%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM781^4 : 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 : n002.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 08:17:05 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 26 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 39 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 183 ( 4 ~; 0 |; 3 &; 168 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 59 ( 54 ^; 5 !; 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_30,type,
power: $i > $i ).
thf(decl_43,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_112,type,
anec: $i > ( $i > $i > $o ) > $i > $o ).
thf(decl_113,type,
ect: $i > ( $i > $i > $o ) > $i ).
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_177,type,
pair1type: $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_205,type,
rat: $i ).
thf(decl_206,type,
rt_is: $i > $i > $o ).
thf(decl_216,type,
esk1_0: $i ).
thf(decl_217,type,
esk2_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YwYqjHRvZw/E---3.1_1232718.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.YwYqjHRvZw/E---3.1_1232718.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YwYqjHRvZw/E---3.1_1232718.p',def_n_is) ).
thf(def_ect,axiom,
( ect
= ( ^ [X1: $i,X147: $i > $i > $o] : ( d_Sep @ ( power @ X1 ) @ ( anec @ X1 @ X147 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YwYqjHRvZw/E---3.1_1232718.p',def_ect) ).
thf(def_rat,axiom,
( rat
= ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YwYqjHRvZw/E---3.1_1232718.p',def_rat) ).
thf(def_frac,axiom,
( frac
= ( pair1type @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.YwYqjHRvZw/E---3.1_1232718.p',def_frac) ).
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.YwYqjHRvZw/E---3.1_1232718.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YwYqjHRvZw/E---3.1_1232718.p',def_is_of) ).
thf(satz79,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X646: $i] : ( in @ X646 @ rat )
@ ^ [X647: $i] :
( ( rt_is @ X1 @ X647 )
=> ( rt_is @ X647 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YwYqjHRvZw/E---3.1_1232718.p',satz79) ).
thf(def_rt_is,axiom,
( rt_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YwYqjHRvZw/E---3.1_1232718.p',def_rt_is) ).
thf(c_0_10,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_11,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_12,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_10]) ).
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_11,c_0_12]) ).
thf(c_0_14,plain,
( ect
= ( ^ [Z0: $i,Z1: $i > $i > $o] : ( d_Sep @ ( power @ Z0 ) @ ( anec @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_ect]) ).
thf(c_0_15,axiom,
( rat
= ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_rat,def_frac]),c_0_13]),c_0_14]) ).
thf(c_0_16,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_17,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_18,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X646: $i] : ( in @ X646 @ rat )
@ ^ [X647: $i] :
( ( rt_is @ X1 @ X647 )
=> ( rt_is @ X647 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[satz79]) ).
thf(c_0_19,axiom,
( rt_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_rt_is,c_0_15]),c_0_10]) ).
thf(c_0_20,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,negated_conjecture,
~ ! [X658: $i] :
( ( in @ X658
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
=> ! [X657: $i] :
( ( in @ X657
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
=> ( ( X658 = X657 )
=> ( X657 = X658 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_18]),c_0_15]),c_0_19]),c_0_20]) ).
thf(c_0_22,negated_conjecture,
( ( in @ esk1_0
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
& ( in @ esk2_0
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
& ( esk1_0 = esk2_0 )
& ( esk2_0 != esk1_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
thf(c_0_23,negated_conjecture,
esk2_0 != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_24,negated_conjecture,
esk1_0 = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM781^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.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 12:58:07 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 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.YwYqjHRvZw/E---3.1_1232718.p
% 0.22/0.34 % Version: 3.5.1-ho
% 0.22/0.34 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.22/0.34 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.34 % Starting pre_casc_4 with 1200s (4) cores
% 0.22/0.34 % Starting full_lambda_6 with 300s (1) cores
% 0.22/0.34 % Starting sh10 with 300s (1) cores
% 0.22/0.34 % Starting post_as_ho9 with 300s (1) cores
% 0.22/0.34 % Starting post_as_ho8 with 300s (1) cores
% 0.22/0.34 % post_as_ho9 with pid 1232734 completed with status 0
% 0.22/0.34 % Result found by post_as_ho9
% 0.22/0.34 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.22/0.34 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.34 % Starting pre_casc_4 with 1200s (4) cores
% 0.22/0.34 % Starting full_lambda_6 with 300s (1) cores
% 0.22/0.34 % Starting sh10 with 300s (1) cores
% 0.22/0.34 % Starting post_as_ho9 with 300s (1) cores
% 0.22/0.34 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.22/0.34 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.22/0.34 % Search class: HGUSF-FFSS21-DHSMMSBN
% 0.22/0.34 % partial match(4): HGUNF-FFSS22-SHSSMSBN
% 0.22/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.34 % SubtermCWHack with pid 1232736 completed with status 0
% 0.22/0.34 % Result found by SubtermCWHack
% 0.22/0.34 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.22/0.34 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.34 % Starting pre_casc_4 with 1200s (4) cores
% 0.22/0.34 % Starting full_lambda_6 with 300s (1) cores
% 0.22/0.34 % Starting sh10 with 300s (1) cores
% 0.22/0.34 % Starting post_as_ho9 with 300s (1) cores
% 0.22/0.34 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.22/0.34 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.22/0.34 % Search class: HGUSF-FFSS21-DHSMMSBN
% 0.22/0.34 % partial match(4): HGUNF-FFSS22-SHSSMSBN
% 0.22/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.34 % Preprocessing time : 0.002 s
% 0.22/0.34
% 0.22/0.34 % Proof found!
% 0.22/0.34 % SZS status Theorem
% 0.22/0.34 % SZS output start CNFRefutation
% See solution above
% 0.22/0.34 % Parsed axioms : 674
% 0.22/0.34 % Removed by relevancy pruning/SinE : 654
% 0.22/0.34 % Initial clauses : 15
% 0.22/0.34 % Removed in clause preprocessing : 5
% 0.22/0.34 % Initial clauses in saturation : 10
% 0.22/0.34 % Processed clauses : 2
% 0.22/0.34 % ...of these trivial : 0
% 0.22/0.34 % ...subsumed : 0
% 0.22/0.34 % ...remaining for further processing : 1
% 0.22/0.34 % Other redundant clauses eliminated : 0
% 0.22/0.34 % Clauses deleted for lack of memory : 0
% 0.22/0.34 % Backward-subsumed : 0
% 0.22/0.34 % Backward-rewritten : 0
% 0.22/0.34 % Generated clauses : 0
% 0.22/0.34 % ...of the previous two non-redundant : 0
% 0.22/0.34 % ...aggressively subsumed : 0
% 0.22/0.34 % Contextual simplify-reflections : 0
% 0.22/0.34 % Paramodulations : 0
% 0.22/0.34 % Factorizations : 0
% 0.22/0.34 % NegExts : 0
% 0.22/0.34 % Equation resolutions : 0
% 0.22/0.34 % Disequality decompositions : 0
% 0.22/0.34 % Total rewrite steps : 1
% 0.22/0.34 % ...of those cached : 0
% 0.22/0.34 % Propositional unsat checks : 0
% 0.22/0.34 % Propositional check models : 0
% 0.22/0.34 % Propositional check unsatisfiable : 0
% 0.22/0.34 % Propositional clauses : 0
% 0.22/0.34 % Propositional clauses after purity: 0
% 0.22/0.34 % Propositional unsat core size : 0
% 0.22/0.34 % Propositional preprocessing time : 0.000
% 0.22/0.34 % Propositional encoding time : 0.000
% 0.22/0.34 % Propositional solver time : 0.000
% 0.22/0.34 % Success case prop preproc time : 0.000
% 0.22/0.34 % Success case prop encoding time : 0.000
% 0.22/0.34 % Success case prop solver time : 0.000
% 0.22/0.34 % Current number of processed clauses : 1
% 0.22/0.34 % Positive orientable unit clauses : 1
% 0.22/0.34 % Positive unorientable unit clauses: 0
% 0.22/0.34 % Negative unit clauses : 0
% 0.22/0.34 % Non-unit-clauses : 0
% 0.22/0.34 % Current number of unprocessed clauses: 8
% 0.22/0.34 % ...number of literals in the above : 17
% 0.22/0.34 % Current number of archived formulas : 0
% 0.22/0.34 % Current number of archived clauses : 0
% 0.22/0.34 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.34 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.34 % Non-unit clause-clause subsumptions : 0
% 0.22/0.34 % Unit Clause-clause subsumption calls : 0
% 0.22/0.34 % Rewrite failures with RHS unbound : 0
% 0.22/0.34 % BW rewrite match attempts : 0
% 0.22/0.34 % BW rewrite match successes : 0
% 0.22/0.34 % Condensation attempts : 0
% 0.22/0.34 % Condensation successes : 0
% 0.22/0.34 % Termbank termtop insertions : 14064
% 0.22/0.34 % Search garbage collected termcells : 6822
% 0.22/0.34
% 0.22/0.34 % -------------------------------------------------
% 0.22/0.34 % User time : 0.006 s
% 0.22/0.34 % System time : 0.007 s
% 0.22/0.34 % Total time : 0.013 s
% 0.22/0.34 % Maximum resident set size: 5732 pages
% 0.22/0.34
% 0.22/0.34 % -------------------------------------------------
% 0.22/0.34 % User time : 0.025 s
% 0.22/0.34 % System time : 0.015 s
% 0.22/0.34 % Total time : 0.040 s
% 0.22/0.34 % Maximum resident set size: 5888 pages
% 0.22/0.34 % E exiting
%------------------------------------------------------------------------------