%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM505+3 : 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 : 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 04:57:36 PM UTC 2026
% Result : Theorem 1.80s 1.88s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 98 ( 27 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 119 ( 48 ~; 43 |; 22 &)
% ( 1 <=>; 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 13 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
| sdtlseqdt0(xk,xp) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(c_0_7,negated_conjecture,
~ ( ~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xk,X1) = xp )
| sdtlseqdt0(xk,xp) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,negated_conjecture,
! [X212,X213] :
( ( ~ aNaturalNumber0(X212)
| sdtpldt0(xp,X212) != xk )
& ~ sdtlseqdt0(xp,xk)
& ( ~ aNaturalNumber0(X213)
| sdtpldt0(xk,X213) != xp
| xk = xp )
& ( ~ sdtlseqdt0(xk,xp)
| xk = xp ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_9,plain,
! [X119] :
( ( sdtpldt0(X119,sz00) = X119
| ~ aNaturalNumber0(X119) )
& ( X119 = sdtpldt0(sz00,X119)
| ~ aNaturalNumber0(X119) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_10,plain,
! [X140,X141,X143] :
( ( aNaturalNumber0(esk1_2(X140,X141))
| ~ sdtlseqdt0(X140,X141)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141) )
& ( sdtpldt0(X140,esk1_2(X140,X141)) = X141
| ~ sdtlseqdt0(X140,X141)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141) )
& ( ~ aNaturalNumber0(X143)
| sdtpldt0(X140,X143) != X141
| sdtlseqdt0(X140,X141)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
cnf(c_0_11,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xp,X1) != xk ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_15,plain,
! [X153,X154] :
( ( X154 != X153
| sdtlseqdt0(X153,X154)
| ~ aNaturalNumber0(X153)
| ~ aNaturalNumber0(X154) )
& ( sdtlseqdt0(X154,X153)
| sdtlseqdt0(X153,X154)
| ~ aNaturalNumber0(X153)
| ~ aNaturalNumber0(X154) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_16,negated_conjecture,
( xk = xp
| ~ aNaturalNumber0(X1)
| sdtpldt0(xk,X1) != xp ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_19,negated_conjecture,
xk != xp,
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_20,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( ~ sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(esk1_2(xk,xp)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])])]),c_0_14])]),c_0_19]) ).
cnf(c_0_22,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,hypothesis,
( sdtlseqdt0(X1,xk)
| sdtlseqdt0(xk,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
~ sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
~ sdtlseqdt0(xk,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14]),c_0_18])]) ).
cnf(c_0_26,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_14]),c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM505+3 : 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 : n002.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 00:41:16 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.80/1.88 % Version : CSE_E---1.7
% 1.80/1.88 % Problem : theBenchmark.p
% 1.80/1.88 % SZS status Theorem for theBenchmark.p
% 1.80/1.88 % SZS output start CNFRefutation
% See solution above
% 1.80/1.88 % Total time : 1.373s
%------------------------------------------------------------------------------