%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM525+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 : n026.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 1.33s 1.71s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 16 unt; 0 def)
% Number of atoms : 97 ( 41 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 113 ( 48 ~; 46 |; 14 &)
% ( 1 <=>; 4 =>; 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; 5 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 16 !; 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,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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__3046,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_8,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_9,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_8]) ).
cnf(c_0_10,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_12,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_13,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_15,hypothesis,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_18,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_19,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_20,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_22,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,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_13,c_0_14]),c_0_15]),c_0_16]),c_0_17])]),c_0_18]) ).
cnf(c_0_24,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_19,c_0_14]),c_0_15]),c_0_16]),c_0_17])]),c_0_18]) ).
fof(c_0_25,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_26,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xn,xn),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,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_22,c_0_23]),c_0_24]),c_0_16])]) ).
cnf(c_0_28,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xn,xq)) != sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24])]) ).
cnf(c_0_30,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_27,c_0_28]),c_0_24])]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM525+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.13/0.30 % Computer : n026.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue May 5 00:42:08 EDT 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.31 % start to proof: theBenchmark
% 1.33/1.71 % Version : CSE_E---1.7
% 1.33/1.71 % Problem : theBenchmark.p
% 1.33/1.71 % SZS status Theorem for theBenchmark.p
% 1.33/1.71 % SZS output start CNFRefutation
% See solution above
% 1.33/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------