%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET671^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:22:17 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 8 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 137 ( 16 ~; 13 |; 14 &; 84 @)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 47 ( 18 ^; 29 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_34,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_41,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_42,type,
restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(decl_58,type,
epred1_0: $i > $o ).
thf(decl_59,type,
epred2_0: $i > $i > $o ).
thf(decl_60,type,
epred3_0: $i > $o ).
thf(decl_61,type,
epred4_0: $i > $o ).
thf(decl_62,type,
esk1_0: $i ).
thf(decl_63,type,
esk2_0: $i ).
thf(thm,conjecture,
! [X36: $i > $o,X28: $i > $i > $o,X37: $i > $o,X38: $i > $o] :
( ( ( is_rel_on @ X28 @ X37 @ X38 )
& ( subset @ X37 @ X36 ) )
=> ( ( restrict_rel_domain @ X28 @ X36 )
= X28 ) ),
file('/export/starexec/sandbox2/tmp/tmp.nPxbFA99q7/E---3.1_2672840.p',thm) ).
thf(subset,axiom,
( subset
= ( ^ [X16: $i > $o,X17: $i > $o] :
! [X4: $i] :
( ( X16 @ X4 )
=> ( X17 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nPxbFA99q7/E---3.1_2672840.p',subset) ).
thf(is_rel_on,axiom,
( is_rel_on
= ( ^ [X28: $i > $i > $o,X29: $i > $o,X30: $i > $o] :
! [X1: $i,X3: $i] :
( ( X28 @ X1 @ X3 )
=> ( ( X29 @ X1 )
& ( X30 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nPxbFA99q7/E---3.1_2672840.p',is_rel_on) ).
thf(restrict_rel_domain,axiom,
( restrict_rel_domain
= ( ^ [X28: $i > $i > $o,X25: $i > $o,X1: $i,X3: $i] :
( ( X25 @ X1 )
& ( X28 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nPxbFA99q7/E---3.1_2672840.p',restrict_rel_domain) ).
thf(c_0_4,negated_conjecture,
~ ! [X36: $i > $o,X28: $i > $i > $o,X37: $i > $o,X38: $i > $o] :
( ( ( is_rel_on @ X28 @ X37 @ X38 )
& ( subset @ X37 @ X36 ) )
=> ( ( restrict_rel_domain @ X28 @ X36 )
= X28 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
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,plain,
( is_rel_on
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i > $o] :
! [X1: $i,X3: $i] :
( ( Z0 @ X1 @ X3 )
=> ( ( Z1 @ X1 )
& ( Z2 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[is_rel_on]) ).
thf(c_0_7,plain,
( restrict_rel_domain
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i,Z3: $i] :
( ( Z1 @ Z2 )
& ( Z0 @ Z2 @ Z3 ) ) ) ),
inference(fof_simplification,[status(thm)],[restrict_rel_domain]) ).
thf(c_0_8,negated_conjecture,
~ ! [X36: $i > $o,X28: $i > $i > $o,X37: $i > $o,X38: $i > $o] :
( ( ! [X51: $i,X52: $i] :
( ( X28 @ X51 @ X52 )
=> ( ( X37 @ X51 )
& ( X38 @ X52 ) ) )
& ! [X53: $i] :
( ( X37 @ X53 )
=> ( X36 @ X53 ) ) )
=> ! [X54: $i,X55: $i] :
( ( ( X36 @ X54 )
& ( X28 @ X54 @ X55 ) )
<=> ( X28 @ X54 @ X55 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]),c_0_7])]) ).
thf(c_0_9,negated_conjecture,
! [X60: $i,X61: $i,X62: $i] :
( ( ( epred3_0 @ X60 )
| ~ ( epred2_0 @ X60 @ X61 ) )
& ( ( epred4_0 @ X61 )
| ~ ( epred2_0 @ X60 @ X61 ) )
& ( ~ ( epred3_0 @ X62 )
| ( epred1_0 @ X62 ) )
& ( ~ ( epred1_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 @ esk2_0 )
| ~ ( epred2_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred2_0 @ esk1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 @ esk2_0 ) ) ),
inference(distribute,[status(thm)],[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_8])])])])])]) ).
thf(c_0_10,negated_conjecture,
( ( epred2_0 @ esk1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ~ ( epred1_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 @ esk2_0 )
| ~ ( epred2_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred3_0 @ X1 )
| ~ ( epred2_0 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
epred2_0 @ esk1_0 @ esk2_0,
inference(cn,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
( ~ ( epred1_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 @ esk2_0 ) ),
inference(cn,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( epred3_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,negated_conjecture,
epred3_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,negated_conjecture,
~ ( epred1_0 @ esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_13])]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET671^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n014.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 13:40:30 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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.nPxbFA99q7/E---3.1_2672840.p
% 0.09/0.24 % Version: 3.5.1-ho
% 0.09/0.24 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.24 % Starting post_as_ho11 with 300s (1) cores
% 0.09/0.24 % Starting full_lambda_8 with 300s (1) cores
% 0.09/0.24 % post_as_ho3 with pid 2672854 completed with status 0
% 0.09/0.24 % Result found by post_as_ho3
% 0.09/0.24 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HGHNF-FFSF00-SHSSMFNN
% 0.09/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.24 % SubtermCWHack with pid 2672859 completed with status 0
% 0.09/0.24 % Result found by SubtermCWHack
% 0.09/0.24 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HGHNF-FFSF00-SHSSMFNN
% 0.09/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.24 % Preprocessing time : 0.001 s
% 0.09/0.24
% 0.09/0.24 % Proof found!
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24 % Parsed axioms : 71
% 0.09/0.24 % Removed by relevancy pruning/SinE : 0
% 0.09/0.24 % Initial clauses : 41
% 0.09/0.24 % Removed in clause preprocessing : 35
% 0.09/0.24 % Initial clauses in saturation : 6
% 0.09/0.24 % Processed clauses : 6
% 0.09/0.24 % ...of these trivial : 1
% 0.09/0.24 % ...subsumed : 0
% 0.09/0.24 % ...remaining for further processing : 5
% 0.09/0.24 % Other redundant clauses eliminated : 0
% 0.09/0.24 % Clauses deleted for lack of memory : 0
% 0.09/0.24 % Backward-subsumed : 0
% 0.09/0.24 % Backward-rewritten : 0
% 0.09/0.24 % Generated clauses : 2
% 0.09/0.24 % ...of the previous two non-redundant : 1
% 0.09/0.24 % ...aggressively subsumed : 0
% 0.09/0.24 % Contextual simplify-reflections : 0
% 0.09/0.24 % Paramodulations : 2
% 0.09/0.24 % Factorizations : 0
% 0.09/0.24 % NegExts : 0
% 0.09/0.24 % Equation resolutions : 0
% 0.09/0.24 % Disequality decompositions : 0
% 0.09/0.24 % Total rewrite steps : 2
% 0.09/0.24 % ...of those cached : 1
% 0.09/0.24 % Propositional unsat checks : 0
% 0.09/0.24 % Propositional check models : 0
% 0.09/0.24 % Propositional check unsatisfiable : 0
% 0.09/0.24 % Propositional clauses : 0
% 0.09/0.24 % Propositional clauses after purity: 0
% 0.09/0.24 % Propositional unsat core size : 0
% 0.09/0.24 % Propositional preprocessing time : 0.000
% 0.09/0.24 % Propositional encoding time : 0.000
% 0.09/0.24 % Propositional solver time : 0.000
% 0.09/0.24 % Success case prop preproc time : 0.000
% 0.09/0.24 % Success case prop encoding time : 0.000
% 0.09/0.24 % Success case prop solver time : 0.000
% 0.09/0.24 % Current number of processed clauses : 5
% 0.09/0.24 % Positive orientable unit clauses : 2
% 0.09/0.24 % Positive unorientable unit clauses: 0
% 0.09/0.24 % Negative unit clauses : 1
% 0.09/0.24 % Non-unit-clauses : 2
% 0.09/0.24 % Current number of unprocessed clauses: 1
% 0.09/0.24 % ...number of literals in the above : 2
% 0.09/0.24 % Current number of archived formulas : 0
% 0.09/0.24 % Current number of archived clauses : 0
% 0.09/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.24 % Non-unit clause-clause subsumptions : 0
% 0.09/0.24 % Unit Clause-clause subsumption calls : 0
% 0.09/0.24 % Rewrite failures with RHS unbound : 0
% 0.09/0.24 % BW rewrite match attempts : 0
% 0.09/0.24 % BW rewrite match successes : 0
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 2233
% 0.09/0.25 % Search garbage collected termcells : 316
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.003 s
% 0.09/0.25 % System time : 0.003 s
% 0.09/0.25 % Total time : 0.005 s
% 0.09/0.25 % Maximum resident set size: 3660 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.004 s
% 0.09/0.25 % System time : 0.009 s
% 0.09/0.25 % Total time : 0.013 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------