%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM525+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 0.21s 0.55s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 60 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 12 |; 20 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(m__3059,hypothesis,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_6,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_7,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
fof(c_0_9,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X59,X60,X61] :
( sdtasdt0(sdtasdt0(X59,X60),X61) = sdtasdt0(X59,sdtasdt0(X60,X61))
| ~ aNaturalNumber0(X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_11,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_14,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
xn = sdtasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X57,X58] :
( sdtasdt0(X57,X58) = sdtasdt0(X58,X57)
| ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_19,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xn,xn),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,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_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xn,xq)) != sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16])]) ).
cnf(c_0_23,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_20,c_0_21]),c_0_16])]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM525+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:37:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.21/0.55 % Version: 3.5.1
% 0.21/0.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.55 % Starting sh5l with 300s (1) cores
% 0.21/0.55 % new_bool_3 with pid 663503 completed with status 0
% 0.21/0.55 % Result found by new_bool_3
% 0.21/0.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.55 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.21/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.55 % SubtermCWHack with pid 663508 completed with status 0
% 0.21/0.55 % Result found by SubtermCWHack
% 0.21/0.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.55 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.21/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.55 % Preprocessing time : 0.004 s
% 0.21/0.55
% 0.21/0.55 % Proof found!
% 0.21/0.55 % SZS status Theorem
% 0.21/0.55 % SZS output start CNFRefutation
% See solution above
% 0.21/0.55 % Parsed axioms : 46
% 0.21/0.55 % Removed by relevancy pruning/SinE : 1
% 0.21/0.55 % Initial clauses : 96
% 0.21/0.55 % Removed in clause preprocessing : 3
% 0.21/0.55 % Initial clauses in saturation : 93
% 0.21/0.55 % Processed clauses : 710
% 0.21/0.55 % ...of these trivial : 9
% 0.21/0.55 % ...subsumed : 350
% 0.21/0.55 % ...remaining for further processing : 351
% 0.21/0.55 % Other redundant clauses eliminated : 31
% 0.21/0.55 % Clauses deleted for lack of memory : 0
% 0.21/0.55 % Backward-subsumed : 12
% 0.21/0.55 % Backward-rewritten : 26
% 0.21/0.55 % Generated clauses : 1953
% 0.21/0.55 % ...of the previous two non-redundant : 1659
% 0.21/0.55 % ...aggressively subsumed : 0
% 0.21/0.55 % Contextual simplify-reflections : 0
% 0.21/0.55 % Paramodulations : 1912
% 0.21/0.55 % Factorizations : 1
% 0.21/0.55 % NegExts : 0
% 0.21/0.55 % Equation resolutions : 40
% 0.21/0.55 % Disequality decompositions : 0
% 0.21/0.55 % Total rewrite steps : 1990
% 0.21/0.55 % ...of those cached : 1950
% 0.21/0.55 % Propositional unsat checks : 0
% 0.21/0.55 % Propositional check models : 0
% 0.21/0.55 % Propositional check unsatisfiable : 0
% 0.21/0.55 % Propositional clauses : 0
% 0.21/0.55 % Propositional clauses after purity: 0
% 0.21/0.55 % Propositional unsat core size : 0
% 0.21/0.55 % Propositional preprocessing time : 0.000
% 0.21/0.55 % Propositional encoding time : 0.000
% 0.21/0.55 % Propositional solver time : 0.000
% 0.21/0.55 % Success case prop preproc time : 0.000
% 0.21/0.55 % Success case prop encoding time : 0.000
% 0.21/0.55 % Success case prop solver time : 0.000
% 0.21/0.55 % Current number of processed clauses : 305
% 0.21/0.55 % Positive orientable unit clauses : 39
% 0.21/0.55 % Positive unorientable unit clauses: 0
% 0.21/0.55 % Negative unit clauses : 10
% 0.21/0.55 % Non-unit-clauses : 256
% 0.21/0.55 % Current number of unprocessed clauses: 975
% 0.21/0.55 % ...number of literals in the above : 5271
% 0.21/0.55 % Current number of archived formulas : 0
% 0.21/0.55 % Current number of archived clauses : 38
% 0.21/0.55 % Clause-clause subsumption calls (NU) : 6213
% 0.21/0.55 % Rec. Clause-clause subsumption calls : 3501
% 0.21/0.55 % Non-unit clause-clause subsumptions : 326
% 0.21/0.55 % Unit Clause-clause subsumption calls : 345
% 0.21/0.55 % Rewrite failures with RHS unbound : 0
% 0.21/0.55 % BW rewrite match attempts : 12
% 0.21/0.55 % BW rewrite match successes : 12
% 0.21/0.55 % Condensation attempts : 0
% 0.21/0.55 % Condensation successes : 0
% 0.21/0.55 % Termbank termtop insertions : 38208
% 0.21/0.55 % Search garbage collected termcells : 1598
% 0.21/0.55
% 0.21/0.55 % -------------------------------------------------
% 0.21/0.55 % User time : 0.096 s
% 0.21/0.55 % System time : 0.010 s
% 0.21/0.55 % Total time : 0.106 s
% 0.21/0.55 % Maximum resident set size: 3948 pages
% 0.21/0.55
% 0.21/0.55 % -------------------------------------------------
% 0.21/0.55 % User time : 0.100 s
% 0.21/0.55 % System time : 0.017 s
% 0.21/0.55 % Total time : 0.117 s
% 0.21/0.55 % Maximum resident set size: 4864 pages
% 0.21/0.55 % E exiting
%------------------------------------------------------------------------------