%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM460+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 : n027.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 04:57:25 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% 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)
& sdtpldt0(xm,X1) = xn )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xl )
& sdtlseqdt0(xn,xl) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xl )
| sdtlseqdt0(xm,xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__773,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__773) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(c_0_5,negated_conjecture,
~ ( ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xn )
& sdtlseqdt0(xm,xn)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xl )
& sdtlseqdt0(xn,xl) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xl )
| sdtlseqdt0(xm,xl) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,negated_conjecture,
! [X89] :
( aNaturalNumber0(esk2_0)
& sdtpldt0(xm,esk2_0) = xn
& sdtlseqdt0(xm,xn)
& aNaturalNumber0(esk3_0)
& sdtpldt0(xn,esk3_0) = xl
& sdtlseqdt0(xn,xl)
& ( ~ aNaturalNumber0(X89)
| sdtpldt0(xm,X89) != xl )
& ~ sdtlseqdt0(xm,xl) ),
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,
! [X51,X52] :
( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X52)
| sdtpldt0(X51,X52) = sdtpldt0(X52,X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_8,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xm,X1) != xl ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__773]) ).
fof(c_0_11,plain,
! [X53,X54,X55] :
( ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54)
| ~ aNaturalNumber0(X55)
| sdtpldt0(sdtpldt0(X53,X54),X55) = sdtpldt0(X53,sdtpldt0(X54,X55)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_12,plain,
! [X47,X48] :
( ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48)
| aNaturalNumber0(sdtpldt0(X47,X48)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_13,negated_conjecture,
( sdtpldt0(X1,xm) != xl
| ~ 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,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(X2,xm)) != xl
| ~ 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,
( sdtpldt0(X1,sdtpldt0(xm,X2)) != xl
| ~ 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,
sdtpldt0(xm,esk2_0) = xn,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
aNaturalNumber0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
( sdtpldt0(X1,xn) != xl
| ~ 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(xn),
inference(split_conjunct,[status(thm)],[m__773]) ).
cnf(c_0_22,negated_conjecture,
( sdtpldt0(xn,X1) != xl
| ~ 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,
sdtpldt0(xn,esk3_0) = xl,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
aNaturalNumber0(esk3_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
% 0.00/0.12 % Problem : NUM460+2 : 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
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:36:35 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % 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 : 1.374s
%------------------------------------------------------------------------------