%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM800^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:17:09 AM UTC 2026
% Result : Theorem 0.10s 0.27s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 155 ( 10 ~; 4 |; 2 &; 139 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 111 ( 111 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 56 ( 12 ^; 42 !; 2 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
one: ( $i > $i ) > $i > $i ).
thf(decl_25,type,
two: ( $i > $i ) > $i > $i ).
thf(decl_26,type,
three: ( $i > $i ) > $i > $i ).
thf(decl_29,type,
six: ( $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_2: ( ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > $i > $i ).
thf(decl_41,type,
esk5_1: ( ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > $i ).
thf(thm,conjecture,
? [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ two @ three )
= six )
& ( ( X5 @ one @ two )
= two ) ),
file('/export/starexec/sandbox2/tmp/tmp.XbLP2h3yQO/E---3.1_53160.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.XbLP2h3yQO/E---3.1_53160.p',mult_ax) ).
thf(one_ax,axiom,
( one
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XbLP2h3yQO/E---3.1_53160.p',one_ax) ).
thf(six_ax,axiom,
( six
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XbLP2h3yQO/E---3.1_53160.p',six_ax) ).
thf(three_ax,axiom,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XbLP2h3yQO/E---3.1_53160.p',three_ax) ).
thf(two_ax,axiom,
( two
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XbLP2h3yQO/E---3.1_53160.p',two_ax) ).
thf(c_0_6,negated_conjecture,
~ ? [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ two @ three )
= six )
& ( ( X5 @ one @ two )
= two ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_7,negated_conjecture,
! [X73: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X73 @ two @ three )
!= six )
| ( ( X73 @ one @ two )
!= two ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_8,negated_conjecture,
! [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ two @ three )
!= six )
| ( ( X5 @ one @ two )
!= two ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,plain,
! [X36: ( $i > $i ) > $i > $i,X37: ( $i > $i ) > $i > $i,X38: $i > $i,X39: $i] :
( ( mult @ X36 @ X37 @ X38 @ X39 )
= ( X36 @ ( X37 @ X38 ) @ X39 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).
thf(c_0_10,plain,
! [X9: $i > $i,X10: $i] :
( ( one @ X9 @ X10 )
= ( X9 @ X10 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[one_ax])]) ).
thf(c_0_11,plain,
! [X19: $i > $i,X20: $i] :
( ( six @ X19 @ X20 )
= ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ ( X19 @ X20 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[six_ax])]) ).
thf(c_0_12,plain,
! [X13: $i > $i,X14: $i] :
( ( three @ X13 @ X14 )
= ( X13 @ ( X13 @ ( X13 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).
thf(c_0_13,plain,
! [X11: $i > $i,X12: $i] :
( ( two @ X11 @ X12 )
= ( X11 @ ( X11 @ X12 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).
thf(c_0_14,negated_conjecture,
! [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ one @ two @ ( esk1_2 @ X5 ) )
!= ( two @ ( esk1_2 @ X5 ) ) )
| ( ( X5 @ two @ three )
!= six ) ),
inference(neg_ext,[status(thm)],[c_0_8]) ).
thf(c_0_15,plain,
! [X69: ( $i > $i ) > $i > $i,X70: ( $i > $i ) > $i > $i,X71: $i > $i,X72: $i] :
( ( mult @ X69 @ X70 @ X71 @ X72 )
= ( X69 @ ( X70 @ X71 ) @ X72 ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_16,plain,
! [X42: $i > $i,X43: $i] :
( ( one @ X42 @ X43 )
= ( X42 @ X43 ) ),
inference(variable_rename,[status(thm)],[c_0_10]) ).
thf(c_0_17,plain,
! [X52: $i > $i,X53: $i] :
( ( six @ X52 @ X53 )
= ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ ( X52 @ X53 ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_11]) ).
thf(c_0_18,plain,
! [X46: $i > $i,X47: $i] :
( ( three @ X46 @ X47 )
= ( X46 @ ( X46 @ ( X46 @ X47 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
! [X44: $i > $i,X45: $i] :
( ( two @ X44 @ X45 )
= ( X44 @ ( X44 @ X45 ) ) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
thf(c_0_20,negated_conjecture,
! [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ one @ two @ ( esk1_2 @ X5 ) @ ( esk5_1 @ X5 ) )
!= ( two @ ( esk1_2 @ X5 ) @ ( esk5_1 @ X5 ) ) )
| ( ( X5 @ two @ three )
!= six ) ),
inference(neg_ext,[status(thm)],[c_0_14]) ).
thf(c_0_21,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_15]) ).
thf(c_0_22,plain,
! [X1: $i > $i,X2: $i] :
( ( one @ X1 @ X2 )
= ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,plain,
! [X1: $i > $i,X2: $i] :
( ( six @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_26,negated_conjecture,
( ( mult @ two @ three )
!= six ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
thf(c_0_27,plain,
! [X1: $i > $i,X2: $i] :
( ( six @ X1 @ X2 )
= ( two @ ( three @ X1 ) @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]),c_0_25]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_26]),c_0_21]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM800^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n011.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:00:31 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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.XbLP2h3yQO/E---3.1_53160.p
% 0.10/0.27 % Version: 3.5.1-ho
% 0.10/0.27 % Preprocessing class: HSSSSMSSMSSNHHA.
% 0.10/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.10/0.27 % Starting sh4l with 300s (1) cores
% 0.10/0.27 % Starting ehoh_best_nonlift with 300s (1) cores
% 0.10/0.27 % new_ho_10 with pid 53173 completed with status 0
% 0.10/0.27 % Result found by new_ho_10
% 0.10/0.27 % Preprocessing class: HSSSSMSSMSSNHHA.
% 0.10/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.27 % No SInE strategy applied
% 0.10/0.27 % Search class: HUHPM-FFSF32-DHHSFMNN
% 0.10/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.27 % Starting new_ho_10 with 901s (1) cores
% 0.10/0.27 % Starting ho_unfolding_6 with 151s (1) cores
% 0.10/0.27 % Starting sh4l with 151s (1) cores
% 0.10/0.27 % Starting ehoh_best_nonlift with 146s (1) cores
% 0.10/0.27 % new_ho_10 with pid 53181 completed with status 0
% 0.10/0.27 % Result found by new_ho_10
% 0.10/0.27 % Preprocessing class: HSSSSMSSMSSNHHA.
% 0.10/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.27 % No SInE strategy applied
% 0.10/0.27 % Search class: HUHPM-FFSF32-DHHSFMNN
% 0.10/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.27 % Starting new_ho_10 with 901s (1) cores
% 0.10/0.27 % Preprocessing time : 0.001 s
% 0.10/0.27 % Presaturation interreduction done
% 0.10/0.27
% 0.10/0.27 % Proof found!
% 0.10/0.27 % SZS status Theorem
% 0.10/0.27 % SZS output start CNFRefutation
% See solution above
% 0.10/0.27 % Parsed axioms : 29
% 0.10/0.27 % Removed by relevancy pruning/SinE : 0
% 0.10/0.27 % Initial clauses : 29
% 0.10/0.27 % Removed in clause preprocessing : 14
% 0.10/0.27 % Initial clauses in saturation : 15
% 0.10/0.27 % Processed clauses : 35
% 0.10/0.27 % ...of these trivial : 1
% 0.10/0.27 % ...subsumed : 0
% 0.10/0.27 % ...remaining for further processing : 34
% 0.10/0.27 % Other redundant clauses eliminated : 0
% 0.10/0.27 % Clauses deleted for lack of memory : 0
% 0.10/0.27 % Backward-subsumed : 0
% 0.10/0.27 % Backward-rewritten : 0
% 0.10/0.27 % Generated clauses : 70
% 0.10/0.27 % ...of the previous two non-redundant : 61
% 0.10/0.27 % ...aggressively subsumed : 0
% 0.10/0.27 % Contextual simplify-reflections : 0
% 0.10/0.27 % Paramodulations : 43
% 0.10/0.27 % Factorizations : 0
% 0.10/0.27 % NegExts : 22
% 0.10/0.27 % Equation resolutions : 0
% 0.10/0.27 % Disequality decompositions : 0
% 0.10/0.27 % Total rewrite steps : 103
% 0.10/0.27 % ...of those cached : 67
% 0.10/0.27 % Propositional unsat checks : 0
% 0.10/0.27 % Propositional check models : 0
% 0.10/0.27 % Propositional check unsatisfiable : 0
% 0.10/0.27 % Propositional clauses : 0
% 0.10/0.27 % Propositional clauses after purity: 0
% 0.10/0.27 % Propositional unsat core size : 0
% 0.10/0.27 % Propositional preprocessing time : 0.000
% 0.10/0.27 % Propositional encoding time : 0.000
% 0.10/0.27 % Propositional solver time : 0.000
% 0.10/0.27 % Success case prop preproc time : 0.000
% 0.10/0.27 % Success case prop encoding time : 0.000
% 0.10/0.27 % Success case prop solver time : 0.000
% 0.10/0.27 % Current number of processed clauses : 19
% 0.10/0.27 % Positive orientable unit clauses : 9
% 0.10/0.27 % Positive unorientable unit clauses: 1
% 0.10/0.27 % Negative unit clauses : 1
% 0.10/0.27 % Non-unit-clauses : 8
% 0.10/0.27 % Current number of unprocessed clauses: 55
% 0.10/0.27 % ...number of literals in the above : 68
% 0.10/0.27 % Current number of archived formulas : 0
% 0.10/0.27 % Current number of archived clauses : 15
% 0.10/0.27 % Clause-clause subsumption calls (NU) : 37
% 0.10/0.27 % Rec. Clause-clause subsumption calls : 28
% 0.10/0.27 % Non-unit clause-clause subsumptions : 0
% 0.10/0.27 % Unit Clause-clause subsumption calls : 10
% 0.10/0.27 % Rewrite failures with RHS unbound : 0
% 0.10/0.27 % BW rewrite match attempts : 281
% 0.10/0.27 % BW rewrite match successes : 2
% 0.10/0.27 % Condensation attempts : 35
% 0.10/0.27 % Condensation successes : 0
% 0.10/0.27 % Termbank termtop insertions : 2964
% 0.10/0.27 % Search garbage collected termcells : 98
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.008 s
% 0.10/0.27 % System time : 0.003 s
% 0.10/0.27 % Total time : 0.011 s
% 0.10/0.27 % Maximum resident set size: 3600 pages
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.026 s
% 0.10/0.27 % System time : 0.010 s
% 0.10/0.27 % Total time : 0.036 s
% 0.10/0.27 % Maximum resident set size: 4608 pages
% 0.10/0.27 % E exiting
%------------------------------------------------------------------------------