%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM467+2 : 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 : n018.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 04:57:26 PM UTC 2026
% Result : Theorem 1.41s 1.71s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 96 ( 20 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 107 ( 40 ~; 37 |; 25 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 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 : 38 ( 0 sgn 20 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(m__1240_04,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240_04) ).
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(m__1240,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240) ).
fof(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X1) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(c_0_7,plain,
! [X91,X92,X93] :
( ( sdtasdt0(X91,sdtpldt0(X92,X93)) = sdtpldt0(sdtasdt0(X91,X92),sdtasdt0(X91,X93))
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) )
& ( sdtasdt0(sdtpldt0(X92,X93),X91) = sdtpldt0(sdtasdt0(X92,X91),sdtasdt0(X93,X91))
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
fof(c_0_8,hypothesis,
( aNaturalNumber0(esk3_0)
& xm = sdtasdt0(xl,esk3_0)
& doDivides0(xl,xm)
& aNaturalNumber0(esk4_0)
& xn = sdtasdt0(xl,esk4_0)
& doDivides0(xl,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1240_04])]) ).
fof(c_0_9,plain,
! [X130,X131,X133] :
( ( aNaturalNumber0(esk2_2(X130,X131))
| ~ doDivides0(X130,X131)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131) )
& ( X131 = sdtasdt0(X130,esk2_2(X130,X131))
| ~ doDivides0(X130,X131)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131) )
& ( ~ aNaturalNumber0(X133)
| X131 != sdtasdt0(X130,X133)
| doDivides0(X130,X131)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131) ) ),
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_10,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_11,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
xn = sdtasdt0(xl,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1240]) ).
fof(c_0_15,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X1) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_16,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,hypothesis,
( sdtpldt0(sdtasdt0(xl,X1),xn) = sdtasdt0(xl,sdtpldt0(X1,esk4_0))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_19,hypothesis,
xm = sdtasdt0(xl,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_21,negated_conjecture,
! [X142] :
( ( ~ aNaturalNumber0(X142)
| sdtpldt0(xm,xn) != sdtasdt0(xl,X142) )
& ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_22,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).
cnf(c_0_23,hypothesis,
sdtasdt0(xl,sdtpldt0(esk3_0,esk4_0)) = sdtpldt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,negated_conjecture,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
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,hypothesis,
~ aNaturalNumber0(sdtpldt0(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14])]),c_0_24]) ).
cnf(c_0_27,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_13]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM467+2 : 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
% 0.10/0.28 % Computer : n018.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue May 5 00:36:32 EDT 2026
% 0.10/0.28 % CPUTime :
% 0.10/0.29 % start to proof: theBenchmark
% 1.41/1.71 % Version : CSE_E---1.7
% 1.41/1.71 % Problem : theBenchmark.p
% 1.41/1.71 % SZS status Theorem for theBenchmark.p
% 1.41/1.71 % SZS output start CNFRefutation
% See solution above
% 1.41/1.71 % Total time : 1.366s
%------------------------------------------------------------------------------