%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM524+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.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 04:57:41 PM UTC 2026
% Result : Theorem 1.42s 1.77s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 26 unt; 0 def)
% Number of atoms : 164 ( 58 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 190 ( 82 ~; 81 |; 19 &)
% ( 2 <=>; 6 =>; 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 : 57 ( 0 sgn 25 !; 1 ?)
% 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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__3046,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_10,plain,
! [X152,X153,X154] :
( ( aNaturalNumber0(X154)
| X154 != sdtsldt0(X153,X152)
| X152 = sz00
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) )
& ( X153 = sdtasdt0(X152,X154)
| X154 != sdtsldt0(X153,X152)
| X152 = sz00
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) )
& ( ~ aNaturalNumber0(X154)
| X153 != sdtasdt0(X152,X154)
| X154 = sdtsldt0(X153,X152)
| X152 = sz00
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_11,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_10]) ).
cnf(c_0_12,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X104,X105,X106] :
( ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106)
| sdtasdt0(sdtasdt0(X104,X105),X106) = sdtasdt0(X104,sdtasdt0(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_14,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,hypothesis,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_16,hypothesis,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_18,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_19,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_20,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_12]) ).
fof(c_0_21,plain,
! [X148,X149,X151] :
( ( aNaturalNumber0(esk2_2(X148,X149))
| ~ doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) )
& ( X149 = sdtasdt0(X148,esk2_2(X148,X149))
| ~ doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) )
& ( ~ aNaturalNumber0(X151)
| X149 != sdtasdt0(X148,X151)
| doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) ) ),
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_22,plain,
! [X94,X95] :
( ~ aNaturalNumber0(X94)
| ~ aNaturalNumber0(X95)
| aNaturalNumber0(sdtasdt0(X94,X95)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
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_13]) ).
cnf(c_0_24,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_25,hypothesis,
sdtasdt0(xp,xq) = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xq),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
fof(c_0_27,plain,
! [X102,X103] :
( ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| sdtasdt0(X102,X103) = sdtasdt0(X103,X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_28,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
( sdtasdt0(xp,sdtasdt0(sdtasdt0(xm,xm),X1)) = sdtasdt0(sdtasdt0(xn,xn),X1)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17])]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_32,hypothesis,
( sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_25]),c_0_26]),c_0_17])]) ).
cnf(c_0_33,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,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_10]) ).
cnf(c_0_35,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29]) ).
cnf(c_0_36,hypothesis,
( sdtasdt0(xp,sdtasdt0(sdtasdt0(xm,xm),X1)) = sdtasdt0(sdtasdt0(xn,xn),X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_29]),c_0_31])]) ).
cnf(c_0_37,hypothesis,
( sdtasdt0(xp,sdtasdt0(X1,xq)) = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_26])]) ).
cnf(c_0_38,hypothesis,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_24]),c_0_17])]) ).
cnf(c_0_39,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_34]),c_0_29]),c_0_35]) ).
cnf(c_0_40,hypothesis,
( sdtasdt0(sdtasdt0(xn,xn),xq) = sdtasdt0(xn,sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_26])]) ).
cnf(c_0_41,hypothesis,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_31])]) ).
cnf(c_0_43,hypothesis,
( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_24]),c_0_17])]),c_0_19]) ).
cnf(c_0_44,hypothesis,
sdtasdt0(sdtasdt0(xn,xn),xq) = sdtasdt0(xn,sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_29]),c_0_31])]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xn),xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_41]),c_0_17]),c_0_42])]),c_0_19]) ).
cnf(c_0_46,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_29]),c_0_31])]) ).
fof(c_0_47,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_48,hypothesis,
sdtasdt0(xn,sdtasdt0(xm,xm)) = sdtasdt0(xn,sdtasdt0(xn,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_44]),c_0_26]),c_0_18])]) ).
cnf(c_0_49,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_50,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,hypothesis,
sdtsldt0(sdtasdt0(xn,sdtasdt0(xn,xq)),xn) = sdtasdt0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_48]),c_0_18])]),c_0_49]),c_0_50])]) ).
cnf(c_0_53,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_32]),c_0_26])]) ).
cnf(c_0_54,hypothesis,
~ aNaturalNumber0(sdtasdt0(xn,xq)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_52]),c_0_18])]),c_0_53]),c_0_49]) ).
cnf(c_0_55,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_29]),c_0_26]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM524+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n006.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 5 00:41:46 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.42/1.77 % Version : CSE_E---1.7
% 1.42/1.77 % Problem : theBenchmark.p
% 1.42/1.77 % SZS status Theorem for theBenchmark.p
% 1.42/1.77 % SZS output start CNFRefutation
% See solution above
% 1.42/1.77 % Total time : 1.373s
%------------------------------------------------------------------------------