%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM478+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 : n011.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 04:57:29 PM UTC 2026
% Result : Theorem 1.41s 1.77s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 14 unt; 0 def)
% Number of atoms : 137 ( 50 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 160 ( 64 ~; 61 |; 25 &)
% ( 2 <=>; 8 =>; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 25 !; 2 ?)
% 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,
( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1524_04,hypothesis,
( xl != sz00
& ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1) )
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524_04) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__1524,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1553,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1553) ).
fof(c_0_9,plain,
! [X136,X137,X139] :
( ( aNaturalNumber0(esk2_2(X136,X137))
| ~ doDivides0(X136,X137)
| ~ aNaturalNumber0(X136)
| ~ aNaturalNumber0(X137) )
& ( X137 = sdtasdt0(X136,esk2_2(X136,X137))
| ~ doDivides0(X136,X137)
| ~ aNaturalNumber0(X136)
| ~ aNaturalNumber0(X137) )
& ( ~ aNaturalNumber0(X139)
| X137 != sdtasdt0(X136,X139)
| doDivides0(X136,X137)
| ~ aNaturalNumber0(X136)
| ~ aNaturalNumber0(X137) ) ),
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_10,plain,
! [X82,X83] :
( ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X83)
| aNaturalNumber0(sdtasdt0(X82,X83)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_11,plain,
! [X140,X141,X142] :
( ( aNaturalNumber0(X142)
| X142 != sdtsldt0(X141,X140)
| X140 = sz00
| ~ doDivides0(X140,X141)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141) )
& ( X141 = sdtasdt0(X140,X142)
| X142 != sdtsldt0(X141,X140)
| X140 = sz00
| ~ doDivides0(X140,X141)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141) )
& ( ~ aNaturalNumber0(X142)
| X141 != sdtasdt0(X140,X142)
| X142 = sdtsldt0(X141,X140)
| X140 = sz00
| ~ doDivides0(X140,X141)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_12,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_15,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_11]) ).
cnf(c_0_16,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13]) ).
fof(c_0_17,hypothesis,
( xl != sz00
& aNaturalNumber0(esk3_0)
& xm = sdtasdt0(xl,esk3_0)
& doDivides0(xl,xm) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1524_04])]) ).
fof(c_0_18,plain,
! [X92,X93,X94] :
( ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93)
| ~ aNaturalNumber0(X94)
| sdtasdt0(sdtasdt0(X92,X93),X94) = sdtasdt0(X92,sdtasdt0(X93,X94)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_19,negated_conjecture,
( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
& sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
cnf(c_0_20,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_15]),c_0_13]),c_0_16]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1524]) ).
cnf(c_0_22,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,hypothesis,
( sdtsldt0(sdtasdt0(xl,X1),xl) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_27,hypothesis,
xm = sdtasdt0(xl,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,negated_conjecture,
( sdtasdt0(xl,sdtasdt0(sdtsldt0(xm,xl),X1)) = sdtasdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_21])]) ).
cnf(c_0_30,hypothesis,
sdtsldt0(xm,xl) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
fof(c_0_31,plain,
! [X90,X91] :
( ~ aNaturalNumber0(X90)
| ~ aNaturalNumber0(X91)
| sdtasdt0(X90,X91) = sdtasdt0(X91,X90) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_32,negated_conjecture,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,negated_conjecture,
( sdtasdt0(xl,sdtasdt0(esk3_0,X1)) = sdtasdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,negated_conjecture,
sdtasdt0(xl,sdtasdt0(xn,esk3_0)) != sdtasdt0(xn,xm),
inference(rw,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( sdtasdt0(xl,sdtasdt0(X1,esk3_0)) = sdtasdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_28])]) ).
cnf(c_0_37,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1553]) ).
cnf(c_0_38,negated_conjecture,
sdtasdt0(xn,xm) != sdtasdt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_39,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1524]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_34]),c_0_39]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM478+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
% 0.15/0.33 % Computer : n011.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 00:37:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.41/1.77 % Version : CSE_E---1.7
% 1.41/1.77 % Problem : theBenchmark.p
% 1.41/1.77 % SZS status Theorem for theBenchmark.p
% 1.41/1.77 % SZS output start CNFRefutation
% See solution above
% 1.41/1.77 % Total time : 1.371s
%------------------------------------------------------------------------------