%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM752^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:17:01 AM UTC 2026
% Result : Theorem 0.22s 0.37s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 33 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 360 ( 16 ~; 12 |; 4 &; 311 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 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 : 64 ( 46 ^; 18 !; 0 ?; 64 :)
% 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_199,type,
n_pf: $i > $i > $i ).
thf(decl_200,type,
esk1_0: $i ).
thf(decl_201,type,
esk2_0: $i ).
thf(decl_202,type,
esk3_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.O3LbdsHMvb/E---3.1_710210.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/sandbox2/tmp/tmp.O3LbdsHMvb/E---3.1_710210.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.O3LbdsHMvb/E---3.1_710210.p',def_n_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/sandbox2/tmp/tmp.O3LbdsHMvb/E---3.1_710210.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.O3LbdsHMvb/E---3.1_710210.p',def_is_of) ).
thf(satz62e,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X530: $i] : ( in @ X530 @ frac )
@ ^ [X531: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( n_eq @ X1 @ X531 )
=> ( n_eq @ ( n_pf @ X4 @ X1 ) @ ( n_pf @ X4 @ X531 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.O3LbdsHMvb/E---3.1_710210.p',satz62e) ).
thf(satz56,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X508: $i] : ( in @ X508 @ frac )
@ ^ [X509: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( n_eq @ X1 @ X509 )
=> ( ( n_eq @ X4 @ X13 )
=> ( n_eq @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X509 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.O3LbdsHMvb/E---3.1_710210.p',satz56) ).
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,
( 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_9,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_7]) ).
thf(c_0_10,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_11,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_12,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X530: $i] : ( in @ X530 @ frac )
@ ^ [X531: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( n_eq @ X1 @ X531 )
=> ( n_eq @ ( n_pf @ X4 @ X1 ) @ ( n_pf @ X4 @ X531 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz62e]) ).
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_8,c_0_9]) ).
thf(c_0_14,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
~ ! [X574: $i] :
( ( in @ X574 @ frac )
=> ! [X573: $i] :
( ( in @ X573 @ frac )
=> ! [X572: $i] :
( ( in @ X572 @ frac )
=> ( ( ( n_ts @ ( num @ X574 ) @ ( den @ X573 ) )
= ( n_ts @ ( num @ X573 ) @ ( den @ X574 ) ) )
=> ( ( n_ts @ ( num @ ( n_pf @ X572 @ X574 ) ) @ ( den @ ( n_pf @ X572 @ X573 ) ) )
= ( n_ts @ ( num @ ( n_pf @ X572 @ X573 ) ) @ ( den @ ( n_pf @ X572 @ X574 ) ) ) ) ) ) ) ),
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,
! [X584: $i] :
( ( in @ X584 @ frac )
=> ! [X583: $i] :
( ( in @ X583 @ frac )
=> ! [X582: $i] :
( ( in @ X582 @ frac )
=> ! [X581: $i] :
( ( in @ X581 @ frac )
=> ( ( ( n_ts @ ( num @ X584 ) @ ( den @ X583 ) )
= ( n_ts @ ( num @ X583 ) @ ( den @ X584 ) ) )
=> ( ( ( n_ts @ ( num @ X582 ) @ ( den @ X581 ) )
= ( n_ts @ ( num @ X581 ) @ ( den @ X582 ) ) )
=> ( ( n_ts @ ( num @ ( n_pf @ X584 @ X582 ) ) @ ( den @ ( n_pf @ X583 @ X581 ) ) )
= ( n_ts @ ( num @ ( n_pf @ X583 @ X581 ) ) @ ( den @ ( n_pf @ X584 @ X582 ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz56]),c_0_13]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
( ( in @ esk1_0 @ frac )
& ( in @ esk2_0 @ frac )
& ( in @ esk3_0 @ frac )
& ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
= ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) )
& ( ( n_ts @ ( num @ ( n_pf @ esk3_0 @ esk1_0 ) ) @ ( den @ ( n_pf @ esk3_0 @ esk2_0 ) ) )
!= ( n_ts @ ( num @ ( n_pf @ esk3_0 @ esk2_0 ) ) @ ( den @ ( n_pf @ esk3_0 @ esk1_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,
! [X845: $i,X846: $i,X847: $i,X848: $i] :
( ~ ( in @ X845 @ frac )
| ~ ( in @ X846 @ frac )
| ~ ( in @ X847 @ frac )
| ~ ( in @ X848 @ frac )
| ( ( n_ts @ ( num @ X845 ) @ ( den @ X846 ) )
!= ( n_ts @ ( num @ X846 ) @ ( den @ X845 ) ) )
| ( ( n_ts @ ( num @ X847 ) @ ( den @ X848 ) )
!= ( n_ts @ ( num @ X848 ) @ ( den @ X847 ) ) )
| ( ( n_ts @ ( num @ ( n_pf @ X845 @ X847 ) ) @ ( den @ ( n_pf @ X846 @ X848 ) ) )
= ( n_ts @ ( num @ ( n_pf @ X846 @ X848 ) ) @ ( den @ ( n_pf @ X845 @ X847 ) ) ) ) ),
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_pf @ esk3_0 @ esk1_0 ) ) @ ( den @ ( n_pf @ esk3_0 @ esk2_0 ) ) )
!= ( n_ts @ ( num @ ( n_pf @ esk3_0 @ esk2_0 ) ) @ ( den @ ( n_pf @ esk3_0 @ esk1_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ( ( n_ts @ ( num @ ( n_pf @ X1 @ X5 ) ) @ ( den @ ( n_pf @ X4 @ X6 ) ) )
= ( n_ts @ ( num @ ( n_pf @ X4 @ X6 ) ) @ ( den @ ( n_pf @ X1 @ X5 ) ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X6 @ frac )
| ( ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) )
!= ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) )
| ( ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) )
!= ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
= ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
in @ esk2_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
in @ esk1_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,negated_conjecture,
in @ esk3_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[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]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM752^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n019.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 12:50:48 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.22/0.28 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.O3LbdsHMvb/E---3.1_710210.p
% 0.22/0.37 % Version: 3.5.1-ho
% 0.22/0.37 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.22/0.37 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.37 % Starting pre_casc_4 with 1200s (4) cores
% 0.22/0.37 % Starting full_lambda_6 with 300s (1) cores
% 0.22/0.37 % Starting sh10 with 300s (1) cores
% 0.22/0.37 % Starting post_as_ho9 with 300s (1) cores
% 0.22/0.37 % Starting post_as_ho8 with 300s (1) cores
% 0.22/0.37 % pre_casc_4 with pid 710245 completed with status 0
% 0.22/0.37 % Result found by pre_casc_4
% 0.22/0.37 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.22/0.37 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.37 % Starting pre_casc_4 with 1200s (4) cores
% 0.22/0.37 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.22/0.37 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.37 % Search class: HGUSM-FSLM31-DHSMMFBN
% 0.22/0.37 % partial match(2): HGUSM-FSLM31-DHSFFFBN
% 0.22/0.37 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.22/0.37 % Starting SubtermCWHack with 109s (1) cores
% 0.22/0.37 % Starting pre_casc_4 with 121s (1) cores
% 0.22/0.37 % Starting sh5l with 135s (1) cores
% 0.22/0.37 % Starting ehoh_best8_lambda with 135s (1) cores
% 0.22/0.37 % SubtermCWHack with pid 710253 completed with status 0
% 0.22/0.37 % Result found by SubtermCWHack
% 0.22/0.37 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.22/0.37 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.37 % Starting pre_casc_4 with 1200s (4) cores
% 0.22/0.37 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.22/0.37 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.22/0.37 % Search class: HGUSM-FSLM31-DHSMMFBN
% 0.22/0.37 % partial match(2): HGUSM-FSLM31-DHSFFFBN
% 0.22/0.37 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.22/0.37 % Starting SubtermCWHack with 109s (1) cores
% 0.22/0.37 % Preprocessing time : 0.004 s
% 0.22/0.37
% 0.22/0.37 % Proof found!
% 0.22/0.37 % SZS status Theorem
% 0.22/0.37 % SZS output start CNFRefutation
% See solution above
% 0.22/0.37 % Parsed axioms : 586
% 0.22/0.37 % Removed by relevancy pruning/SinE : 446
% 0.22/0.37 % Initial clauses : 141
% 0.22/0.37 % Removed in clause preprocessing : 12
% 0.22/0.37 % Initial clauses in saturation : 129
% 0.22/0.37 % Processed clauses : 693
% 0.22/0.37 % ...of these trivial : 43
% 0.22/0.37 % ...subsumed : 388
% 0.22/0.37 % ...remaining for further processing : 262
% 0.22/0.37 % Other redundant clauses eliminated : 11
% 0.22/0.37 % Clauses deleted for lack of memory : 0
% 0.22/0.37 % Backward-subsumed : 2
% 0.22/0.37 % Backward-rewritten : 50
% 0.22/0.37 % Generated clauses : 1942
% 0.22/0.37 % ...of the previous two non-redundant : 1681
% 0.22/0.37 % ...aggressively subsumed : 0
% 0.22/0.37 % Contextual simplify-reflections : 0
% 0.22/0.37 % Paramodulations : 1919
% 0.22/0.37 % Factorizations : 0
% 0.22/0.37 % NegExts : 0
% 0.22/0.37 % Equation resolutions : 16
% 0.22/0.37 % Disequality decompositions : 0
% 0.22/0.37 % Total rewrite steps : 1981
% 0.22/0.37 % ...of those cached : 1911
% 0.22/0.37 % Propositional unsat checks : 0
% 0.22/0.37 % Propositional check models : 0
% 0.22/0.37 % Propositional check unsatisfiable : 0
% 0.22/0.37 % Propositional clauses : 0
% 0.22/0.37 % Propositional clauses after purity: 0
% 0.22/0.37 % Propositional unsat core size : 0
% 0.22/0.37 % Propositional preprocessing time : 0.000
% 0.22/0.37 % Propositional encoding time : 0.000
% 0.22/0.37 % Propositional solver time : 0.000
% 0.22/0.37 % Success case prop preproc time : 0.000
% 0.22/0.37 % Success case prop encoding time : 0.000
% 0.22/0.37 % Success case prop solver time : 0.000
% 0.22/0.37 % Current number of processed clauses : 202
% 0.22/0.37 % Positive orientable unit clauses : 76
% 0.22/0.37 % Positive unorientable unit clauses: 0
% 0.22/0.37 % Negative unit clauses : 27
% 0.22/0.37 % Non-unit-clauses : 99
% 0.22/0.37 % Current number of unprocessed clauses: 1067
% 0.22/0.37 % ...number of literals in the above : 4413
% 0.22/0.37 % Current number of archived formulas : 0
% 0.22/0.37 % Current number of archived clauses : 52
% 0.22/0.37 % Clause-clause subsumption calls (NU) : 5968
% 0.22/0.37 % Rec. Clause-clause subsumption calls : 1736
% 0.22/0.37 % Non-unit clause-clause subsumptions : 145
% 0.22/0.37 % Unit Clause-clause subsumption calls : 197
% 0.22/0.37 % Rewrite failures with RHS unbound : 0
% 0.22/0.37 % BW rewrite match attempts : 108
% 0.22/0.37 % BW rewrite match successes : 12
% 0.22/0.37 % Condensation attempts : 0
% 0.22/0.37 % Condensation successes : 0
% 0.22/0.37 % Termbank termtop insertions : 76347
% 0.22/0.37 % Search garbage collected termcells : 16862
% 0.22/0.37
% 0.22/0.37 % -------------------------------------------------
% 0.22/0.37 % User time : 0.049 s
% 0.22/0.37 % System time : 0.016 s
% 0.22/0.37 % Total time : 0.065 s
% 0.22/0.37 % Maximum resident set size: 7024 pages
% 0.22/0.37
% 0.22/0.37 % -------------------------------------------------
% 0.22/0.37 % User time : 0.130 s
% 0.22/0.37 % System time : 0.041 s
% 0.22/0.37 % Total time : 0.171 s
% 0.22/0.37 % Maximum resident set size: 5632 pages
% 0.22/0.37 % E exiting
%------------------------------------------------------------------------------