%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP226^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:05:56 AM UTC 2026
% Result : Theorem 7.73s 4.23s
% Output : CNFRefutation 7.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 197 ( 26 ~; 24 |; 3 &; 137 @)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 3 ^; 29 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
set_nat: $tType ).
thf(decl_sort3,type,
vEBT_VEBT: $tType ).
thf(decl_854,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(decl_953,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(decl_965,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(decl_966,type,
vEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(decl_973,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(decl_994,type,
member_nat: nat > set_nat > $o ).
thf(decl_1001,type,
n: nat ).
thf(decl_1002,type,
t: vEBT_VEBT ).
thf(decl_1003,type,
x: nat ).
thf(conj_1,conjecture,
( ( vEBT_vebt_member @ t @ x )
<=> ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9a3v1viBbD/E---3.1_645409.p',conj_1) ).
thf(fact_8231_set__vebt__def,axiom,
( vEBT_set_vebt
= ( ^ [X13: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ X13 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9a3v1viBbD/E---3.1_645409.p',fact_8231_set__vebt__def) ).
thf(fact_4_both__member__options__equiv__member,axiom,
! [X1: vEBT_VEBT,X4: nat,X2: nat] :
( ( vEBT_invar_vebt @ X1 @ X4 )
=> ( ( vEBT_V8194947554948674370ptions @ X1 @ X2 )
<=> ( vEBT_vebt_member @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9a3v1viBbD/E---3.1_645409.p',fact_4_both__member__options__equiv__member) ).
thf(fact_48_mem__Collect__eq,axiom,
! [X54: nat,X40: nat > $o] :
( ( member_nat @ X54 @ ( collect_nat @ X40 ) )
<=> ( X40 @ X54 ) ),
file('/export/starexec/sandbox2/tmp/tmp.9a3v1viBbD/E---3.1_645409.p',fact_48_mem__Collect__eq) ).
thf(conj_0,hypothesis,
vEBT_invar_vebt @ t @ n,
file('/export/starexec/sandbox2/tmp/tmp.9a3v1viBbD/E---3.1_645409.p',conj_0) ).
thf(fact_5_valid__member__both__member__options,axiom,
! [X1: vEBT_VEBT,X4: nat,X2: nat] :
( ( vEBT_invar_vebt @ X1 @ X4 )
=> ( ( vEBT_V8194947554948674370ptions @ X1 @ X2 )
=> ( vEBT_vebt_member @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9a3v1viBbD/E---3.1_645409.p',fact_5_valid__member__both__member__options) ).
thf(c_0_6,negated_conjecture,
~ ( ( vEBT_vebt_member @ t @ x )
<=> ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(c_0_7,plain,
( vEBT_set_vebt
= ( ^ [Z0: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_8231_set__vebt__def]) ).
thf(c_0_8,negated_conjecture,
( ( ~ ( vEBT_vebt_member @ t @ x )
| ~ ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) )
& ( ( vEBT_vebt_member @ t @ x )
| ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
( vEBT_set_vebt
= ( ^ [Z0: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X23395: vEBT_VEBT,X23396: nat,X23397: nat] :
( ( ~ ( vEBT_V8194947554948674370ptions @ X23395 @ X23397 )
| ( vEBT_vebt_member @ X23395 @ X23397 )
| ~ ( vEBT_invar_vebt @ X23395 @ X23396 ) )
& ( ~ ( vEBT_vebt_member @ X23395 @ X23397 )
| ( vEBT_V8194947554948674370ptions @ X23395 @ X23397 )
| ~ ( vEBT_invar_vebt @ X23395 @ X23396 ) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_both__member__options__equiv__member])])]) ).
thf(c_0_11,plain,
! [X25546: nat,X25547: nat > $o] :
( ( ~ ( member_nat @ X25546 @ ( collect_nat @ X25547 ) )
| ( X25547 @ X25546 ) )
& ( ~ ( X25547 @ X25546 )
| ( member_nat @ X25546 @ ( collect_nat @ X25547 ) ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_mem__Collect__eq])]) ).
thf(c_0_12,negated_conjecture,
( ( vEBT_vebt_member @ t @ x )
| ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X1: vEBT_VEBT] :
( ( vEBT_set_vebt @ X1 )
= ( collect_nat @ ( vEBT_V8194947554948674370ptions @ X1 ) ) ),
inference(arg_cong,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ~ ( vEBT_vebt_member @ t @ x )
| ~ ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,plain,
! [X1: vEBT_VEBT,X2: nat,X3: nat] :
( ( vEBT_V8194947554948674370ptions @ X1 @ X2 )
| ~ ( vEBT_vebt_member @ X1 @ X2 )
| ~ ( vEBT_invar_vebt @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,hypothesis,
vEBT_invar_vebt @ t @ n,
inference(split_conjunct,[status(thm)],[conj_0]) ).
thf(c_0_17,plain,
! [X2: nat,X40: nat > $o] :
( ( X40 @ X2 )
| ~ ( member_nat @ X2 @ ( collect_nat @ X40 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
( ( member_nat @ x @ ( collect_nat @ ( vEBT_V8194947554948674370ptions @ t ) ) )
| ( vEBT_vebt_member @ t @ x ) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_19,negated_conjecture,
( ~ ( member_nat @ x @ ( collect_nat @ ( vEBT_V8194947554948674370ptions @ t ) ) )
| ~ ( vEBT_vebt_member @ t @ x ) ),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
thf(c_0_20,plain,
! [X40: nat > $o,X2: nat] :
( ( member_nat @ X2 @ ( collect_nat @ X40 ) )
| ~ ( X40 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_21,hypothesis,
! [X2: nat] :
( ( vEBT_V8194947554948674370ptions @ t @ X2 )
| ~ ( vEBT_vebt_member @ t @ X2 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_22,negated_conjecture,
( ( vEBT_vebt_member @ t @ x )
| ( vEBT_V8194947554948674370ptions @ t @ x ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_23,plain,
! [X23398: vEBT_VEBT,X23399: nat,X23400: nat] :
( ~ ( vEBT_invar_vebt @ X23398 @ X23399 )
| ~ ( vEBT_V8194947554948674370ptions @ X23398 @ X23400 )
| ( vEBT_vebt_member @ X23398 @ X23400 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_valid__member__both__member__options])]) ).
thf(c_0_24,negated_conjecture,
( ~ ( vEBT_vebt_member @ t @ x )
| ~ ( vEBT_V8194947554948674370ptions @ t @ x ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_25,negated_conjecture,
vEBT_V8194947554948674370ptions @ t @ x,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_26,plain,
! [X1: vEBT_VEBT,X2: nat,X3: nat] :
( ( vEBT_vebt_member @ X1 @ X3 )
| ~ ( vEBT_invar_vebt @ X1 @ X2 )
| ~ ( vEBT_V8194947554948674370ptions @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
~ ( vEBT_vebt_member @ t @ x ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_28,hypothesis,
! [X2: nat] :
( ( vEBT_vebt_member @ t @ X2 )
| ~ ( vEBT_V8194947554948674370ptions @ t @ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
thf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP226^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.03 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.11 % Computer : n012.cluster.edu
% 0.07/0.11 % Model : x86_64 x86_64
% 0.07/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.11 % Memory : 8046.5625MB
% 0.07/0.11 % OS : Linux 6.8.0-71-generic
% 0.07/0.11 % CPULimit : 300
% 0.07/0.11 % WCLimit : 300
% 0.07/0.11 % DateTime : Tue Sep 29 20:21:03 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.15 Running higher-order theorem proving
% 2.04/2.16 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.9a3v1viBbD/E---3.1_645409.p
% 7.73/4.23 % Version: 3.5.1-ho
% 7.73/4.23 % partial match(1): HMLMSMSMSSLCHFA
% 7.73/4.23 % Preprocessing class: HMLMSMLMSSLCHFA.
% 7.73/4.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.73/4.23 % Starting new_ho_10 with 1500s (5) cores
% 7.73/4.23 % Starting sh5l with 300s (1) cores
% 7.73/4.23 % Starting new_bool_1 with 300s (1) cores
% 7.73/4.23 % Starting new_bool_2 with 300s (1) cores
% 7.73/4.23 % new_bool_2 with pid 645593 completed with status 0
% 7.73/4.23 % Result found by new_bool_2
% 7.73/4.23 % partial match(1): HMLMSMSMSSLCHFA
% 7.73/4.23 % Preprocessing class: HMLMSMLMSSLCHFA.
% 7.73/4.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.73/4.23 % Starting new_ho_10 with 1500s (5) cores
% 7.73/4.23 % Starting sh5l with 300s (1) cores
% 7.73/4.23 % Starting new_bool_1 with 300s (1) cores
% 7.73/4.23 % Starting new_bool_2 with 300s (1) cores
% 7.73/4.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 7.73/4.23 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.73/4.23 % Search class: HGHSM-SMLM32-DHFFFSBN
% 7.73/4.23 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 7.73/4.23 % Starting SubtermCWHack with 31s (1) cores
% 7.73/4.23 % SubtermCWHack with pid 645595 completed with status 0
% 7.73/4.23 % Result found by SubtermCWHack
% 7.73/4.23 % partial match(1): HMLMSMSMSSLCHFA
% 7.73/4.23 % Preprocessing class: HMLMSMLMSSLCHFA.
% 7.73/4.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.73/4.23 % Starting new_ho_10 with 1500s (5) cores
% 7.73/4.23 % Starting sh5l with 300s (1) cores
% 7.73/4.23 % Starting new_bool_1 with 300s (1) cores
% 7.73/4.23 % Starting new_bool_2 with 300s (1) cores
% 7.73/4.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 7.73/4.23 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.73/4.23 % Search class: HGHSM-SMLM32-DHFFFSBN
% 7.73/4.23 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 7.73/4.23 % Starting SubtermCWHack with 31s (1) cores
% 7.73/4.23 % Preprocessing time : 0.068 s
% 7.73/4.23
% 7.73/4.23 % Proof found!
% 7.73/4.23 % SZS status Theorem
% 7.73/4.23 % SZS output start CNFRefutation
% See solution above
% 7.73/4.23 % Parsed axioms : 11247
% 7.73/4.23 % Removed by relevancy pruning/SinE : 8122
% 7.73/4.23 % Initial clauses : 8118
% 7.73/4.23 % Removed in clause preprocessing : 1929
% 7.73/4.23 % Initial clauses in saturation : 6189
% 7.73/4.23 % Processed clauses : 9857
% 7.73/4.23 % ...of these trivial : 668
% 7.73/4.23 % ...subsumed : 4948
% 7.73/4.23 % ...remaining for further processing : 4241
% 7.73/4.23 % Other redundant clauses eliminated : 617
% 7.73/4.23 % Clauses deleted for lack of memory : 0
% 7.73/4.23 % Backward-subsumed : 24
% 7.73/4.23 % Backward-rewritten : 157
% 7.73/4.23 % Generated clauses : 34129
% 7.73/4.23 % ...of the previous two non-redundant : 26156
% 7.73/4.23 % ...aggressively subsumed : 0
% 7.73/4.23 % Contextual simplify-reflections : 12
% 7.73/4.23 % Paramodulations : 33437
% 7.73/4.23 % Factorizations : 15
% 7.73/4.23 % NegExts : 0
% 7.73/4.23 % Equation resolutions : 642
% 7.73/4.23 % Disequality decompositions : 0
% 7.73/4.23 % Total rewrite steps : 12239
% 7.73/4.23 % ...of those cached : 9620
% 7.73/4.23 % Propositional unsat checks : 0
% 7.73/4.23 % Propositional check models : 0
% 7.73/4.23 % Propositional check unsatisfiable : 0
% 7.73/4.23 % Propositional clauses : 0
% 7.73/4.23 % Propositional clauses after purity: 0
% 7.73/4.23 % Propositional unsat core size : 0
% 7.73/4.23 % Propositional preprocessing time : 0.000
% 7.73/4.23 % Propositional encoding time : 0.000
% 7.73/4.23 % Propositional solver time : 0.000
% 7.73/4.23 % Success case prop preproc time : 0.000
% 7.73/4.23 % Success case prop encoding time : 0.000
% 7.73/4.23 % Success case prop solver time : 0.000
% 7.73/4.23 % Current number of processed clauses : 3712
% 7.73/4.23 % Positive orientable unit clauses : 1724
% 7.73/4.23 % Positive unorientable unit clauses: 15
% 7.73/4.23 % Negative unit clauses : 1310
% 7.73/4.23 % Non-unit-clauses : 663
% 7.73/4.23 % Current number of unprocessed clauses: 22335
% 7.73/4.23 % ...number of literals in the above : 50816
% 7.73/4.23 % Current number of archived formulas : 0
% 7.73/4.23 % Current number of archived clauses : 184
% 7.73/4.23 % Clause-clause subsumption calls (NU) : 91008
% 7.73/4.23 % Rec. Clause-clause subsumption calls : 80877
% 7.73/4.23 % Non-unit clause-clause subsumptions : 790
% 7.73/4.23 % Unit Clause-clause subsumption calls : 401529
% 7.73/4.23 % Rewrite failures with RHS unbound : 0
% 7.73/4.23 % BW rewrite match attempts : 5031
% 7.73/4.23 % BW rewrite match successes : 256
% 7.73/4.23 % Condensation attempts : 0
% 7.73/4.23 % Condensation successes : 0
% 7.73/4.23 % Termbank termtop insertions : 932319
% 7.73/4.23 % Search garbage collected termcells : 162724
% 7.73/4.23
% 7.73/4.23 % -------------------------------------------------
% 7.73/4.23 % User time : 1.348 s
% 7.73/4.23 % System time : 0.082 s
% 7.73/4.23 % Total time : 1.430 s
% 7.73/4.23 % Maximum resident set size: 43772 pages
% 7.73/4.23
% 7.73/4.23 % -------------------------------------------------
% 7.73/4.23 % User time : 1.919 s
% 7.73/4.23 % System time : 0.113 s
% 7.73/4.23 % Total time : 2.032 s
% 7.73/4.23 % Maximum resident set size: 26880 pages
% 7.73/4.23 % E exiting
%------------------------------------------------------------------------------