%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM477+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 : n002.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 1.59s 1.82s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 187 ( 55 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 218 ( 85 ~; 98 |; 22 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 31 !; 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(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1494,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1494) ).
fof(m__1494_04,hypothesis,
( doDivides0(xm,xn)
& xn != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1494_04) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(m__,conjecture,
sdtlseqdt0(xm,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(c_0_12,plain,
! [X137,X138,X139] :
( ( aNaturalNumber0(X139)
| X139 != sdtsldt0(X138,X137)
| X137 = sz00
| ~ doDivides0(X137,X138)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138) )
& ( X138 = sdtasdt0(X137,X139)
| X139 != sdtsldt0(X138,X137)
| X137 = sz00
| ~ doDivides0(X137,X138)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138) )
& ( ~ aNaturalNumber0(X139)
| X138 != sdtasdt0(X137,X139)
| X139 = sdtsldt0(X138,X137)
| X137 = sz00
| ~ doDivides0(X137,X138)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138) ) ),
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,
! [X129,X130] :
( ~ aNaturalNumber0(X129)
| ~ aNaturalNumber0(X130)
| X129 = sz00
| sdtlseqdt0(X130,sdtasdt0(X130,X129)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
cnf(c_0_14,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X107,X108,X110] :
( ( aNaturalNumber0(esk1_2(X107,X108))
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( sdtpldt0(X107,esk1_2(X107,X108)) = X108
| ~ sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) )
& ( ~ aNaturalNumber0(X110)
| sdtpldt0(X107,X110) != X108
| sdtlseqdt0(X107,X108)
| ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
fof(c_0_16,plain,
! [X77,X78] :
( ~ aNaturalNumber0(X77)
| ~ aNaturalNumber0(X78)
| aNaturalNumber0(sdtpldt0(X77,X78)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_17,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1494]) ).
cnf(c_0_19,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_20,hypothesis,
doDivides0(xm,xn),
inference(split_conjunct,[status(thm)],[m__1494_04]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1494]) ).
cnf(c_0_22,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_23,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X86] :
( ( sdtpldt0(X86,sz00) = X86
| ~ aNaturalNumber0(X86) )
& ( X86 = sdtpldt0(sz00,X86)
| ~ aNaturalNumber0(X86) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_26,plain,
! [X120,X121] :
( ( X121 != X120
| sdtlseqdt0(X120,X121)
| ~ aNaturalNumber0(X120)
| ~ aNaturalNumber0(X121) )
& ( sdtlseqdt0(X121,X120)
| sdtlseqdt0(X120,X121)
| ~ aNaturalNumber0(X120)
| ~ aNaturalNumber0(X121) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_27,hypothesis,
( X1 = sz00
| sdtlseqdt0(xm,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_28,hypothesis,
( xm = sz00
| aNaturalNumber0(sdtsldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]),c_0_21])]) ).
cnf(c_0_29,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_22]) ).
fof(c_0_30,negated_conjecture,
~ sdtlseqdt0(xm,xn),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_31,plain,
! [X115,X116] :
( ~ aNaturalNumber0(X115)
| ~ aNaturalNumber0(X116)
| ~ sdtlseqdt0(X115,X116)
| ~ sdtlseqdt0(X116,X115)
| X115 = X116 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_32,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24]) ).
cnf(c_0_33,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_35,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,hypothesis,
( sdtsldt0(xn,xm) = sz00
| xm = sz00
| sdtlseqdt0(xm,sdtasdt0(xm,sdtsldt0(xn,xm))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,hypothesis,
( sdtasdt0(xm,sdtsldt0(xn,xm)) = xn
| xm = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_20]),c_0_18]),c_0_21])]) ).
cnf(c_0_38,negated_conjecture,
~ sdtlseqdt0(xm,xn),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_41,hypothesis,
( sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
fof(c_0_42,plain,
! [X93] :
( ( sdtasdt0(X93,sz00) = sz00
| ~ aNaturalNumber0(X93) )
& ( sz00 = sdtasdt0(sz00,X93)
| ~ aNaturalNumber0(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_43,hypothesis,
( sdtsldt0(xn,xm) = sz00
| xm = sz00 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_44,plain,
( X1 = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_34])]) ).
cnf(c_0_45,hypothesis,
( sdtlseqdt0(xn,sz00)
| sdtlseqdt0(sz00,xn) ),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_46,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[m__1494_04]) ).
cnf(c_0_47,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,hypothesis,
( sdtasdt0(xm,sz00) = xn
| xm = sz00 ),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_49,hypothesis,
sdtlseqdt0(sz00,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_21])]),c_0_46]) ).
cnf(c_0_50,hypothesis,
sdtlseqdt0(xn,xm),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_18]),c_0_38]) ).
cnf(c_0_51,hypothesis,
xm = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_18])]),c_0_46]) ).
cnf(c_0_52,hypothesis,
~ sdtlseqdt0(xn,sz00),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_49]),c_0_34]),c_0_21])]),c_0_46]) ).
cnf(c_0_53,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM477+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
% 0.17/0.34 % Computer : n002.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 00:37:46 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.59/1.82 % Version : CSE_E---1.7
% 1.59/1.82 % Problem : theBenchmark.p
% 1.59/1.82 % SZS status Theorem for theBenchmark.p
% 1.59/1.82 % SZS output start CNFRefutation
% See solution above
% 1.59/1.82 % Total time : 1.375s
%------------------------------------------------------------------------------