%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP163^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:04:33 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 15 ~; 12 |; 3 &; 83 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
refine424419629nres_a: $tType ).
thf(decl_sort2,type,
set_a: $tType ).
thf(decl_sort3,type,
a: $tType ).
thf(decl_38,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(decl_41,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(decl_43,type,
collect_a: ( a > $o ) > set_a ).
thf(decl_48,type,
member_a: a > set_a > $o ).
thf(decl_49,type,
phi: a > $o ).
thf(decl_50,type,
x: a ).
thf(conj_0,conjecture,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
<=> ( phi @ x ) ),
file('/export/starexec/sandbox2/tmp/tmp.Psus4a0yDB/E---3.1_1748920.p',conj_0) ).
thf(fact_2_nf__inres__RES,axiom,
! [X1: set_a,X5: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X1 ) @ X5 )
<=> ( member_a @ X5 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Psus4a0yDB/E---3.1_1748920.p',fact_2_nf__inres__RES) ).
thf(fact_41_mem__Collect__eq,axiom,
! [X56: a,X57: a > $o] :
( ( member_a @ X56 @ ( collect_a @ X57 ) )
<=> ( X57 @ X56 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Psus4a0yDB/E---3.1_1748920.p',fact_41_mem__Collect__eq) ).
thf(c_0_3,negated_conjecture,
~ ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
<=> ( phi @ x ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_4,negated_conjecture,
( ( ~ ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
| ~ ( phi @ x ) )
& ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
| ( phi @ x ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])]) ).
thf(c_0_5,plain,
! [X1194: set_a,X1195: a] :
( ( ~ ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X1194 ) @ X1195 )
| ( member_a @ X1195 @ X1194 ) )
& ( ~ ( member_a @ X1195 @ X1194 )
| ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X1194 ) @ X1195 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_nf__inres__RES])])]) ).
thf(c_0_6,plain,
! [X1282: a,X1283: a > $o] :
( ( ~ ( member_a @ X1282 @ ( collect_a @ X1283 ) )
| ( X1283 @ X1282 ) )
& ( ~ ( X1283 @ X1282 )
| ( member_a @ X1282 @ ( collect_a @ X1283 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_mem__Collect__eq])])]) ).
thf(c_0_7,negated_conjecture,
( ~ ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
| ~ ( phi @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_8,plain,
! [X5: a,X1: set_a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X1 ) @ X5 )
| ~ ( member_a @ X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X5: a,X57: a > $o] :
( ( X57 @ X5 )
| ~ ( member_a @ X5 @ ( collect_a @ X57 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
~ ( member_a @ x @ ( collect_a @ phi ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
thf(c_0_11,plain,
! [X57: a > $o,X5: a] :
( ( member_a @ X5 @ ( collect_a @ X57 ) )
| ~ ( X57 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,negated_conjecture,
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
| ( phi @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_13,negated_conjecture,
~ ( phi @ x ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,plain,
! [X1: set_a,X5: a] :
( ( member_a @ X5 @ X1 )
| ~ ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X1 ) @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_15,negated_conjecture,
refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x,
inference(sr,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP163^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n001.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 20:10:06 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.27 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.Psus4a0yDB/E---3.1_1748920.p
% 0.24/0.33 % Version: 3.5.1-ho
% 0.24/0.33 % Preprocessing class: HSLSSMSSSSSCHSA.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.33 % Starting sh5l with 300s (1) cores
% 0.24/0.33 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.33 % Starting new_bool_2 with 300s (1) cores
% 0.24/0.33 % sh5l with pid 1748934 completed with status 0
% 0.24/0.33 % Result found by sh5l
% 0.24/0.33 % Preprocessing class: HSLSSMSSSSSCHSA.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.33 % Starting sh5l with 300s (1) cores
% 0.24/0.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.24/0.33 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.24/0.33 % Search class: HGHSM-FSLM33-DHSFFSBN
% 0.24/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.33 % SubtermCWHack with pid 1748937 completed with status 0
% 0.24/0.33 % Result found by SubtermCWHack
% 0.24/0.33 % Preprocessing class: HSLSSMSSSSSCHSA.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.33 % Starting sh5l with 300s (1) cores
% 0.24/0.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.24/0.33 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.24/0.33 % Search class: HGHSM-FSLM33-DHSFFSBN
% 0.24/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.33 % Preprocessing time : 0.007 s
% 0.24/0.33
% 0.24/0.33 % Proof found!
% 0.24/0.33 % SZS status Theorem
% 0.24/0.33 % SZS output start CNFRefutation
% See solution above
% 0.24/0.33 % Parsed axioms : 304
% 0.24/0.33 % Removed by relevancy pruning/SinE : 59
% 0.24/0.33 % Initial clauses : 443
% 0.24/0.33 % Removed in clause preprocessing : 73
% 0.24/0.33 % Initial clauses in saturation : 370
% 0.24/0.33 % Processed clauses : 113
% 0.24/0.33 % ...of these trivial : 4
% 0.24/0.33 % ...subsumed : 47
% 0.24/0.33 % ...remaining for further processing : 62
% 0.24/0.33 % Other redundant clauses eliminated : 19
% 0.24/0.33 % Clauses deleted for lack of memory : 0
% 0.24/0.33 % Backward-subsumed : 1
% 0.24/0.33 % Backward-rewritten : 1
% 0.24/0.33 % Generated clauses : 62
% 0.24/0.33 % ...of the previous two non-redundant : 41
% 0.24/0.33 % ...aggressively subsumed : 0
% 0.24/0.33 % Contextual simplify-reflections : 1
% 0.24/0.33 % Paramodulations : 36
% 0.24/0.33 % Factorizations : 0
% 0.24/0.33 % NegExts : 0
% 0.24/0.33 % Equation resolutions : 21
% 0.24/0.33 % Disequality decompositions : 0
% 0.24/0.33 % Total rewrite steps : 14
% 0.24/0.33 % ...of those cached : 7
% 0.24/0.33 % Propositional unsat checks : 0
% 0.24/0.33 % Propositional check models : 0
% 0.24/0.33 % Propositional check unsatisfiable : 0
% 0.24/0.33 % Propositional clauses : 0
% 0.24/0.33 % Propositional clauses after purity: 0
% 0.24/0.33 % Propositional unsat core size : 0
% 0.24/0.33 % Propositional preprocessing time : 0.000
% 0.24/0.33 % Propositional encoding time : 0.000
% 0.24/0.33 % Propositional solver time : 0.000
% 0.24/0.33 % Success case prop preproc time : 0.000
% 0.24/0.33 % Success case prop encoding time : 0.000
% 0.24/0.33 % Success case prop solver time : 0.000
% 0.24/0.33 % Current number of processed clauses : 42
% 0.24/0.33 % Positive orientable unit clauses : 14
% 0.24/0.33 % Positive unorientable unit clauses: 0
% 0.24/0.33 % Negative unit clauses : 7
% 0.24/0.33 % Non-unit-clauses : 21
% 0.24/0.33 % Current number of unprocessed clauses: 297
% 0.24/0.33 % ...number of literals in the above : 926
% 0.24/0.33 % Current number of archived formulas : 0
% 0.24/0.33 % Current number of archived clauses : 3
% 0.24/0.33 % Clause-clause subsumption calls (NU) : 121
% 0.24/0.33 % Rec. Clause-clause subsumption calls : 117
% 0.24/0.33 % Non-unit clause-clause subsumptions : 27
% 0.24/0.33 % Unit Clause-clause subsumption calls : 45
% 0.24/0.33 % Rewrite failures with RHS unbound : 0
% 0.24/0.33 % BW rewrite match attempts : 2
% 0.24/0.33 % BW rewrite match successes : 1
% 0.24/0.33 % Condensation attempts : 0
% 0.24/0.33 % Condensation successes : 0
% 0.24/0.33 % Termbank termtop insertions : 37127
% 0.24/0.33 % Search garbage collected termcells : 11708
% 0.24/0.33
% 0.24/0.33 % -------------------------------------------------
% 0.24/0.33 % User time : 0.022 s
% 0.24/0.33 % System time : 0.008 s
% 0.24/0.33 % Total time : 0.030 s
% 0.24/0.33 % Maximum resident set size: 6180 pages
% 0.24/0.33
% 0.24/0.33 % -------------------------------------------------
% 0.24/0.33 % User time : 0.034 s
% 0.24/0.33 % System time : 0.012 s
% 0.24/0.33 % Total time : 0.046 s
% 0.24/0.33 % Maximum resident set size: 5632 pages
% 0.24/0.33 % E exiting
%------------------------------------------------------------------------------