%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM726^4 : 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 : n019.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 08:16:56 AM UTC 2026
% Result : Theorem 1.45s 0.71s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 24 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 130 ( 4 ~; 0 |; 3 &; 115 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 39 ( 34 ^; 5 !; 0 ?; 39 :)
% 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_125,type,
n_is: $i > $i > $o ).
thf(decl_163,type,
n_ts: $i > $i > $i ).
thf(decl_190,type,
frac: $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.Qf4xbNJUEb/E---3.1_700973.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.Qf4xbNJUEb/E---3.1_700973.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qf4xbNJUEb/E---3.1_700973.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.Qf4xbNJUEb/E---3.1_700973.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qf4xbNJUEb/E---3.1_700973.p',def_n_is) ).
thf(satz38,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X437: $i] : ( in @ X437 @ frac )
@ ^ [X438: $i] :
( ( n_eq @ X1 @ X438 )
=> ( n_eq @ X438 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qf4xbNJUEb/E---3.1_700973.p',satz38) ).
thf(c_0_6,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_7,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_8,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_9,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_10,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_6]) ).
thf(c_0_11,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X437: $i] : ( in @ X437 @ frac )
@ ^ [X438: $i] :
( ( n_eq @ X1 @ X438 )
=> ( n_eq @ X438 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[satz38]) ).
thf(c_0_12,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,c_0_8]) ).
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_9,c_0_10]) ).
thf(c_0_14,negated_conjecture,
~ ! [X1253: $i] :
( ( in @ X1253 @ frac )
=> ! [X1252: $i] :
( ( in @ X1252 @ frac )
=> ( ( ( n_ts @ ( num @ X1253 ) @ ( den @ X1252 ) )
= ( n_ts @ ( num @ X1252 ) @ ( den @ X1253 ) ) )
=> ( ( n_ts @ ( num @ X1252 ) @ ( den @ X1253 ) )
= ( n_ts @ ( num @ X1253 ) @ ( den @ X1252 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_11]),c_0_12]),c_0_13]) ).
thf(c_0_15,negated_conjecture,
( ( in @ esk131_0 @ frac )
& ( in @ esk132_0 @ frac )
& ( ( n_ts @ ( num @ esk131_0 ) @ ( den @ esk132_0 ) )
= ( n_ts @ ( num @ esk132_0 ) @ ( den @ esk131_0 ) ) )
& ( ( n_ts @ ( num @ esk132_0 ) @ ( den @ esk131_0 ) )
!= ( n_ts @ ( num @ esk131_0 ) @ ( den @ esk132_0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_16,negated_conjecture,
( ( n_ts @ ( num @ esk131_0 ) @ ( den @ esk132_0 ) )
= ( n_ts @ ( num @ esk132_0 ) @ ( den @ esk131_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_17,negated_conjecture,
( ( n_ts @ ( num @ esk132_0 ) @ ( den @ esk131_0 ) )
!= ( n_ts @ ( num @ esk131_0 ) @ ( den @ esk132_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_16,c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM726^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 % Computer : n019.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Sep 29 12:45:17 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running higher-order theorem proving
% 0.26/0.38 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.Qf4xbNJUEb/E---3.1_700973.p
% 1.45/0.71 % Version: 3.5.1-ho
% 1.45/0.71 % Preprocessing class: HSLMSMSMLMLCHSA.
% 1.45/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.71 % Starting new_ho_10 with 1500s (5) cores
% 1.45/0.71 % Starting ho_unfolding_6 with 300s (1) cores
% 1.45/0.71 % Starting sh4l with 300s (1) cores
% 1.45/0.71 % Starting ehoh_best_nonlift_nonlambdatoforall with 300s (1) cores
% 1.45/0.71 % new_ho_10 with pid 700986 completed with status 0
% 1.45/0.71 % Result found by new_ho_10
% 1.45/0.71 % Preprocessing class: HSLMSMSMLMLCHSA.
% 1.45/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.71 % Starting new_ho_10 with 1500s (5) cores
% 1.45/0.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.45/0.71 % No SInE strategy applied
% 1.45/0.71 % Search class: HGHSM-FSLM32-MHSMSSBN
% 1.45/0.71 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.45/0.71 % Starting SubtermCWHack with 151s (1) cores
% 1.45/0.71 % Starting new_ho_10 with 901s (1) cores
% 1.45/0.71 % Starting ho_unfolding_6 with 151s (1) cores
% 1.45/0.71 % Starting sh4l with 151s (1) cores
% 1.45/0.71 % Starting ehoh_best_nonlift_nonlambdatoforall with 146s (1) cores
% 1.45/0.71 % ho_unfolding_6 with pid 700995 completed with status 0
% 1.45/0.71 % Result found by ho_unfolding_6
% 1.45/0.71 % Preprocessing class: HSLMSMSMLMLCHSA.
% 1.45/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.45/0.71 % Starting new_ho_10 with 1500s (5) cores
% 1.45/0.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.45/0.71 % No SInE strategy applied
% 1.45/0.71 % Search class: HGHSM-FSLM32-MHSMSSBN
% 1.45/0.71 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.45/0.71 % Starting SubtermCWHack with 151s (1) cores
% 1.45/0.71 % Starting new_ho_10 with 901s (1) cores
% 1.45/0.71 % Starting ho_unfolding_6 with 151s (1) cores
% 1.45/0.71 % Preprocessing time : 0.021 s
% 1.45/0.71
% 1.45/0.71 % Proof found!
% 1.45/0.71 % SZS status Theorem
% 1.45/0.71 % SZS output start CNFRefutation
% See solution above
% 1.45/0.71 % Parsed axioms : 531
% 1.45/0.71 % Removed by relevancy pruning/SinE : 0
% 1.45/0.71 % Initial clauses : 1741
% 1.45/0.71 % Removed in clause preprocessing : 1122
% 1.45/0.71 % Initial clauses in saturation : 619
% 1.45/0.71 % Processed clauses : 4
% 1.45/0.71 % ...of these trivial : 0
% 1.45/0.71 % ...subsumed : 0
% 1.45/0.71 % ...remaining for further processing : 3
% 1.45/0.71 % Other redundant clauses eliminated : 0
% 1.45/0.71 % Clauses deleted for lack of memory : 0
% 1.45/0.71 % Backward-subsumed : 0
% 1.45/0.71 % Backward-rewritten : 0
% 1.45/0.71 % Generated clauses : 0
% 1.45/0.71 % ...of the previous two non-redundant : 0
% 1.45/0.71 % ...aggressively subsumed : 0
% 1.45/0.71 % Contextual simplify-reflections : 0
% 1.45/0.71 % Paramodulations : 0
% 1.45/0.71 % Factorizations : 0
% 1.45/0.71 % NegExts : 0
% 1.45/0.71 % Equation resolutions : 0
% 1.45/0.71 % Disequality decompositions : 0
% 1.45/0.71 % Total rewrite steps : 0
% 1.45/0.71 % ...of those cached : 0
% 1.45/0.71 % Propositional unsat checks : 0
% 1.45/0.71 % Propositional check models : 0
% 1.45/0.71 % Propositional check unsatisfiable : 0
% 1.45/0.71 % Propositional clauses : 0
% 1.45/0.71 % Propositional clauses after purity: 0
% 1.45/0.71 % Propositional unsat core size : 0
% 1.45/0.71 % Propositional preprocessing time : 0.000
% 1.45/0.71 % Propositional encoding time : 0.000
% 1.45/0.71 % Propositional solver time : 0.000
% 1.45/0.71 % Success case prop preproc time : 0.000
% 1.45/0.71 % Success case prop encoding time : 0.000
% 1.45/0.71 % Success case prop solver time : 0.000
% 1.45/0.71 % Current number of processed clauses : 3
% 1.45/0.71 % Positive orientable unit clauses : 2
% 1.45/0.71 % Positive unorientable unit clauses: 0
% 1.45/0.71 % Negative unit clauses : 1
% 1.45/0.71 % Non-unit-clauses : 0
% 1.45/0.71 % Current number of unprocessed clauses: 615
% 1.45/0.71 % ...number of literals in the above : 2696
% 1.45/0.71 % Current number of archived formulas : 0
% 1.45/0.71 % Current number of archived clauses : 0
% 1.45/0.71 % Clause-clause subsumption calls (NU) : 0
% 1.45/0.71 % Rec. Clause-clause subsumption calls : 0
% 1.45/0.71 % Non-unit clause-clause subsumptions : 0
% 1.45/0.71 % Unit Clause-clause subsumption calls : 0
% 1.45/0.71 % Rewrite failures with RHS unbound : 0
% 1.45/0.71 % BW rewrite match attempts : 0
% 1.45/0.71 % BW rewrite match successes : 0
% 1.45/0.71 % Condensation attempts : 4
% 1.45/0.71 % Condensation successes : 0
% 1.45/0.71 % Termbank termtop insertions : 197383
% 1.45/0.71 % Search garbage collected termcells : 72388
% 1.45/0.71
% 1.45/0.71 % -------------------------------------------------
% 1.45/0.71 % User time : 0.243 s
% 1.45/0.71 % System time : 0.030 s
% 1.45/0.71 % Total time : 0.273 s
% 1.45/0.71 % Maximum resident set size: 13752 pages
% 1.45/0.71
% 1.45/0.71 % -------------------------------------------------
% 1.45/0.71 % User time : 0.318 s
% 1.45/0.71 % System time : 0.090 s
% 1.45/0.71 % Total time : 0.408 s
% 1.45/0.71 % Maximum resident set size: 5632 pages
% 1.45/0.71 % E exiting
%------------------------------------------------------------------------------