%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM457+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 : n026.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 04:57:24 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 61 ( 35 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 67 ( 26 ~; 27 |; 7 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__,conjecture,
( sdtasdt0(xm,xn) = sz00
=> ( xm = sz00
| xn = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__624,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__624) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_5,plain,
! [X56,X57,X58] :
( ( sdtasdt0(X56,X57) != sdtasdt0(X56,X58)
| X57 = X58
| ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X58)
| X56 = sz00
| ~ aNaturalNumber0(X56) )
& ( sdtasdt0(X57,X56) != sdtasdt0(X58,X56)
| X57 = X58
| ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X58)
| X56 = sz00
| ~ aNaturalNumber0(X56) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
fof(c_0_6,negated_conjecture,
~ ( sdtasdt0(xm,xn) = sz00
=> ( xm = sz00
| xn = sz00 ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_7,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__624]) ).
fof(c_0_9,negated_conjecture,
( sdtasdt0(xm,xn) = sz00
& xm != sz00
& xn != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
sdtasdt0(xm,xn) = sz00,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__624]) ).
cnf(c_0_13,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X49] :
( ( sdtasdt0(X49,sz00) = sz00
| ~ aNaturalNumber0(X49) )
& ( sz00 = sdtasdt0(sz00,X49)
| ~ aNaturalNumber0(X49) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_15,negated_conjecture,
( X1 = xn
| sdtasdt0(xm,X1) != sz00
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_16,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_18,negated_conjecture,
xn != sz00,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_12])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM457+1 : 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
% 0.14/0.32 % Computer : n026.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:35:23 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------