%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM466+2 : 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 : n001.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 1.23s 1.71s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 81 ( 23 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 87 ( 32 ~; 25 |; 25 &)
% ( 0 <=>; 5 =>; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 15 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xm,X1) )
& doDivides0(xm,xn) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
| doDivides0(xl,xn) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1218,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1218) ).
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/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(c_0_5,negated_conjecture,
~ ( ( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xm,X1) )
& doDivides0(xm,xn) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
| doDivides0(xl,xn) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,negated_conjecture,
! [X136] :
( aNaturalNumber0(esk3_0)
& xm = sdtasdt0(xl,esk3_0)
& doDivides0(xl,xm)
& aNaturalNumber0(esk4_0)
& xn = sdtasdt0(xm,esk4_0)
& doDivides0(xm,xn)
& ( ~ aNaturalNumber0(X136)
| xn != sdtasdt0(xl,X136) )
& ~ doDivides0(xl,xn) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_7,plain,
! [X81,X82] :
( ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82)
| sdtasdt0(X81,X82) = sdtasdt0(X82,X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_8,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xl,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1218]) ).
fof(c_0_11,plain,
! [X83,X84,X85] :
( ~ aNaturalNumber0(X83)
| ~ aNaturalNumber0(X84)
| ~ aNaturalNumber0(X85)
| sdtasdt0(sdtasdt0(X83,X84),X85) = sdtasdt0(X83,sdtasdt0(X84,X85)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_12,plain,
! [X73,X74] :
( ~ aNaturalNumber0(X73)
| ~ aNaturalNumber0(X74)
| aNaturalNumber0(sdtasdt0(X73,X74)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_13,negated_conjecture,
( sdtasdt0(X1,xl) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
cnf(c_0_14,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( sdtasdt0(X1,sdtasdt0(X2,xl)) != xn
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_10])]),c_0_15]) ).
cnf(c_0_17,negated_conjecture,
( sdtasdt0(X1,sdtasdt0(xl,X2)) != xn
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_9]),c_0_10])]) ).
cnf(c_0_18,negated_conjecture,
xm = sdtasdt0(xl,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
( sdtasdt0(X1,xm) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1218]) ).
cnf(c_0_22,negated_conjecture,
( sdtasdt0(xm,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_9]),c_0_21])]) ).
cnf(c_0_23,negated_conjecture,
xn = sdtasdt0(xm,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM466+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.11/0.31 % Computer : n001.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue May 5 00:37:18 EDT 2026
% 0.11/0.31 % CPUTime :
% 0.11/0.32 % start to proof: theBenchmark
% 1.23/1.71 % Version : CSE_E---1.7
% 1.23/1.71 % Problem : theBenchmark.p
% 1.23/1.71 % SZS status Theorem for theBenchmark.p
% 1.23/1.71 % SZS output start CNFRefutation
% See solution above
% 1.23/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------