%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM417^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Wed Sep 30 08:16:37 AM UTC 2026
% Result : Theorem 0.05s 0.26s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 121 ( 7 ~; 0 |; 0 &; 114 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 16 ( 4 ^; 12 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_33,type,
ten: ( $i > $i ) > $i > $i ).
thf(decl_36,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_37,type,
esk1_1: $i > $i ).
thf(decl_42,type,
esk6_0: $i ).
thf(thm,conjecture,
( ( mult @ ( mult @ ten @ ten ) @ ( mult @ ten @ ten ) )
= ( mult @ ( mult @ ( mult @ ten @ ten ) @ ten ) @ ten ) ),
file('/export/starexec/sandbox2/tmp/tmp.7lQL4nc3WT/E---3.1_2008974.p',thm) ).
thf(mult_ax,axiom,
( mult
= ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ ( X3 @ X1 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7lQL4nc3WT/E---3.1_2008974.p',mult_ax) ).
thf(c_0_2,negated_conjecture,
( ( mult @ ( mult @ ten @ ten ) @ ( mult @ ten @ ten ) )
!= ( mult @ ( mult @ ( mult @ ten @ ten ) @ ten ) @ ten ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_3,negated_conjecture,
( ( mult @ ( mult @ ten @ ten ) @ ( mult @ ten @ ten ) )
!= ( mult @ ( mult @ ( mult @ ten @ ten ) @ ten ) @ ten ) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
( ( mult @ ( mult @ ten @ ten ) @ ( mult @ ten @ ten ) )
!= ( mult @ ( mult @ ( mult @ ten @ ten ) @ ten ) @ ten ) ),
inference(fof_nnf,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
! [X34: ( $i > $i ) > $i > $i,X35: ( $i > $i ) > $i > $i,X36: $i > $i,X37: $i] :
( ( mult @ X34 @ X35 @ X36 @ X37 )
= ( X34 @ ( X35 @ X36 ) @ X37 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).
thf(c_0_6,negated_conjecture,
( ( mult @ ( mult @ ten @ ten ) @ ( mult @ ten @ ten ) )
!= ( mult @ ( mult @ ( mult @ ten @ ten ) @ ten ) @ ten ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X67: ( $i > $i ) > $i > $i,X68: ( $i > $i ) > $i > $i,X69: $i > $i,X70: $i] :
( ( mult @ X67 @ X68 @ X69 @ X70 )
= ( X67 @ ( X68 @ X69 ) @ X70 ) ),
inference(variable_rename,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
( ( mult @ ( mult @ ( mult @ ten @ ten ) @ ten ) @ ten @ esk1_1 )
!= ( mult @ ( mult @ ten @ ten ) @ ( mult @ ten @ ten ) @ esk1_1 ) ),
inference(neg_ext,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X1: $i > $i,X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( mult @ X3 @ X4 @ X1 @ X2 )
= ( X3 @ ( X4 @ X1 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
( ( ten @ ( ten @ ( mult @ ten @ ten @ esk1_1 ) ) @ esk6_0 )
!= ( ten @ ( ten @ ( ten @ ( ten @ esk1_1 ) ) ) @ esk6_0 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_8]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ( mult @ ten @ ten @ esk1_1 )
!= ( ten @ ( ten @ esk1_1 ) ) ),
inference(ext_eqres,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_11]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM417^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.17 % Computer : n013.cluster.edu
% 0.05/0.17 % Model : x86_64 x86_64
% 0.05/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.17 % Memory : 8046.5625MB
% 0.05/0.17 % OS : Linux 6.8.0-71-generic
% 0.05/0.17 % CPULimit : 300
% 0.05/0.17 % WCLimit : 300
% 0.05/0.17 % DateTime : Tue Sep 29 11:58:36 UTC 2026
% 0.05/0.17 % CPUTime :
% 0.05/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.21 Running higher-order theorem proving
% 0.05/0.22 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.7lQL4nc3WT/E---3.1_2008974.p
% 0.05/0.26 % Version: 3.5.1-ho
% 0.05/0.26 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.05/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.05/0.26 % Starting pre_casc_2 with 1500s (5) cores
% 0.05/0.26 % Starting sh2 with 300s (1) cores
% 0.05/0.26 % Starting sh3 with 300s (1) cores
% 0.05/0.26 % Starting new_ho_10 with 300s (1) cores
% 0.05/0.26 % pre_casc_2 with pid 2008987 completed with status 0
% 0.05/0.26 % Result found by pre_casc_2
% 0.05/0.26 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.05/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.05/0.26 % Starting pre_casc_2 with 1500s (5) cores
% 0.05/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.05/0.26 % No SInE strategy applied
% 0.05/0.26 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.05/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.05/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.05/0.26 % Starting pre_casc_2 with 901s (1) cores
% 0.05/0.26 % Starting sh2 with 151s (1) cores
% 0.05/0.26 % Starting sh3 with 151s (1) cores
% 0.05/0.26 % Starting sh9 with 146s (1) cores
% 0.05/0.26 % pre_casc_2 with pid 2008994 completed with status 0
% 0.05/0.26 % Result found by pre_casc_2
% 0.05/0.26 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.05/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.05/0.26 % Starting pre_casc_2 with 1500s (5) cores
% 0.05/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.05/0.26 % No SInE strategy applied
% 0.05/0.26 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.05/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.05/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.05/0.26 % Starting pre_casc_2 with 901s (1) cores
% 0.05/0.26 % Preprocessing time : 0.001 s
% 0.05/0.26 % Presaturation interreduction done
% 0.05/0.26
% 0.05/0.26 % Proof found!
% 0.05/0.26 % SZS status Theorem
% 0.05/0.26 % SZS output start CNFRefutation
% See solution above
% 0.05/0.26 % Parsed axioms : 29
% 0.05/0.26 % Removed by relevancy pruning/SinE : 0
% 0.05/0.26 % Initial clauses : 29
% 0.05/0.26 % Removed in clause preprocessing : 14
% 0.05/0.26 % Initial clauses in saturation : 15
% 0.05/0.26 % Processed clauses : 36
% 0.05/0.26 % ...of these trivial : 0
% 0.05/0.26 % ...subsumed : 1
% 0.05/0.26 % ...remaining for further processing : 35
% 0.05/0.26 % Other redundant clauses eliminated : 0
% 0.05/0.26 % Clauses deleted for lack of memory : 0
% 0.05/0.26 % Backward-subsumed : 0
% 0.05/0.26 % Backward-rewritten : 0
% 0.05/0.26 % Generated clauses : 323
% 0.05/0.26 % ...of the previous two non-redundant : 321
% 0.05/0.26 % ...aggressively subsumed : 0
% 0.05/0.26 % Contextual simplify-reflections : 0
% 0.05/0.26 % Paramodulations : 310
% 0.05/0.26 % Factorizations : 0
% 0.05/0.26 % NegExts : 7
% 0.05/0.26 % Equation resolutions : 0
% 0.05/0.26 % Disequality decompositions : 0
% 0.05/0.26 % Total rewrite steps : 330
% 0.05/0.26 % ...of those cached : 301
% 0.05/0.26 % Propositional unsat checks : 0
% 0.05/0.26 % Propositional check models : 0
% 0.05/0.26 % Propositional check unsatisfiable : 0
% 0.05/0.26 % Propositional clauses : 0
% 0.05/0.26 % Propositional clauses after purity: 0
% 0.05/0.26 % Propositional unsat core size : 0
% 0.05/0.26 % Propositional preprocessing time : 0.000
% 0.05/0.26 % Propositional encoding time : 0.000
% 0.05/0.26 % Propositional solver time : 0.000
% 0.05/0.26 % Success case prop preproc time : 0.000
% 0.05/0.26 % Success case prop encoding time : 0.000
% 0.05/0.26 % Success case prop solver time : 0.000
% 0.05/0.26 % Current number of processed clauses : 20
% 0.05/0.26 % Positive orientable unit clauses : 6
% 0.05/0.26 % Positive unorientable unit clauses: 6
% 0.05/0.26 % Negative unit clauses : 8
% 0.05/0.26 % Non-unit-clauses : 0
% 0.05/0.26 % Current number of unprocessed clauses: 315
% 0.05/0.26 % ...number of literals in the above : 315
% 0.05/0.26 % Current number of archived formulas : 0
% 0.05/0.26 % Current number of archived clauses : 15
% 0.05/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.05/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.05/0.26 % Non-unit clause-clause subsumptions : 0
% 0.05/0.26 % Unit Clause-clause subsumption calls : 18
% 0.05/0.26 % Rewrite failures with RHS unbound : 0
% 0.05/0.26 % BW rewrite match attempts : 389
% 0.05/0.26 % BW rewrite match successes : 4
% 0.05/0.26 % Condensation attempts : 36
% 0.05/0.26 % Condensation successes : 0
% 0.05/0.26 % Termbank termtop insertions : 6365
% 0.05/0.26 % Search garbage collected termcells : 76
% 0.05/0.26
% 0.05/0.26 % -------------------------------------------------
% 0.05/0.26 % User time : 0.010 s
% 0.05/0.26 % System time : 0.004 s
% 0.05/0.26 % Total time : 0.015 s
% 0.05/0.26 % Maximum resident set size: 3596 pages
% 0.05/0.26
% 0.05/0.26 % -------------------------------------------------
% 0.05/0.26 % User time : 0.030 s
% 0.05/0.26 % System time : 0.015 s
% 0.05/0.26 % Total time : 0.044 s
% 0.05/0.26 % Maximum resident set size: 4864 pages
% 0.05/0.26 % E exiting
%------------------------------------------------------------------------------