%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM473+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 04:57:28 PM UTC 2026
% Result : Theorem 4.23s 3.26s
% Output : CNFRefutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 25 unt; 0 def)
% Number of atoms : 218 ( 71 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 263 ( 103 ~; 119 |; 27 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 34 !; 0 ?)
% 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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(m__1324_04,hypothesis,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
fof(m__1360,hypothesis,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
fof(m__1347,hypothesis,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
fof(m__1379,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m__,conjecture,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
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/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__1409,hypothesis,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).
fof(c_0_14,plain,
! [X134,X135,X136] :
( ( aNaturalNumber0(X136)
| X136 != sdtsldt0(X135,X134)
| X134 = sz00
| ~ doDivides0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( X135 = sdtasdt0(X134,X136)
| X136 != sdtsldt0(X135,X134)
| X134 = sz00
| ~ doDivides0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( ~ aNaturalNumber0(X136)
| X135 != sdtasdt0(X134,X136)
| X136 = sdtsldt0(X135,X134)
| X134 = sz00
| ~ doDivides0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
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_14]) ).
fof(c_0_16,plain,
! [X117,X118] :
( ( X118 != X117
| sdtlseqdt0(X117,X118)
| ~ aNaturalNumber0(X117)
| ~ aNaturalNumber0(X118) )
& ( sdtlseqdt0(X118,X117)
| sdtlseqdt0(X117,X118)
| ~ aNaturalNumber0(X117)
| ~ aNaturalNumber0(X118) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_17,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_18,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[m__1324_04]) ).
cnf(c_0_19,hypothesis,
xp = sdtsldt0(xm,xl),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_22,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[m__1347]) ).
cnf(c_0_23,hypothesis,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[m__1324_04]) ).
cnf(c_0_24,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(split_conjunct,[status(thm)],[m__1379]) ).
fof(c_0_25,plain,
! [X74,X75] :
( ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X75)
| aNaturalNumber0(sdtpldt0(X74,X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_26,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xp),
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_17,c_0_18]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_28,hypothesis,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_24]),c_0_20])]),c_0_22]) ).
cnf(c_0_29,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1324]) ).
fof(c_0_31,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_32,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_14]) ).
fof(c_0_33,plain,
! [X122,X123,X124] :
( ( sdtasdt0(X122,X123) != sdtasdt0(X122,X124)
| X122 = sz00
| X123 = X124
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtlseqdt0(sdtasdt0(X122,X123),sdtasdt0(X122,X124))
| X122 = sz00
| X123 = X124
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtasdt0(X123,X122) != sdtasdt0(X124,X122)
| X122 = sz00
| X123 = X124
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtlseqdt0(sdtasdt0(X123,X122),sdtasdt0(X124,X122))
| X122 = sz00
| X123 = X124
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_34,hypothesis,
( sdtlseqdt0(X1,xp)
| sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_21])]) ).
cnf(c_0_36,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_32]) ).
fof(c_0_38,plain,
! [X97,X98,X99] :
( ( sdtasdt0(X97,X98) != sdtasdt0(X97,X99)
| X98 = X99
| ~ aNaturalNumber0(X98)
| ~ aNaturalNumber0(X99)
| X97 = sz00
| ~ aNaturalNumber0(X97) )
& ( sdtasdt0(X98,X97) != sdtasdt0(X99,X97)
| X98 = X99
| ~ aNaturalNumber0(X98)
| ~ aNaturalNumber0(X99)
| X97 = sz00
| ~ aNaturalNumber0(X97) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_39,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,hypothesis,
sdtlseqdt0(xq,xp),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_41,hypothesis,
( sdtasdt0(xl,xq) = sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_23]),c_0_24]),c_0_20])]),c_0_22]) ).
fof(c_0_42,plain,
! [X76,X77] :
( ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| aNaturalNumber0(sdtasdt0(X76,X77)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_43,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_44,plain,
! [X112,X113] :
( ~ aNaturalNumber0(X112)
| ~ aNaturalNumber0(X113)
| ~ sdtlseqdt0(X112,X113)
| ~ sdtlseqdt0(X113,X112)
| X112 = X113 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_45,hypothesis,
( xq = xp
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,xq),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_27]),c_0_35])]) ).
cnf(c_0_46,hypothesis,
sdtasdt0(xl,xq) = sdtpldt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29]),c_0_30]),c_0_21])]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(xl,xp) = xm,
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_37,c_0_18]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_48,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,hypothesis,
( X1 = xp
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_27]) ).
cnf(c_0_50,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,hypothesis,
( xq = xp
| sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_20]),c_0_46]),c_0_47]),c_0_22]) ).
cnf(c_0_52,hypothesis,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[m__1409]) ).
cnf(c_0_53,hypothesis,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_35]),c_0_20])]) ).
cnf(c_0_54,hypothesis,
( xq = xp
| sdtpldt0(xm,xn) != xm ),
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_49,c_0_46]),c_0_47]),c_0_35]),c_0_20])]),c_0_22]) ).
cnf(c_0_55,hypothesis,
xq = xp,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]),c_0_21])]),c_0_54]) ).
cnf(c_0_56,hypothesis,
sdtlseqdt0(xp,xp),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_55]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM473+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:36:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.23/3.26 % Version : CSE_E---1.7
% 4.23/3.26 % Problem : theBenchmark.p
% 4.23/3.26 % SZS status Theorem for theBenchmark.p
% 4.23/3.26 % SZS output start CNFRefutation
% See solution above
% 4.23/3.28 % Total time : 2.371s
%------------------------------------------------------------------------------