),c_0_26]) ).
cnf(c_0_38,hypothesis,
( sdtasdt0(sz10,xn) = xn
| ~ aNaturalNumber0(sdtasdt0(sz10,xn)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),c_0_31])]) ).
fof(c_0_39,negated_conjecture,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_40,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_34]) ).
cnf(c_0_42,hypothesis,
( sdtasdt0(xl,sdtasdt0(sdtsldt0(xm,xl),X1)) = sdtasdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_24])]) ).
cnf(c_0_43,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_34]) ).
cnf(c_0_44,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_34]),c_0_17]),c_0_30])]) ).
cnf(c_0_45,negated_conjecture,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X2,sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_40]) ).
cnf(c_0_47,hypothesis,
( doDivides0(xl,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xm,xl),X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_24])]) ).
cnf(c_0_48,hypothesis,
( aNaturalNumber0(sdtasdt0(X1,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17]),c_0_30])]) ).
cnf(c_0_49,negated_conjecture,
sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(xn,xm),
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_45,c_0_46]),c_0_36]),c_0_37]),c_0_24]),c_0_17])]) ).
cnf(c_0_50,hypothesis,
doDivides0(xl,sdtasdt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_17]),c_0_37])]) ).
cnf(c_0_51,negated_conjecture,
sdtasdt0(xl,sdtsldt0(sdtasdt0(xm,xn),xl)) != sdtasdt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_40]),c_0_25]),c_0_17])]) ).
cnf(c_0_52,hypothesis,
~ aNaturalNumber0(sdtasdt0(xm,xn)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_50]),c_0_24])]),c_0_51]),c_0_26]) ).
cnf(c_0_53,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_34]),c_0_17]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM479+1 : 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
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:37:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.82/3.53 % Version : CSE_E---1.7
% 4.82/3.53 % Problem : theBenchmark.p
% 4.82/3.53 % SZS status Theorem for theBenchmark.p
% 4.82/3.53 % SZS output start CNFRefutation
% See solution above
% 4.82/3.55 % Total time : 2.374s
%------------------------------------------------------------------------------