%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM468+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 : n028.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 3.90s 3.18s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 90 ( 35 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 108 ( 45 ~; 44 |; 13 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__,conjecture,
( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(m__1240_04,hypothesis,
( doDivides0(xl,xm)
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(c_0_5,plain,
! [X131,X132,X133] :
( ( aNaturalNumber0(X133)
| X133 != sdtsldt0(X132,X131)
| X131 = sz00
| ~ doDivides0(X131,X132)
| ~ aNaturalNumber0(X131)
| ~ aNaturalNumber0(X132) )
& ( X132 = sdtasdt0(X131,X133)
| X133 != sdtsldt0(X132,X131)
| X131 = sz00
| ~ doDivides0(X131,X132)
| ~ aNaturalNumber0(X131)
| ~ aNaturalNumber0(X132) )
& ( ~ aNaturalNumber0(X133)
| X132 != sdtasdt0(X131,X133)
| X133 = sdtsldt0(X132,X131)
| X131 = sz00
| ~ doDivides0(X131,X132)
| ~ aNaturalNumber0(X131)
| ~ aNaturalNumber0(X132) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
fof(c_0_6,negated_conjecture,
~ ( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_7,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,negated_conjecture,
( xl != sz00
& sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,plain,
! [X88,X89,X90] :
( ( sdtasdt0(X88,sdtpldt0(X89,X90)) = sdtpldt0(sdtasdt0(X88,X89),sdtasdt0(X88,X90))
| ~ aNaturalNumber0(X88)
| ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X90) )
& ( sdtasdt0(sdtpldt0(X89,X90),X88) = sdtpldt0(sdtasdt0(X89,X88),sdtasdt0(X90,X88))
| ~ aNaturalNumber0(X88)
| ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_11,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
doDivides0(xl,xn),
inference(split_conjunct,[status(thm)],[m__1240_04]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_15,negated_conjecture,
xl != sz00,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,hypothesis,
sdtasdt0(xl,sdtsldt0(xn,xl)) = xn,
inference(sr,[status(thm)],[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])]),c_0_15]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_20,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[m__1240_04]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_22,negated_conjecture,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,hypothesis,
( sdtasdt0(xl,sdtpldt0(X1,sdtsldt0(xn,xl))) = sdtpldt0(sdtasdt0(xl,X1),xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_13])]) ).
cnf(c_0_24,hypothesis,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_20]),c_0_13]),c_0_21])]),c_0_15]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_20]),c_0_13]),c_0_21])]),c_0_15]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM468+1 : 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
% 0.15/0.32 % Computer : n028.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:36:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.90/3.18 % Version : CSE_E---1.7
% 3.90/3.18 % Problem : theBenchmark.p
% 3.90/3.18 % SZS status Theorem for theBenchmark.p
% 3.90/3.18 % SZS output start CNFRefutation
% See solution above
% 3.90/3.19 % Total time : 2.373s
%------------------------------------------------------------------------------