%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET014^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:21:51 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 4 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 77 ( 8 ~; 9 |; 6 &; 46 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 28 ( 10 ^; 18 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_28,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_37,type,
epred1_0: $i > $o ).
thf(decl_38,type,
epred2_0: $i > $o ).
thf(decl_39,type,
epred3_0: $i > $o ).
thf(decl_40,type,
esk1_0: $i ).
thf(thm,conjecture,
! [X22: $i > $o,X23: $i > $o,X24: $i > $o] :
( ( ( subset @ X22 @ X24 )
& ( subset @ X23 @ X24 ) )
=> ( subset @ ( union @ X22 @ X23 ) @ X24 ) ),
file('/export/starexec/sandbox/tmp/tmp.j9sUuDnn7B/E---3.1_714130.p',thm) ).
thf(union,axiom,
( union
= ( ^ [X5: $i > $o,X6: $i > $o,X4: $i] :
( ( X5 @ X4 )
| ( X6 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.j9sUuDnn7B/E---3.1_714130.p',union) ).
thf(subset,axiom,
( subset
= ( ^ [X16: $i > $o,X17: $i > $o] :
! [X4: $i] :
( ( X16 @ X4 )
=> ( X17 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.j9sUuDnn7B/E---3.1_714130.p',subset) ).
thf(c_0_3,negated_conjecture,
~ ! [X22: $i > $o,X23: $i > $o,X24: $i > $o] :
( ( ( subset @ X22 @ X24 )
& ( subset @ X23 @ X24 ) )
=> ( subset @ ( union @ X22 @ X23 ) @ X24 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_4,plain,
( union
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[union]) ).
thf(c_0_5,plain,
( subset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_6,negated_conjecture,
~ ! [X22: $i > $o,X23: $i > $o,X24: $i > $o] :
( ( ! [X28: $i] :
( ( X22 @ X28 )
=> ( X24 @ X28 ) )
& ! [X29: $i] :
( ( X23 @ X29 )
=> ( X24 @ X29 ) ) )
=> ! [X30: $i] :
( ( ( X22 @ X30 )
| ( X23 @ X30 ) )
=> ( X24 @ X30 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,c_0_4]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X34: $i,X35: $i] :
( ( ~ ( epred1_0 @ X34 )
| ( epred3_0 @ X34 ) )
& ( ~ ( epred2_0 @ X35 )
| ( epred3_0 @ X35 ) )
& ( ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) )
& ~ ( epred3_0 @ esk1_0 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i] :
( ( epred3_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
( ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ( epred3_0 @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( epred3_0 @ X1 )
| ~ ( epred1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
epred1_0 @ esk1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:34:54 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.j9sUuDnn7B/E---3.1_714130.p
% 0.21/0.27 % Version: 3.5.1-ho
% 0.21/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.21/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.21/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.21/0.27 % Starting sh1l with 300s (1) cores
% 0.21/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.21/0.27 % post_as_ho10 with pid 714146 completed with status 0
% 0.21/0.27 % Result found by post_as_ho10
% 0.21/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.21/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.21/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.21/0.27 % Starting sh1l with 300s (1) cores
% 0.21/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.21/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.27 % No SInE strategy applied
% 0.21/0.27 % Search class: HGUNF-FFSF00-SHSSMFNN
% 0.21/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.27 % SubtermCWHack with pid 714147 completed with status 0
% 0.21/0.27 % Result found by SubtermCWHack
% 0.21/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.21/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.21/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.21/0.27 % Starting sh1l with 300s (1) cores
% 0.21/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.21/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.27 % No SInE strategy applied
% 0.21/0.27 % Search class: HGUNF-FFSF00-SHSSMFNN
% 0.21/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.27 % Preprocessing time : 0.001 s
% 0.21/0.27
% 0.21/0.27 % Proof found!
% 0.21/0.27 % SZS status Theorem
% 0.21/0.27 % SZS output start CNFRefutation
% See solution above
% 0.21/0.27 % Parsed axioms : 29
% 0.21/0.27 % Removed by relevancy pruning/SinE : 0
% 0.21/0.27 % Initial clauses : 18
% 0.21/0.27 % Removed in clause preprocessing : 14
% 0.21/0.27 % Initial clauses in saturation : 4
% 0.21/0.27 % Processed clauses : 5
% 0.21/0.27 % ...of these trivial : 0
% 0.21/0.27 % ...subsumed : 0
% 0.21/0.27 % ...remaining for further processing : 5
% 0.21/0.27 % Other redundant clauses eliminated : 0
% 0.21/0.27 % Clauses deleted for lack of memory : 0
% 0.21/0.27 % Backward-subsumed : 0
% 0.21/0.27 % Backward-rewritten : 1
% 0.21/0.27 % Generated clauses : 2
% 0.21/0.27 % ...of the previous two non-redundant : 1
% 0.21/0.27 % ...aggressively subsumed : 0
% 0.21/0.27 % Contextual simplify-reflections : 0
% 0.21/0.27 % Paramodulations : 2
% 0.21/0.27 % Factorizations : 0
% 0.21/0.27 % NegExts : 0
% 0.21/0.27 % Equation resolutions : 0
% 0.21/0.27 % Disequality decompositions : 0
% 0.21/0.27 % Total rewrite steps : 1
% 0.21/0.27 % ...of those cached : 0
% 0.21/0.27 % Propositional unsat checks : 0
% 0.21/0.27 % Propositional check models : 0
% 0.21/0.27 % Propositional check unsatisfiable : 0
% 0.21/0.27 % Propositional clauses : 0
% 0.21/0.27 % Propositional clauses after purity: 0
% 0.21/0.27 % Propositional unsat core size : 0
% 0.21/0.27 % Propositional preprocessing time : 0.000
% 0.21/0.27 % Propositional encoding time : 0.000
% 0.21/0.27 % Propositional solver time : 0.000
% 0.21/0.27 % Success case prop preproc time : 0.000
% 0.21/0.27 % Success case prop encoding time : 0.000
% 0.21/0.27 % Success case prop solver time : 0.000
% 0.21/0.27 % Current number of processed clauses : 4
% 0.21/0.27 % Positive orientable unit clauses : 1
% 0.21/0.27 % Positive unorientable unit clauses: 0
% 0.21/0.27 % Negative unit clauses : 1
% 0.21/0.27 % Non-unit-clauses : 2
% 0.21/0.27 % Current number of unprocessed clauses: 0
% 0.21/0.27 % ...number of literals in the above : 0
% 0.21/0.27 % Current number of archived formulas : 0
% 0.21/0.27 % Current number of archived clauses : 1
% 0.21/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.27 % Non-unit clause-clause subsumptions : 0
% 0.21/0.27 % Unit Clause-clause subsumption calls : 0
% 0.21/0.27 % Rewrite failures with RHS unbound : 0
% 0.21/0.27 % BW rewrite match attempts : 1
% 0.21/0.27 % BW rewrite match successes : 1
% 0.21/0.27 % Condensation attempts : 0
% 0.21/0.27 % Condensation successes : 0
% 0.21/0.27 % Termbank termtop insertions : 1023
% 0.21/0.27 % Search garbage collected termcells : 232
% 0.21/0.27
% 0.21/0.27 % -------------------------------------------------
% 0.21/0.27 % User time : 0.003 s
% 0.21/0.27 % System time : 0.001 s
% 0.21/0.27 % Total time : 0.004 s
% 0.21/0.27 % Maximum resident set size: 3660 pages
% 0.21/0.27
% 0.21/0.27 % -------------------------------------------------
% 0.21/0.27 % User time : 0.004 s
% 0.21/0.27 % System time : 0.006 s
% 0.21/0.27 % Total time : 0.010 s
% 0.21/0.27 % Maximum resident set size: 4864 pages
% 0.21/0.27 % E exiting
%------------------------------------------------------------------------------