%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM782^4 : 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 : n012.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 0.07s 0.18s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 45 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 235 ( 4 ~; 0 |; 5 &; 214 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 68 ( 62 ^; 6 !; 0 ?; 68 :)
% 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(decl_218,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.KnzCJvhHTM/E---3.1_66272.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.KnzCJvhHTM/E---3.1_66272.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KnzCJvhHTM/E---3.1_66272.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.KnzCJvhHTM/E---3.1_66272.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.KnzCJvhHTM/E---3.1_66272.p',def_rat) ).
thf(def_frac,axiom,
( frac
= ( pair1type @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.KnzCJvhHTM/E---3.1_66272.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.KnzCJvhHTM/E---3.1_66272.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KnzCJvhHTM/E---3.1_66272.p',def_is_of) ).
thf(satz80,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X648: $i] : ( in @ X648 @ rat )
@ ^ [X649: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ rat )
@ ^ [X4: $i] :
( ( rt_is @ X1 @ X649 )
=> ( ( rt_is @ X649 @ X4 )
=> ( rt_is @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KnzCJvhHTM/E---3.1_66272.p',satz80) ).
thf(def_rt_is,axiom,
( rt_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KnzCJvhHTM/E---3.1_66272.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
@ ^ [X648: $i] : ( in @ X648 @ rat )
@ ^ [X649: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ rat )
@ ^ [X4: $i] :
( ( rt_is @ X1 @ X649 )
=> ( ( rt_is @ X649 @ X4 )
=> ( rt_is @ X1 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz80]) ).
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_10]),c_0_15]) ).
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,
~ ! [X661: $i] :
( ( in @ X661
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
=> ! [X660: $i] :
( ( in @ X660
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
=> ! [X659: $i] :
( ( in @ X659
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
=> ( ( X661 = X660 )
=> ( ( X660 = X659 )
=> ( X661 = X659 ) ) ) ) ) ),
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_19]),c_0_15]),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 ) ) ) ) ) )
& ( in @ esk3_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 = esk3_0 )
& ( esk1_0 != esk3_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 = esk3_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,
esk1_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,negated_conjecture,
esk3_0 = esk1_0,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM782^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 12:55:03 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.12 Running higher-order theorem proving
% 0.07/0.16 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.KnzCJvhHTM/E---3.1_66272.p
% 0.07/0.18 % Version: 3.5.1-ho
% 0.07/0.18 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.07/0.18 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.18 % Starting pre_casc_4 with 1200s (4) cores
% 0.07/0.18 % Starting full_lambda_6 with 300s (1) cores
% 0.07/0.18 % Starting sh10 with 300s (1) cores
% 0.07/0.18 % Starting post_as_ho9 with 300s (1) cores
% 0.07/0.18 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.18 % post_as_ho9 with pid 66288 completed with status 0
% 0.07/0.18 % Result found by post_as_ho9
% 0.07/0.18 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.07/0.18 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.18 % Starting pre_casc_4 with 1200s (4) cores
% 0.07/0.18 % Starting full_lambda_6 with 300s (1) cores
% 0.07/0.18 % Starting sh10 with 300s (1) cores
% 0.07/0.18 % Starting post_as_ho9 with 300s (1) cores
% 0.07/0.18 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.07/0.18 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.07/0.18 % Search class: HGUSF-FFSM21-DHSMMSBN
% 0.07/0.18 % partial match(5): HGUNF-FFSS22-SHSSMSBN
% 0.07/0.18 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.18 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.18 % SubtermCWHack with pid 66290 completed with status 0
% 0.07/0.18 % Result found by SubtermCWHack
% 0.07/0.18 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.07/0.18 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.18 % Starting pre_casc_4 with 1200s (4) cores
% 0.07/0.18 % Starting full_lambda_6 with 300s (1) cores
% 0.07/0.18 % Starting sh10 with 300s (1) cores
% 0.07/0.18 % Starting post_as_ho9 with 300s (1) cores
% 0.07/0.18 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.07/0.18 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.07/0.18 % Search class: HGUSF-FFSM21-DHSMMSBN
% 0.07/0.18 % partial match(5): HGUNF-FFSS22-SHSSMSBN
% 0.07/0.18 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.18 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.18 % Preprocessing time : 0.001 s
% 0.07/0.18
% 0.07/0.18 % Proof found!
% 0.07/0.18 % SZS status Theorem
% 0.07/0.18 % SZS output start CNFRefutation
% See solution above
% 0.07/0.19 % Parsed axioms : 675
% 0.07/0.19 % Removed by relevancy pruning/SinE : 654
% 0.07/0.19 % Initial clauses : 18
% 0.07/0.19 % Removed in clause preprocessing : 6
% 0.07/0.19 % Initial clauses in saturation : 12
% 0.07/0.19 % Processed clauses : 3
% 0.07/0.19 % ...of these trivial : 0
% 0.07/0.19 % ...subsumed : 0
% 0.07/0.19 % ...remaining for further processing : 2
% 0.07/0.19 % Other redundant clauses eliminated : 0
% 0.07/0.19 % Clauses deleted for lack of memory : 0
% 0.07/0.19 % Backward-subsumed : 0
% 0.07/0.19 % Backward-rewritten : 0
% 0.07/0.19 % Generated clauses : 0
% 0.07/0.19 % ...of the previous two non-redundant : 0
% 0.07/0.19 % ...aggressively subsumed : 0
% 0.07/0.19 % Contextual simplify-reflections : 0
% 0.07/0.19 % Paramodulations : 0
% 0.07/0.19 % Factorizations : 0
% 0.07/0.19 % NegExts : 0
% 0.07/0.19 % Equation resolutions : 0
% 0.07/0.19 % Disequality decompositions : 0
% 0.07/0.19 % Total rewrite steps : 2
% 0.07/0.19 % ...of those cached : 0
% 0.07/0.19 % Propositional unsat checks : 0
% 0.07/0.19 % Propositional check models : 0
% 0.07/0.19 % Propositional check unsatisfiable : 0
% 0.07/0.19 % Propositional clauses : 0
% 0.07/0.19 % Propositional clauses after purity: 0
% 0.07/0.19 % Propositional unsat core size : 0
% 0.07/0.19 % Propositional preprocessing time : 0.000
% 0.07/0.19 % Propositional encoding time : 0.000
% 0.07/0.19 % Propositional solver time : 0.000
% 0.07/0.19 % Success case prop preproc time : 0.000
% 0.07/0.19 % Success case prop encoding time : 0.000
% 0.07/0.19 % Success case prop solver time : 0.000
% 0.07/0.19 % Current number of processed clauses : 2
% 0.07/0.19 % Positive orientable unit clauses : 2
% 0.07/0.19 % Positive unorientable unit clauses: 0
% 0.07/0.19 % Negative unit clauses : 0
% 0.07/0.19 % Non-unit-clauses : 0
% 0.07/0.19 % Current number of unprocessed clauses: 9
% 0.07/0.19 % ...number of literals in the above : 18
% 0.07/0.19 % Current number of archived formulas : 0
% 0.07/0.19 % Current number of archived clauses : 0
% 0.07/0.19 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.19 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.19 % Non-unit clause-clause subsumptions : 0
% 0.07/0.19 % Unit Clause-clause subsumption calls : 0
% 0.07/0.19 % Rewrite failures with RHS unbound : 0
% 0.07/0.19 % BW rewrite match attempts : 0
% 0.07/0.19 % BW rewrite match successes : 0
% 0.07/0.19 % Condensation attempts : 0
% 0.07/0.19 % Condensation successes : 0
% 0.07/0.19 % Termbank termtop insertions : 14646
% 0.07/0.19 % Search garbage collected termcells : 7009
% 0.07/0.19
% 0.07/0.19 % -------------------------------------------------
% 0.07/0.19 % User time : 0.005 s
% 0.07/0.19 % System time : 0.003 s
% 0.07/0.19 % Total time : 0.008 s
% 0.07/0.19 % Maximum resident set size: 5480 pages
% 0.07/0.19
% 0.07/0.19 % -------------------------------------------------
% 0.07/0.19 % User time : 0.015 s
% 0.07/0.19 % System time : 0.005 s
% 0.07/0.19 % Total time : 0.020 s
% 0.07/0.19 % Maximum resident set size: 6144 pages
% 0.07/0.19 % E exiting
%------------------------------------------------------------------------------