%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM468+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 : n023.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 2.18s 2.01s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 137 ( 50 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 164 ( 60 ~; 56 |; 35 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
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
=> ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( ( aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(m__1240_04,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
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(c_0_7,plain,
! [X129,X130,X132] :
( ( aNaturalNumber0(esk2_2(X129,X130))
| ~ doDivides0(X129,X130)
| ~ aNaturalNumber0(X129)
| ~ aNaturalNumber0(X130) )
& ( X130 = sdtasdt0(X129,esk2_2(X129,X130))
| ~ doDivides0(X129,X130)
| ~ aNaturalNumber0(X129)
| ~ aNaturalNumber0(X130) )
& ( ~ aNaturalNumber0(X132)
| X130 != sdtasdt0(X129,X132)
| doDivides0(X129,X130)
| ~ aNaturalNumber0(X129)
| ~ aNaturalNumber0(X130) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_8,plain,
! [X75,X76] :
( ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76)
| aNaturalNumber0(sdtasdt0(X75,X76)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_9,plain,
! [X133,X134,X135] :
( ( aNaturalNumber0(X135)
| X135 != sdtsldt0(X134,X133)
| X133 = sz00
| ~ doDivides0(X133,X134)
| ~ aNaturalNumber0(X133)
| ~ aNaturalNumber0(X134) )
& ( X134 = sdtasdt0(X133,X135)
| X135 != sdtsldt0(X134,X133)
| X133 = sz00
| ~ doDivides0(X133,X134)
| ~ aNaturalNumber0(X133)
| ~ aNaturalNumber0(X134) )
& ( ~ aNaturalNumber0(X135)
| X134 != sdtasdt0(X133,X135)
| X135 = sdtsldt0(X134,X133)
| X133 = sz00
| ~ doDivides0(X133,X134)
| ~ aNaturalNumber0(X133)
| ~ aNaturalNumber0(X134) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_10,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
~ ( xl != sz00
=> ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( ( aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_13,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11]) ).
fof(c_0_15,negated_conjecture,
( xl != sz00
& aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_11]),c_0_14]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_18,negated_conjecture,
xl != sz00,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,hypothesis,
( aNaturalNumber0(esk3_0)
& xm = sdtasdt0(xl,esk3_0)
& doDivides0(xl,xm)
& aNaturalNumber0(esk4_0)
& xn = sdtasdt0(xl,esk4_0)
& doDivides0(xl,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1240_04])]) ).
fof(c_0_20,plain,
! [X90,X91,X92] :
( ( sdtasdt0(X90,sdtpldt0(X91,X92)) = sdtpldt0(sdtasdt0(X90,X91),sdtasdt0(X90,X92))
| ~ aNaturalNumber0(X90)
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92) )
& ( sdtasdt0(sdtpldt0(X91,X92),X90) = sdtpldt0(sdtasdt0(X91,X90),sdtasdt0(X92,X90))
| ~ aNaturalNumber0(X90)
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_21,hypothesis,
( sdtsldt0(sdtasdt0(xl,X1),xl) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_22,hypothesis,
xn = sdtasdt0(xl,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
xm = sdtasdt0(xl,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,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_20]) ).
cnf(c_0_27,negated_conjecture,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,hypothesis,
sdtsldt0(xn,xl) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_29,hypothesis,
sdtsldt0(xm,xl) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_25])]) ).
cnf(c_0_30,hypothesis,
( sdtpldt0(sdtasdt0(xl,X1),xn) = sdtasdt0(xl,sdtpldt0(X1,esk4_0))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_23]),c_0_17])]) ).
cnf(c_0_31,negated_conjecture,
sdtasdt0(xl,sdtpldt0(esk3_0,esk4_0)) != sdtpldt0(xm,xn),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_25])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM468+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 : n023.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 00:38:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.18/2.01 % Version : CSE_E---1.7
% 2.18/2.01 % Problem : theBenchmark.p
% 2.18/2.01 % SZS status Theorem for theBenchmark.p
% 2.18/2.01 % SZS output start CNFRefutation
% See solution above
% 2.18/2.02 % Total time : 1.373s
%------------------------------------------------------------------------------