%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM729^4 : 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 : n017.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 2.51s 0.76s
% Output : CNFRefutation 2.51s
% 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 : 309 ( 10 ~; 6 |; 3 &; 281 @)
% ( 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 : 16 ( 14 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_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_329,type,
esk131_0: $i ).
thf(decl_330,type,
esk132_0: $i ).
thf(decl_331,type,
esk133_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ntguZmdnnM/E---3.1_283612.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.ntguZmdnnM/E---3.1_283612.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ntguZmdnnM/E---3.1_283612.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.ntguZmdnnM/E---3.1_283612.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ntguZmdnnM/E---3.1_283612.p',def_n_is) ).
thf(satz40c,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X447: $i] : ( in @ X447 @ nat )
@ ^ [X448: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] : ( n_eq @ ( n_fr @ ( n_ts @ X1 @ X4 ) @ ( n_ts @ X448 @ X4 ) ) @ ( n_fr @ X1 @ X448 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ntguZmdnnM/E---3.1_283612.p',satz40c) ).
thf(satz40b,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X445: $i] : ( in @ X445 @ nat )
@ ^ [X446: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] : ( n_eq @ ( n_fr @ X1 @ X446 ) @ ( n_fr @ ( n_ts @ X1 @ X4 ) @ ( n_ts @ X446 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ntguZmdnnM/E---3.1_283612.p',satz40b) ).
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 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X447: $i] : ( in @ X447 @ nat )
@ ^ [X448: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] : ( n_eq @ ( n_fr @ ( n_ts @ X1 @ X4 ) @ ( n_ts @ X448 @ X4 ) ) @ ( n_fr @ X1 @ X448 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz40c]) ).
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,
~ ! [X1276: $i] :
( ( in @ X1276 @ nat )
=> ! [X1275: $i] :
( ( in @ X1275 @ nat )
=> ! [X1274: $i] :
( ( in @ X1274 @ nat )
=> ( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ X1276 @ X1274 ) @ ( n_ts @ X1275 @ X1274 ) ) ) @ ( den @ ( n_fr @ X1276 @ X1275 ) ) )
= ( n_ts @ ( num @ ( n_fr @ X1276 @ X1275 ) ) @ ( den @ ( n_fr @ ( n_ts @ X1276 @ X1274 ) @ ( n_ts @ X1275 @ X1274 ) ) ) ) ) ) ) ),
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,
! [X1273: $i] :
( ( in @ X1273 @ nat )
=> ! [X1272: $i] :
( ( in @ X1272 @ nat )
=> ! [X1271: $i] :
( ( in @ X1271 @ nat )
=> ( ( n_ts @ ( num @ ( n_fr @ X1273 @ X1272 ) ) @ ( den @ ( n_fr @ ( n_ts @ X1273 @ X1271 ) @ ( n_ts @ X1272 @ X1271 ) ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_ts @ X1273 @ X1271 ) @ ( n_ts @ X1272 @ X1271 ) ) ) @ ( den @ ( n_fr @ X1273 @ X1272 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz40b]),c_0_13]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
( ( in @ esk131_0 @ nat )
& ( in @ esk132_0 @ nat )
& ( in @ esk133_0 @ nat )
& ( ( n_ts @ ( num @ ( n_fr @ ( n_ts @ esk131_0 @ esk133_0 ) @ ( n_ts @ esk132_0 @ esk133_0 ) ) ) @ ( den @ ( n_fr @ esk131_0 @ esk132_0 ) ) )
!= ( n_ts @ ( num @ ( n_fr @ esk131_0 @ esk132_0 ) ) @ ( den @ ( n_fr @ ( n_ts @ esk131_0 @ esk133_0 ) @ ( n_ts @ esk132_0 @ esk133_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,
! [X2367: $i,X2368: $i,X2369: $i] :
( ~ ( in @ X2367 @ nat )
| ~ ( in @ X2368 @ nat )
| ~ ( in @ X2369 @ nat )
| ( ( n_ts @ ( num @ ( n_fr @ X2367 @ X2368 ) ) @ ( den @ ( n_fr @ ( n_ts @ X2367 @ X2369 ) @ ( n_ts @ X2368 @ X2369 ) ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_ts @ X2367 @ X2369 ) @ ( n_ts @ X2368 @ X2369 ) ) ) @ ( den @ ( n_fr @ X2367 @ X2368 ) ) ) ) ),
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 @ esk131_0 @ esk133_0 ) @ ( n_ts @ esk132_0 @ esk133_0 ) ) ) @ ( den @ ( n_fr @ esk131_0 @ esk132_0 ) ) )
!= ( n_ts @ ( num @ ( n_fr @ esk131_0 @ esk132_0 ) ) @ ( den @ ( n_fr @ ( n_ts @ esk131_0 @ esk133_0 ) @ ( n_ts @ esk132_0 @ esk133_0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( ( n_ts @ ( num @ ( n_fr @ X1 @ X4 ) ) @ ( den @ ( n_fr @ ( n_ts @ X1 @ X5 ) @ ( n_ts @ X4 @ X5 ) ) ) )
= ( n_ts @ ( num @ ( n_fr @ ( n_ts @ X1 @ X5 ) @ ( n_ts @ X4 @ X5 ) ) ) @ ( den @ ( n_fr @ X1 @ X4 ) ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
in @ esk133_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
in @ esk132_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
in @ esk131_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
% 0.00/0.02 % Problem : NUM729^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n017.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:41:22 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.20/0.29 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.ntguZmdnnM/E---3.1_283612.p
% 2.51/0.76 % Version: 3.5.1-ho
% 2.51/0.76 % Preprocessing class: HSLMSMSMLMLCHSA.
% 2.51/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.51/0.76 % Starting new_ho_10 with 1500s (5) cores
% 2.51/0.76 % Starting ho_unfolding_6 with 300s (1) cores
% 2.51/0.76 % Starting sh4l with 300s (1) cores
% 2.51/0.76 % Starting ehoh_best_nonlift_nonlambdatoforall with 300s (1) cores
% 2.51/0.76 % new_ho_10 with pid 283625 completed with status 0
% 2.51/0.76 % Result found by new_ho_10
% 2.51/0.76 % Preprocessing class: HSLMSMSMLMLCHSA.
% 2.51/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.51/0.76 % Starting new_ho_10 with 1500s (5) cores
% 2.51/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.51/0.76 % No SInE strategy applied
% 2.51/0.76 % Search class: HGHSM-FSLM32-MHSMSSBN
% 2.51/0.76 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 2.51/0.76 % Starting SubtermCWHack with 151s (1) cores
% 2.51/0.76 % Starting new_ho_10 with 901s (1) cores
% 2.51/0.76 % Starting ho_unfolding_6 with 151s (1) cores
% 2.51/0.76 % Starting sh4l with 151s (1) cores
% 2.51/0.76 % Starting ehoh_best_nonlift_nonlambdatoforall with 146s (1) cores
% 2.51/0.76 % new_ho_10 with pid 283633 completed with status 0
% 2.51/0.76 % Result found by new_ho_10
% 2.51/0.76 % Preprocessing class: HSLMSMSMLMLCHSA.
% 2.51/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.51/0.76 % Starting new_ho_10 with 1500s (5) cores
% 2.51/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.51/0.76 % No SInE strategy applied
% 2.51/0.76 % Search class: HGHSM-FSLM32-MHSMSSBN
% 2.51/0.76 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 2.51/0.76 % Starting SubtermCWHack with 151s (1) cores
% 2.51/0.76 % Starting new_ho_10 with 901s (1) cores
% 2.51/0.76 % Preprocessing time : 0.014 s
% 2.51/0.76 % Presaturation interreduction done
% 2.51/0.76
% 2.51/0.76 % Proof found!
% 2.51/0.76 % SZS status Theorem
% 2.51/0.76 % SZS output start CNFRefutation
% See solution above
% 2.51/0.76 % Parsed axioms : 536
% 2.51/0.76 % Removed by relevancy pruning/SinE : 0
% 2.51/0.76 % Initial clauses : 1746
% 2.51/0.76 % Removed in clause preprocessing : 1123
% 2.51/0.76 % Initial clauses in saturation : 623
% 2.51/0.76 % Processed clauses : 1496
% 2.51/0.76 % ...of these trivial : 13
% 2.51/0.76 % ...subsumed : 140
% 2.51/0.76 % ...remaining for further processing : 1343
% 2.51/0.76 % Other redundant clauses eliminated : 768
% 2.51/0.76 % Clauses deleted for lack of memory : 0
% 2.51/0.76 % Backward-subsumed : 0
% 2.51/0.76 % Backward-rewritten : 20
% 2.51/0.76 % Generated clauses : 6336
% 2.51/0.76 % ...of the previous two non-redundant : 5722
% 2.51/0.76 % ...aggressively subsumed : 0
% 2.51/0.76 % Contextual simplify-reflections : 10
% 2.51/0.76 % Paramodulations : 5596
% 2.51/0.76 % Factorizations : 2
% 2.51/0.76 % NegExts : 0
% 2.51/0.76 % Equation resolutions : 779
% 2.51/0.76 % Disequality decompositions : 0
% 2.51/0.76 % Total rewrite steps : 1086
% 2.51/0.76 % ...of those cached : 914
% 2.51/0.76 % Propositional unsat checks : 0
% 2.51/0.76 % Propositional check models : 0
% 2.51/0.76 % Propositional check unsatisfiable : 0
% 2.51/0.76 % Propositional clauses : 0
% 2.51/0.76 % Propositional clauses after purity: 0
% 2.51/0.76 % Propositional unsat core size : 0
% 2.51/0.76 % Propositional preprocessing time : 0.000
% 2.51/0.76 % Propositional encoding time : 0.000
% 2.51/0.76 % Propositional solver time : 0.000
% 2.51/0.76 % Success case prop preproc time : 0.000
% 2.51/0.76 % Success case prop encoding time : 0.000
% 2.51/0.76 % Success case prop solver time : 0.000
% 2.51/0.76 % Current number of processed clauses : 546
% 2.51/0.76 % Positive orientable unit clauses : 177
% 2.51/0.76 % Positive unorientable unit clauses: 12
% 2.51/0.76 % Negative unit clauses : 40
% 2.51/0.76 % Non-unit-clauses : 317
% 2.51/0.76 % Current number of unprocessed clauses: 5393
% 2.51/0.76 % ...number of literals in the above : 24962
% 2.51/0.76 % Current number of archived formulas : 0
% 2.51/0.76 % Current number of archived clauses : 597
% 2.51/0.76 % Clause-clause subsumption calls (NU) : 309849
% 2.51/0.76 % Rec. Clause-clause subsumption calls : 20855
% 2.51/0.76 % Non-unit clause-clause subsumptions : 100
% 2.51/0.76 % Unit Clause-clause subsumption calls : 10751
% 2.51/0.76 % Rewrite failures with RHS unbound : 0
% 2.51/0.76 % BW rewrite match attempts : 129
% 2.51/0.76 % BW rewrite match successes : 27
% 2.51/0.76 % Condensation attempts : 1496
% 2.51/0.76 % Condensation successes : 23
% 2.51/0.76 % Termbank termtop insertions : 385974
% 2.51/0.76 % Search garbage collected termcells : 73093
% 2.51/0.76
% 2.51/0.76 % -------------------------------------------------
% 2.51/0.76 % User time : 0.391 s
% 2.51/0.76 % System time : 0.032 s
% 2.51/0.76 % Total time : 0.423 s
% 2.51/0.76 % Maximum resident set size: 13768 pages
% 2.51/0.76
% 2.51/0.76 % -------------------------------------------------
% 2.51/0.76 % User time : 1.348 s
% 2.51/0.76 % System time : 0.126 s
% 2.51/0.76 % Total time : 1.474 s
% 2.51/0.76 % Maximum resident set size: 5632 pages
% 2.51/0.76 % E exiting
%------------------------------------------------------------------------------