%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM736^4 : 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 08:16:58 AM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 33 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 52 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 243 ( 29 ~; 0 |; 0 &; 208 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 7 con; 0-3 aty)
% Number of variables : 77 ( 72 ^; 5 !; 0 ?; 77 :)
% 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_28,type,
emptyset: $i ).
thf(decl_43,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(decl_50,type,
omega: $i ).
thf(decl_59,type,
ap: $i > $i > $i ).
thf(decl_61,type,
d_Pi: $i > ( $i > $i ) > $i ).
thf(decl_124,type,
nat: $i ).
thf(decl_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_150,type,
iii: $i > $i > $o ).
thf(decl_162,type,
times: $i > $i ).
thf(decl_163,type,
n_ts: $i > $i > $i ).
thf(decl_168,type,
d_1to: $i > $i ).
thf(decl_173,type,
n_2: $i ).
thf(decl_177,type,
pair1type: $i > $i ).
thf(decl_179,type,
first1: $i > $i > $i ).
thf(decl_180,type,
second1: $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_195,type,
moref: $i > $i > $o ).
thf(decl_196,type,
lessf: $i > $i > $o ).
thf(def_nat,axiom,
( nat
= ( d_Sep @ omega
@ ^ [X1: $i] : ( X1 != emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_nat) ).
thf(def_pair1type,axiom,
( pair1type
= ( ^ [X1: $i] :
( d_Pi @ ( d_1to @ n_2 )
@ ^ [X425: $i] : X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_pair1type) ).
thf(def_moref,axiom,
( moref
= ( ^ [X1: $i,X449: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X449 ) ) @ ( n_ts @ ( num @ X449 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_moref) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_d_29_ii) ).
thf(def_num,axiom,
( num
= ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_num) ).
thf(def_den,axiom,
( den
= ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_den) ).
thf(def_n_ts,axiom,
( n_ts
= ( ^ [X1: $i] : ( ap @ ( times @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_n_ts) ).
thf(def_lessf,axiom,
( lessf
= ( ^ [X1: $i,X450: $i] : ( iii @ ( n_ts @ ( num @ X1 ) @ ( den @ X450 ) ) @ ( n_ts @ ( num @ X450 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_lessf) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_iii) ).
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.0z6VF10RGr/E---3.1_55098.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_is_of) ).
thf(satz42,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X457: $i] : ( in @ X457 @ frac )
@ ^ [X458: $i] :
( ( moref @ X1 @ X458 )
=> ( lessf @ X458 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',satz42) ).
thf(def_frac,axiom,
( frac
= ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0z6VF10RGr/E---3.1_55098.p',def_frac) ).
thf(c_0_13,plain,
( nat
= ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[def_nat]) ).
thf(c_0_14,plain,
( pair1type
= ( ^ [Z0: $i] :
( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_pair1type]) ).
thf(c_0_15,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moref]) ).
thf(c_0_16,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_17,axiom,
( num
= ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[def_num,c_0_13]) ).
thf(c_0_18,axiom,
( den
= ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[def_den,c_0_13]) ).
thf(c_0_19,plain,
( n_ts
= ( ^ [Z0: $i] : ( ap @ ( times @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_ts]) ).
thf(c_0_20,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessf]) ).
thf(c_0_21,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_22,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_23,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_24,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X457: $i] : ( in @ X457 @ frac )
@ ^ [X458: $i] :
( ( moref @ X1 @ X458 )
=> ( lessf @ X458 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[satz42]) ).
thf(c_0_25,axiom,
( frac
= ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_frac,c_0_13]),c_0_14]) ).
thf(c_0_26,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),c_0_19]) ).
thf(c_0_27,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_17]),c_0_18]),c_0_19]),c_0_21]) ).
thf(c_0_28,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_29,negated_conjecture,
~ ! [X466: $i] :
( ( in @ X466
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X465: $i] : $true ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).
thf(c_0_30,negated_conjecture,
~ $true,
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_29])]) ).
thf(c_0_31,negated_conjecture,
~ $true,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM736^4 : 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 12:46:03 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.15 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.0z6VF10RGr/E---3.1_55098.p
% 0.08/0.20 % Version: 3.5.1-ho
% 0.08/0.20 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.08/0.20 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting pre_casc_4 with 1200s (4) cores
% 0.08/0.20 % Starting full_lambda_6 with 300s (1) cores
% 0.08/0.20 % Starting sh10 with 300s (1) cores
% 0.08/0.20 % Starting post_as_ho9 with 300s (1) cores
% 0.08/0.20 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.20 % post_as_ho9 with pid 55114 completed with status 0
% 0.08/0.20 % Result found by post_as_ho9
% 0.08/0.20 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.08/0.20 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting pre_casc_4 with 1200s (4) cores
% 0.08/0.20 % Starting full_lambda_6 with 300s (1) cores
% 0.08/0.20 % Starting sh10 with 300s (1) cores
% 0.08/0.20 % Starting post_as_ho9 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.08/0.20 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.08/0.20 % Search class: HGHNF-FSLF21-DHSMMFBN
% 0.08/0.20 % partial match(4): HGHNF-FSLF11-SHSSMFNN
% 0.08/0.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % SubtermCWHack with pid 55116 completed with status 0
% 0.08/0.20 % Result found by SubtermCWHack
% 0.08/0.20 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.08/0.20 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting pre_casc_4 with 1200s (4) cores
% 0.08/0.20 % Starting full_lambda_6 with 300s (1) cores
% 0.08/0.20 % Starting sh10 with 300s (1) cores
% 0.08/0.20 % Starting post_as_ho9 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.08/0.20 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.08/0.20 % Search class: HGHNF-FSLF21-DHSMMFBN
% 0.08/0.20 % partial match(4): HGHNF-FSLF11-SHSSMFNN
% 0.08/0.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % Preprocessing time : 0.005 s
% 0.08/0.20
% 0.08/0.20 % Proof found!
% 0.08/0.20 % SZS status Theorem
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20 % Parsed axioms : 544
% 0.08/0.20 % Removed by relevancy pruning/SinE : 472
% 0.08/0.20 % Initial clauses : 514
% 0.08/0.20 % Removed in clause preprocessing : 224
% 0.08/0.20 % Initial clauses in saturation : 290
% 0.08/0.20 % Processed clauses : 1
% 0.08/0.20 % ...of these trivial : 0
% 0.08/0.20 % ...subsumed : 0
% 0.08/0.20 % ...remaining for further processing : 0
% 0.08/0.20 % Other redundant clauses eliminated : 0
% 0.08/0.20 % Clauses deleted for lack of memory : 0
% 0.08/0.20 % Backward-subsumed : 0
% 0.08/0.20 % Backward-rewritten : 0
% 0.08/0.20 % Generated clauses : 0
% 0.08/0.20 % ...of the previous two non-redundant : 0
% 0.08/0.20 % ...aggressively subsumed : 0
% 0.08/0.20 % Contextual simplify-reflections : 0
% 0.08/0.20 % Paramodulations : 0
% 0.08/0.20 % Factorizations : 0
% 0.08/0.20 % NegExts : 0
% 0.08/0.20 % Equation resolutions : 0
% 0.08/0.20 % Disequality decompositions : 0
% 0.08/0.20 % Total rewrite steps : 0
% 0.08/0.20 % ...of those cached : 0
% 0.08/0.20 % Propositional unsat checks : 0
% 0.08/0.20 % Propositional check models : 0
% 0.08/0.20 % Propositional check unsatisfiable : 0
% 0.08/0.20 % Propositional clauses : 0
% 0.08/0.20 % Propositional clauses after purity: 0
% 0.08/0.20 % Propositional unsat core size : 0
% 0.08/0.20 % Propositional preprocessing time : 0.000
% 0.08/0.20 % Propositional encoding time : 0.000
% 0.08/0.20 % Propositional solver time : 0.000
% 0.08/0.20 % Success case prop preproc time : 0.000
% 0.08/0.20 % Success case prop encoding time : 0.000
% 0.08/0.20 % Success case prop solver time : 0.000
% 0.08/0.20 % Current number of processed clauses : 0
% 0.08/0.20 % Positive orientable unit clauses : 0
% 0.08/0.20 % Positive unorientable unit clauses: 0
% 0.08/0.20 % Negative unit clauses : 0
% 0.08/0.20 % Non-unit-clauses : 0
% 0.08/0.20 % Current number of unprocessed clauses: 289
% 0.08/0.20 % ...number of literals in the above : 1765
% 0.08/0.20 % Current number of archived formulas : 0
% 0.08/0.20 % Current number of archived clauses : 0
% 0.08/0.20 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.20 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.20 % Non-unit clause-clause subsumptions : 0
% 0.08/0.20 % Unit Clause-clause subsumption calls : 0
% 0.08/0.20 % Rewrite failures with RHS unbound : 0
% 0.08/0.20 % BW rewrite match attempts : 0
% 0.08/0.20 % BW rewrite match successes : 0
% 0.08/0.20 % Condensation attempts : 0
% 0.08/0.20 % Condensation successes : 0
% 0.08/0.20 % Termbank termtop insertions : 98919
% 0.08/0.20 % Search garbage collected termcells : 15548
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.029 s
% 0.08/0.20 % System time : 0.004 s
% 0.08/0.20 % Total time : 0.033 s
% 0.08/0.20 % Maximum resident set size: 6872 pages
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.034 s
% 0.08/0.20 % System time : 0.009 s
% 0.08/0.20 % Total time : 0.043 s
% 0.08/0.20 % Maximum resident set size: 5632 pages
% 0.08/0.20 % E exiting
%------------------------------------------------------------------------------