%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM728^4 : 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 : n005.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 08:16:57 AM UTC 2026
% Result : Theorem 1.06s 0.60s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 66 ( 24 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 278 ( 8 ~; 4 |; 2 &; 257 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 49 ( 38 ^; 11 !; 0 ?; 49 :)
% 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_163,type,
n_ts: $i > $i > $i ).
thf(decl_190,type,
frac: $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_329,type,
esk131_0: $i ).
thf(decl_330,type,
esk132_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9qEokoc9Fo/E---3.1_1615213.p',def_e_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.9qEokoc9Fo/E---3.1_1615213.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9qEokoc9Fo/E---3.1_1615213.p',def_is_of) ).
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.9qEokoc9Fo/E---3.1_1615213.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9qEokoc9Fo/E---3.1_1615213.p',def_n_is) ).
thf(satz40a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X443: $i] : ( in @ X443 @ nat )
@ ^ [X444: $i] : ( n_eq @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X444 ) @ ( n_ts @ ( den @ X1 ) @ X444 ) ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9qEokoc9Fo/E---3.1_1615213.p',satz40a) ).
thf(satz40,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X441: $i] : ( in @ X441 @ nat )
@ ^ [X442: $i] : ( n_eq @ X1 @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X442 ) @ ( n_ts @ ( den @ X1 ) @ X442 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9qEokoc9Fo/E---3.1_1615213.p',satz40) ).
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,
( 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_9,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_10,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_11,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_7]) ).
thf(c_0_12,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X443: $i] : ( in @ X443 @ nat )
@ ^ [X444: $i] : ( n_eq @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X444 ) @ ( n_ts @ ( den @ X1 ) @ X444 ) ) @ X1 ) ) ),
inference(assume_negation,[status(cth)],[satz40a]) ).
thf(c_0_13,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_14,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_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
~ ! [X1266: $i] :
( ( in @ X1266 @ frac )
=> ! [X1265: $i] :
( ( in @ X1265 @ nat )
=> ( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X1266 ) @ X1265 ) @ ( n_ts @ ( den @ X1266 ) @ X1265 ) ) ) @ ( den @ X1266 ) )
= ( n_ts @ ( num @ X1266 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X1266 ) @ X1265 ) @ ( n_ts @ ( den @ X1266 ) @ X1265 ) ) ) ) ) ) ),
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,
! [X1264: $i] :
( ( in @ X1264 @ frac )
=> ! [X1263: $i] :
( ( in @ X1263 @ nat )
=> ( ( n_ts @ ( num @ X1264 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X1264 ) @ X1263 ) @ ( n_ts @ ( den @ X1264 ) @ X1263 ) ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X1264 ) @ X1263 ) @ ( n_ts @ ( den @ X1264 ) @ X1263 ) ) ) @ ( den @ X1264 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz40]),c_0_13]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
( ( in @ esk131_0 @ frac )
& ( in @ esk132_0 @ nat )
& ( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ esk131_0 ) @ esk132_0 ) @ ( n_ts @ ( den @ esk131_0 ) @ esk132_0 ) ) ) @ ( den @ esk131_0 ) )
!= ( n_ts @ ( num @ esk131_0 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ esk131_0 ) @ esk132_0 ) @ ( n_ts @ ( den @ esk131_0 ) @ esk132_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,
! [X2353: $i,X2354: $i] :
( ~ ( in @ X2353 @ frac )
| ~ ( in @ X2354 @ nat )
| ( ( n_ts @ ( num @ X2353 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X2353 ) @ X2354 ) @ ( n_ts @ ( den @ X2353 ) @ X2354 ) ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X2353 ) @ X2354 ) @ ( n_ts @ ( den @ X2353 ) @ X2354 ) ) ) @ ( den @ X2353 ) ) ) ),
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_ts @ ( num @ esk131_0 ) @ esk132_0 ) @ ( n_ts @ ( den @ esk131_0 ) @ esk132_0 ) ) ) @ ( den @ esk131_0 ) )
!= ( n_ts @ ( num @ esk131_0 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ esk131_0 ) @ esk132_0 ) @ ( n_ts @ ( den @ esk131_0 ) @ esk132_0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
! [X1: $i,X4: $i] :
( ( ( n_ts @ ( num @ X1 ) @ ( den @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X4 ) @ ( n_ts @ ( den @ X1 ) @ X4 ) ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_ts @ ( num @ X1 ) @ X4 ) @ ( n_ts @ ( den @ X1 ) @ X4 ) ) ) @ ( den @ X1 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
in @ esk132_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
in @ esk131_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(cn,[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])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM728^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:45:31 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.21/0.28 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.9qEokoc9Fo/E---3.1_1615213.p
% 1.06/0.60 % Version: 3.5.1-ho
% 1.06/0.60 % Preprocessing class: HSLMSMSMLMLCHSA.
% 1.06/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.60 % Starting new_ho_10 with 1500s (5) cores
% 1.06/0.60 % Starting ho_unfolding_6 with 300s (1) cores
% 1.06/0.60 % Starting sh4l with 300s (1) cores
% 1.06/0.60 % Starting ehoh_best_nonlift_nonlambdatoforall with 300s (1) cores
% 1.06/0.60 % new_ho_10 with pid 1615226 completed with status 0
% 1.06/0.60 % Result found by new_ho_10
% 1.06/0.60 % Preprocessing class: HSLMSMSMLMLCHSA.
% 1.06/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.60 % Starting new_ho_10 with 1500s (5) cores
% 1.06/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.06/0.60 % No SInE strategy applied
% 1.06/0.60 % Search class: HGHSM-FSLM32-MHSMSSBN
% 1.06/0.60 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.06/0.60 % Starting SubtermCWHack with 151s (1) cores
% 1.06/0.60 % Starting new_ho_10 with 901s (1) cores
% 1.06/0.60 % Starting ho_unfolding_6 with 151s (1) cores
% 1.06/0.60 % Starting sh4l with 151s (1) cores
% 1.06/0.60 % Starting ehoh_best_nonlift_nonlambdatoforall with 146s (1) cores
% 1.06/0.60 % ho_unfolding_6 with pid 1615235 completed with status 0
% 1.06/0.60 % Result found by ho_unfolding_6
% 1.06/0.60 % Preprocessing class: HSLMSMSMLMLCHSA.
% 1.06/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.60 % Starting new_ho_10 with 1500s (5) cores
% 1.06/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.06/0.60 % No SInE strategy applied
% 1.06/0.60 % Search class: HGHSM-FSLM32-MHSMSSBN
% 1.06/0.60 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.06/0.60 % Starting SubtermCWHack with 151s (1) cores
% 1.06/0.60 % Starting new_ho_10 with 901s (1) cores
% 1.06/0.60 % Starting ho_unfolding_6 with 151s (1) cores
% 1.06/0.60 % Preprocessing time : 0.016 s
% 1.06/0.60
% 1.06/0.60 % Proof found!
% 1.06/0.60 % SZS status Theorem
% 1.06/0.60 % SZS output start CNFRefutation
% See solution above
% 1.06/0.60 % Parsed axioms : 534
% 1.06/0.60 % Removed by relevancy pruning/SinE : 0
% 1.06/0.60 % Initial clauses : 1743
% 1.06/0.60 % Removed in clause preprocessing : 1123
% 1.06/0.60 % Initial clauses in saturation : 620
% 1.06/0.60 % Processed clauses : 400
% 1.06/0.60 % ...of these trivial : 4
% 1.06/0.60 % ...subsumed : 21
% 1.06/0.60 % ...remaining for further processing : 375
% 1.06/0.60 % Other redundant clauses eliminated : 201
% 1.06/0.60 % Clauses deleted for lack of memory : 0
% 1.06/0.60 % Backward-subsumed : 0
% 1.06/0.60 % Backward-rewritten : 0
% 1.06/0.60 % Generated clauses : 4441
% 1.06/0.60 % ...of the previous two non-redundant : 4252
% 1.06/0.60 % ...aggressively subsumed : 0
% 1.06/0.60 % Contextual simplify-reflections : 0
% 1.06/0.60 % Paramodulations : 3998
% 1.06/0.60 % Factorizations : 18
% 1.06/0.60 % NegExts : 0
% 1.06/0.60 % Equation resolutions : 203
% 1.06/0.60 % Disequality decompositions : 0
% 1.06/0.60 % Total rewrite steps : 252
% 1.06/0.60 % ...of those cached : 156
% 1.06/0.60 % Propositional unsat checks : 0
% 1.06/0.60 % Propositional check models : 0
% 1.06/0.60 % Propositional check unsatisfiable : 0
% 1.06/0.60 % Propositional clauses : 0
% 1.06/0.60 % Propositional clauses after purity: 0
% 1.06/0.60 % Propositional unsat core size : 0
% 1.06/0.60 % Propositional preprocessing time : 0.000
% 1.06/0.60 % Propositional encoding time : 0.000
% 1.06/0.60 % Propositional solver time : 0.000
% 1.06/0.60 % Success case prop preproc time : 0.000
% 1.06/0.60 % Success case prop encoding time : 0.000
% 1.06/0.60 % Success case prop solver time : 0.000
% 1.06/0.60 % Current number of processed clauses : 311
% 1.06/0.60 % Positive orientable unit clauses : 90
% 1.06/0.60 % Positive unorientable unit clauses: 9
% 1.06/0.60 % Negative unit clauses : 3
% 1.06/0.60 % Non-unit-clauses : 209
% 1.06/0.60 % Current number of unprocessed clauses: 4457
% 1.06/0.60 % ...number of literals in the above : 17696
% 1.06/0.60 % Current number of archived formulas : 0
% 1.06/0.60 % Current number of archived clauses : 0
% 1.06/0.60 % Clause-clause subsumption calls (NU) : 28895
% 1.06/0.60 % Rec. Clause-clause subsumption calls : 5130
% 1.06/0.60 % Non-unit clause-clause subsumptions : 21
% 1.06/0.60 % Unit Clause-clause subsumption calls : 1587
% 1.06/0.60 % Rewrite failures with RHS unbound : 0
% 1.06/0.60 % BW rewrite match attempts : 23
% 1.06/0.60 % BW rewrite match successes : 6
% 1.06/0.60 % Condensation attempts : 400
% 1.06/0.60 % Condensation successes : 0
% 1.06/0.60 % Termbank termtop insertions : 374683
% 1.06/0.60 % Search garbage collected termcells : 72769
% 1.06/0.60
% 1.06/0.60 % -------------------------------------------------
% 1.06/0.60 % User time : 0.246 s
% 1.06/0.60 % System time : 0.031 s
% 1.06/0.60 % Total time : 0.277 s
% 1.06/0.60 % Maximum resident set size: 13760 pages
% 1.06/0.60
% 1.06/0.60 % -------------------------------------------------
% 1.06/0.60 % User time : 0.655 s
% 1.06/0.60 % System time : 0.119 s
% 1.06/0.60 % Total time : 0.774 s
% 1.06/0.60 % Maximum resident set size: 5632 pages
% 1.06/0.60 % E exiting
%------------------------------------------------------------------------------