%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM747^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:17:00 AM UTC 2026
% Result : Theorem 1.41s 0.48s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 24 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 339 ( 10 ~; 6 |; 3 &; 311 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 59 ( 44 ^; 15 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_163,type,
n_ts: $i > $i > $i ).
thf(decl_191,type,
n_fr: $i > $i > $i ).
thf(decl_192,type,
num: $i > $i ).
thf(decl_193,type,
den: $i > $i ).
thf(decl_194,type,
n_eq: $i > $i > $o ).
thf(decl_199,type,
n_pf: $i > $i > $i ).
thf(decl_200,type,
esk1_0: $i ).
thf(decl_201,type,
esk2_0: $i ).
thf(decl_202,type,
esk3_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ueMiOKvnqR/E---3.1_2457933.p',def_e_is) ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X1: $i,X436: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X436 ) ) @ ( n_ts @ ( num @ X436 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ueMiOKvnqR/E---3.1_2457933.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ueMiOKvnqR/E---3.1_2457933.p',def_n_is) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ueMiOKvnqR/E---3.1_2457933.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ueMiOKvnqR/E---3.1_2457933.p',def_is_of) ).
thf(satz57a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X512: $i] : ( in @ X512 @ nat )
@ ^ [X513: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] : ( n_eq @ ( n_fr @ ( n_pl @ X1 @ X513 ) @ X4 ) @ ( n_pf @ ( n_fr @ X1 @ X4 ) @ ( n_fr @ X513 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ueMiOKvnqR/E---3.1_2457933.p',satz57a) ).
thf(satz57,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X510: $i] : ( in @ X510 @ nat )
@ ^ [X511: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] : ( n_eq @ ( n_pf @ ( n_fr @ X1 @ X4 ) @ ( n_fr @ X511 @ X4 ) ) @ ( n_fr @ ( n_pl @ X1 @ X511 ) @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ueMiOKvnqR/E---3.1_2457933.p',satz57) ).
thf(c_0_7,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_8,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_eq]) ).
thf(c_0_9,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_7]) ).
thf(c_0_10,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_11,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_12,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X512: $i] : ( in @ X512 @ nat )
@ ^ [X513: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] : ( n_eq @ ( n_fr @ ( n_pl @ X1 @ X513 ) @ X4 ) @ ( n_pf @ ( n_fr @ X1 @ X4 ) @ ( n_fr @ X513 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz57a]) ).
thf(c_0_13,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_14,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
~ ! [X608: $i] :
( ( in @ X608 @ nat )
=> ! [X607: $i] :
( ( in @ X607 @ nat )
=> ! [X606: $i] :
( ( in @ X606 @ nat )
=> ( ( n_ts @ ( num @ ( n_fr @ ( n_pl @ X608 @ X607 ) @ X606 ) ) @ ( den @ ( n_pf @ ( n_fr @ X608 @ X606 ) @ ( n_fr @ X607 @ X606 ) ) ) )
= ( n_ts @ ( num @ ( n_pf @ ( n_fr @ X608 @ X606 ) @ ( n_fr @ X607 @ X606 ) ) ) @ ( den @ ( n_fr @ ( n_pl @ X608 @ X607 ) @ X606 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_12]),c_0_13]),c_0_14]) ).
thf(c_0_16,plain,
! [X621: $i] :
( ( in @ X621 @ nat )
=> ! [X620: $i] :
( ( in @ X620 @ nat )
=> ! [X619: $i] :
( ( in @ X619 @ nat )
=> ( ( n_ts @ ( num @ ( n_pf @ ( n_fr @ X621 @ X619 ) @ ( n_fr @ X620 @ X619 ) ) ) @ ( den @ ( n_fr @ ( n_pl @ X621 @ X620 ) @ X619 ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_pl @ X621 @ X620 ) @ X619 ) ) @ ( den @ ( n_pf @ ( n_fr @ X621 @ X619 ) @ ( n_fr @ X620 @ X619 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz57]),c_0_13]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( ( n_ts @ ( num @ ( n_fr @ ( n_pl @ esk1_0 @ esk2_0 ) @ esk3_0 ) ) @ ( den @ ( n_pf @ ( n_fr @ esk1_0 @ esk3_0 ) @ ( n_fr @ esk2_0 @ esk3_0 ) ) ) )
!= ( n_ts @ ( num @ ( n_pf @ ( n_fr @ esk1_0 @ esk3_0 ) @ ( n_fr @ esk2_0 @ esk3_0 ) ) ) @ ( den @ ( n_fr @ ( n_pl @ esk1_0 @ esk2_0 ) @ esk3_0 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
thf(c_0_18,plain,
! [X895: $i,X896: $i,X897: $i] :
( ~ ( in @ X895 @ nat )
| ~ ( in @ X896 @ nat )
| ~ ( in @ X897 @ nat )
| ( ( n_ts @ ( num @ ( n_pf @ ( n_fr @ X895 @ X897 ) @ ( n_fr @ X896 @ X897 ) ) ) @ ( den @ ( n_fr @ ( n_pl @ X895 @ X896 ) @ X897 ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_pl @ X895 @ X896 ) @ X897 ) ) @ ( den @ ( n_pf @ ( n_fr @ X895 @ X897 ) @ ( n_fr @ X896 @ X897 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
thf(c_0_19,negated_conjecture,
( ( n_ts @ ( num @ ( n_fr @ ( n_pl @ esk1_0 @ esk2_0 ) @ esk3_0 ) ) @ ( den @ ( n_pf @ ( n_fr @ esk1_0 @ esk3_0 ) @ ( n_fr @ esk2_0 @ esk3_0 ) ) ) )
!= ( n_ts @ ( num @ ( n_pf @ ( n_fr @ esk1_0 @ esk3_0 ) @ ( n_fr @ esk2_0 @ esk3_0 ) ) ) @ ( den @ ( n_fr @ ( n_pl @ esk1_0 @ esk2_0 ) @ esk3_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( ( n_ts @ ( num @ ( n_pf @ ( n_fr @ X1 @ X5 ) @ ( n_fr @ X4 @ X5 ) ) ) @ ( den @ ( n_fr @ ( n_pl @ X1 @ X4 ) @ X5 ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_pl @ X1 @ X4 ) @ X5 ) ) @ ( den @ ( n_pf @ ( n_fr @ X1 @ X5 ) @ ( n_fr @ X4 @ X5 ) ) ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,negated_conjecture,
$false,
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_20]),c_0_21]),c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM747^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:51:34 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.22/0.29 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.ueMiOKvnqR/E---3.1_2457933.p
% 1.41/0.48 % Version: 3.5.1-ho
% 1.41/0.48 % Preprocessing class: HSLMSMSMLLLCHSA.
% 1.41/0.48 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.41/0.48 % Starting pre_casc_4 with 1200s (4) cores
% 1.41/0.48 % Starting full_lambda_6 with 300s (1) cores
% 1.41/0.48 % Starting sh10 with 300s (1) cores
% 1.41/0.48 % Starting post_as_ho9 with 300s (1) cores
% 1.41/0.48 % Starting post_as_ho8 with 300s (1) cores
% 1.41/0.48 % pre_casc_4 with pid 2457946 completed with status 0
% 1.41/0.48 % Result found by pre_casc_4
% 1.41/0.48 % Preprocessing class: HSLMSMSMLLLCHSA.
% 1.41/0.48 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.41/0.48 % Starting pre_casc_4 with 1200s (4) cores
% 1.41/0.48 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 1.41/0.48 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 1.41/0.48 % Search class: HGUSM-FSLM31-DHSMMSBN
% 1.41/0.48 % partial match(2): HGHSM-FSLM31-MHSMMSBN
% 1.41/0.48 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 1.41/0.48 % Starting SubtermCWHack with 109s (1) cores
% 1.41/0.48 % Starting pre_casc_4 with 121s (1) cores
% 1.41/0.48 % Starting pre_casc_3 with 171s (1) cores
% 1.41/0.48 % Starting new_bool_3 with 109s (1) cores
% 1.41/0.48 % SubtermCWHack with pid 2457951 completed with status 0
% 1.41/0.48 % Result found by SubtermCWHack
% 1.41/0.48 % Preprocessing class: HSLMSMSMLLLCHSA.
% 1.41/0.48 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.41/0.48 % Starting pre_casc_4 with 1200s (4) cores
% 1.41/0.48 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 1.41/0.48 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 1.41/0.48 % Search class: HGUSM-FSLM31-DHSMMSBN
% 1.41/0.48 % partial match(2): HGHSM-FSLM31-MHSMMSBN
% 1.41/0.48 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 1.41/0.48 % Starting SubtermCWHack with 109s (1) cores
% 1.41/0.48 % Preprocessing time : 0.007 s
% 1.41/0.48
% 1.41/0.48 % Proof found!
% 1.41/0.48 % SZS status Theorem
% 1.41/0.48 % SZS output start CNFRefutation
% See solution above
% 1.41/0.48 % Parsed axioms : 577
% 1.41/0.48 % Removed by relevancy pruning/SinE : 417
% 1.41/0.48 % Initial clauses : 195
% 1.41/0.48 % Removed in clause preprocessing : 13
% 1.41/0.48 % Initial clauses in saturation : 182
% 1.41/0.48 % Processed clauses : 1210
% 1.41/0.48 % ...of these trivial : 46
% 1.41/0.48 % ...subsumed : 737
% 1.41/0.48 % ...remaining for further processing : 427
% 1.41/0.48 % Other redundant clauses eliminated : 32
% 1.41/0.48 % Clauses deleted for lack of memory : 0
% 1.41/0.48 % Backward-subsumed : 3
% 1.41/0.48 % Backward-rewritten : 18
% 1.41/0.48 % Generated clauses : 3412
% 1.41/0.48 % ...of the previous two non-redundant : 3123
% 1.41/0.48 % ...aggressively subsumed : 0
% 1.41/0.48 % Contextual simplify-reflections : 2
% 1.41/0.48 % Paramodulations : 3362
% 1.41/0.48 % Factorizations : 2
% 1.41/0.48 % NegExts : 0
% 1.41/0.48 % Equation resolutions : 38
% 1.41/0.48 % Disequality decompositions : 0
% 1.41/0.48 % Total rewrite steps : 1824
% 1.41/0.48 % ...of those cached : 1720
% 1.41/0.48 % Propositional unsat checks : 0
% 1.41/0.48 % Propositional check models : 0
% 1.41/0.48 % Propositional check unsatisfiable : 0
% 1.41/0.48 % Propositional clauses : 0
% 1.41/0.48 % Propositional clauses after purity: 0
% 1.41/0.48 % Propositional unsat core size : 0
% 1.41/0.48 % Propositional preprocessing time : 0.000
% 1.41/0.48 % Propositional encoding time : 0.000
% 1.41/0.48 % Propositional solver time : 0.000
% 1.41/0.48 % Success case prop preproc time : 0.000
% 1.41/0.48 % Success case prop encoding time : 0.000
% 1.41/0.48 % Success case prop solver time : 0.000
% 1.41/0.48 % Current number of processed clauses : 397
% 1.41/0.48 % Positive orientable unit clauses : 123
% 1.41/0.48 % Positive unorientable unit clauses: 3
% 1.41/0.48 % Negative unit clauses : 69
% 1.41/0.48 % Non-unit-clauses : 202
% 1.41/0.48 % Current number of unprocessed clauses: 2082
% 1.41/0.48 % ...number of literals in the above : 8252
% 1.41/0.48 % Current number of archived formulas : 0
% 1.41/0.48 % Current number of archived clauses : 21
% 1.41/0.48 % Clause-clause subsumption calls (NU) : 18274
% 1.41/0.48 % Rec. Clause-clause subsumption calls : 5429
% 1.41/0.48 % Non-unit clause-clause subsumptions : 154
% 1.41/0.48 % Unit Clause-clause subsumption calls : 3108
% 1.41/0.48 % Rewrite failures with RHS unbound : 76
% 1.41/0.48 % BW rewrite match attempts : 73
% 1.41/0.48 % BW rewrite match successes : 13
% 1.41/0.48 % Condensation attempts : 0
% 1.41/0.48 % Condensation successes : 0
% 1.41/0.48 % Termbank termtop insertions : 106274
% 1.41/0.48 % Search garbage collected termcells : 16890
% 1.41/0.48
% 1.41/0.48 % -------------------------------------------------
% 1.41/0.48 % User time : 0.132 s
% 1.41/0.48 % System time : 0.022 s
% 1.41/0.48 % Total time : 0.154 s
% 1.41/0.48 % Maximum resident set size: 7000 pages
% 1.41/0.48
% 1.41/0.48 % -------------------------------------------------
% 1.41/0.48 % User time : 0.454 s
% 1.41/0.48 % System time : 0.053 s
% 1.41/0.48 % Total time : 0.508 s
% 1.41/0.48 % Maximum resident set size: 5888 pages
% 1.41/0.48 % E exiting
%------------------------------------------------------------------------------