%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM512+3 : 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 : n014.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 04:57:38 PM UTC 2026
% Result : Theorem 1.43s 1.75s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 125 ( 66 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 133 ( 40 ~; 34 |; 51 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
& ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
& sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr)) )
=> sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
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__2342,hypothesis,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(xr,X1) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xr = sdtasdt0(X1,X2) )
| doDivides0(X1,xr) ) )
=> ( X1 = sz10
| X1 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(m__2504,hypothesis,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn )
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
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(c_0_7,negated_conjecture,
~ ( ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) )
& ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
& sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr)) )
=> sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,negated_conjecture,
( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr))
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr))
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
& ( sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr))
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) )
& ( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_9,negated_conjecture,
( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_10,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_11,plain,
! [X123,X124] :
( ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124)
| sdtasdt0(X123,X124) = sdtasdt0(X124,X123) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_12,hypothesis,
! [X211,X212] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X212)
| xr != sdtasdt0(X211,X212)
| ~ aNaturalNumber0(X211)
| X211 = sz10
| X211 = xr )
& ( ~ doDivides0(X211,xr)
| ~ aNaturalNumber0(X211)
| X211 = sz10
| X211 = xr )
& isPrime0(xr) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).
cnf(c_0_13,negated_conjecture,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr))
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
( sdtasdt0(sdtsldt0(sdtasdt0(xn,xm),xr),xr) != sdtasdt0(xn,xm)
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xr))
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(rw,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( sdtasdt0(xr,sdtsldt0(sdtasdt0(xn,xm),xr)) = sdtasdt0(xn,xm)
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_10]),c_0_10]) ).
fof(c_0_20,hypothesis,
( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) != xn
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(esk19_0)
& sdtpldt0(sdtsldt0(xn,xr),esk19_0) = xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2504])])]) ).
cnf(c_0_21,negated_conjecture,
sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X125,X126,X127] :
( ~ aNaturalNumber0(X125)
| ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127)
| sdtasdt0(sdtasdt0(X125,X126),X127) = sdtasdt0(X125,sdtasdt0(X126,X127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_25,negated_conjecture,
sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) != sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_16]),c_0_22]),c_0_23])]) ).
cnf(c_0_26,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
sdtasdt0(xm,sdtasdt0(sdtsldt0(xn,xr),xr)) != sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_17]),c_0_23]),c_0_22])]) ).
cnf(c_0_28,hypothesis,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
sdtasdt0(xm,xn) != sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_16]),c_0_28]),c_0_17]),c_0_23])]) ).
cnf(c_0_30,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_30]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM512+3 : 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
% 0.15/0.33 % Computer : n014.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 00:41:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.43/1.75 % Version : CSE_E---1.7
% 1.43/1.75 % Problem : theBenchmark.p
% 1.43/1.75 % SZS status Theorem for theBenchmark.p
% 1.43/1.75 % SZS output start CNFRefutation
% See solution above
% 1.43/1.75 % Total time : 1.373s
%------------------------------------------------------------------------------