%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM525+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:25 PM UTC 2026
% Result : Theorem 0.27s 0.61s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 118 ( 52 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 138 ( 57 ~; 46 |; 27 &)
% ( 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(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(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,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__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(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_8,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_9,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_10,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
fof(c_0_11,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
fof(c_0_12,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X17,X18,X19] :
( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_18,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_20,hypothesis,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_25,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,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_18,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_29,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_24,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
fof(c_0_30,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_31,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xn,xn),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_21])]) ).
cnf(c_0_33,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xn,xq)) != sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29])]) ).
cnf(c_0_35,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,sdtasdt0(X1,xq)) = sdtasdt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM525+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 % Computer : n014.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 02:37:34 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.27/0.61 % Version: 3.5.1
% 0.27/0.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.61 % Starting sh5l with 300s (1) cores
% 0.27/0.61 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2964935 completed with status 0
% 0.27/0.61 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.27/0.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.61 % No SInE strategy applied
% 0.27/0.61 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.27/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.27/0.61 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.27/0.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 0.27/0.61 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.61 % new_bool_3 with pid 2964946 completed with status 0
% 0.27/0.61 % Result found by new_bool_3
% 0.27/0.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.61 % No SInE strategy applied
% 0.27/0.61 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.27/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.27/0.61 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.27/0.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 0.27/0.61 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.61 % Preprocessing time : 0.003 s
% 0.27/0.61 % Presaturation interreduction done
% 0.27/0.61
% 0.27/0.61 % Proof found!
% 0.27/0.61 % SZS status Theorem
% 0.27/0.61 % SZS output start CNFRefutation
% See solution above
% 0.27/0.61 % Parsed axioms : 46
% 0.27/0.61 % Removed by relevancy pruning/SinE : 0
% 0.27/0.61 % Initial clauses : 84
% 0.27/0.61 % Removed in clause preprocessing : 3
% 0.27/0.61 % Initial clauses in saturation : 81
% 0.27/0.61 % Processed clauses : 409
% 0.27/0.61 % ...of these trivial : 8
% 0.27/0.61 % ...subsumed : 121
% 0.27/0.61 % ...remaining for further processing : 280
% 0.27/0.61 % Other redundant clauses eliminated : 19
% 0.27/0.61 % Clauses deleted for lack of memory : 0
% 0.27/0.61 % Backward-subsumed : 5
% 0.27/0.61 % Backward-rewritten : 23
% 0.27/0.61 % Generated clauses : 970
% 0.27/0.61 % ...of the previous two non-redundant : 845
% 0.27/0.61 % ...aggressively subsumed : 0
% 0.27/0.61 % Contextual simplify-reflections : 6
% 0.27/0.61 % Paramodulations : 945
% 0.27/0.61 % Factorizations : 2
% 0.27/0.61 % NegExts : 0
% 0.27/0.61 % Equation resolutions : 23
% 0.27/0.61 % Disequality decompositions : 0
% 0.27/0.61 % Total rewrite steps : 1194
% 0.27/0.61 % ...of those cached : 1150
% 0.27/0.61 % Propositional unsat checks : 0
% 0.27/0.61 % Propositional check models : 0
% 0.27/0.61 % Propositional check unsatisfiable : 0
% 0.27/0.61 % Propositional clauses : 0
% 0.27/0.61 % Propositional clauses after purity: 0
% 0.27/0.61 % Propositional unsat core size : 0
% 0.27/0.61 % Propositional preprocessing time : 0.000
% 0.27/0.61 % Propositional encoding time : 0.000
% 0.27/0.61 % Propositional solver time : 0.000
% 0.27/0.61 % Success case prop preproc time : 0.000
% 0.27/0.61 % Success case prop encoding time : 0.000
% 0.27/0.61 % Success case prop solver time : 0.000
% 0.27/0.61 % Current number of processed clauses : 165
% 0.27/0.61 % Positive orientable unit clauses : 46
% 0.27/0.61 % Positive unorientable unit clauses: 0
% 0.27/0.61 % Negative unit clauses : 9
% 0.27/0.61 % Non-unit-clauses : 110
% 0.27/0.61 % Current number of unprocessed clauses: 560
% 0.27/0.61 % ...number of literals in the above : 2198
% 0.27/0.61 % Current number of archived formulas : 0
% 0.27/0.61 % Current number of archived clauses : 104
% 0.27/0.61 % Clause-clause subsumption calls (NU) : 1839
% 0.27/0.61 % Rec. Clause-clause subsumption calls : 633
% 0.27/0.61 % Non-unit clause-clause subsumptions : 97
% 0.27/0.61 % Unit Clause-clause subsumption calls : 456
% 0.27/0.61 % Rewrite failures with RHS unbound : 0
% 0.27/0.61 % BW rewrite match attempts : 12
% 0.27/0.61 % BW rewrite match successes : 12
% 0.27/0.61 % Condensation attempts : 0
% 0.27/0.61 % Condensation successes : 0
% 0.27/0.61 % Termbank termtop insertions : 23605
% 0.27/0.61 % Search garbage collected termcells : 1401
% 0.27/0.61
% 0.27/0.61 % -------------------------------------------------
% 0.27/0.61 % User time : 0.057 s
% 0.27/0.61 % System time : 0.011 s
% 0.27/0.61 % Total time : 0.068 s
% 0.27/0.61 % Maximum resident set size: 3940 pages
% 0.27/0.61
% 0.27/0.61 % -------------------------------------------------
% 0.27/0.61 % User time : 0.256 s
% 0.27/0.61 % System time : 0.034 s
% 0.27/0.61 % Total time : 0.291 s
% 0.27/0.61 % Maximum resident set size: 4608 pages
% 0.27/0.61 % E exiting
%------------------------------------------------------------------------------