%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET615^3 : 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 : n010.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 08:22:13 AM UTC 2026
% Result : Theorem 0.09s 0.22s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 6 equ; 0 cnn)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 208 ( 38 ~; 50 |; 16 &; 103 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 22 ( 12 ^; 10 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_28,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $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] :
( ( setminus @ ( union @ X22 @ X23 ) @ X24 )
= ( union @ ( setminus @ X22 @ X24 ) @ ( setminus @ X23 @ X24 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tUZfUlZup8/E---3.1_2864481.p',thm) ).
thf(union,axiom,
( union
= ( ^ [X5: $i > $o,X6: $i > $o,X4: $i] :
( ( X5 @ X4 )
| ( X6 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tUZfUlZup8/E---3.1_2864481.p',union) ).
thf(setminus,axiom,
( setminus
= ( ^ [X11: $i > $o,X12: $i > $o,X4: $i] :
( ( X11 @ X4 )
& ~ ( X12 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tUZfUlZup8/E---3.1_2864481.p',setminus) ).
thf(c_0_3,negated_conjecture,
~ ! [X22: $i > $o,X23: $i > $o,X24: $i > $o] :
( ( setminus @ ( union @ X22 @ X23 ) @ X24 )
= ( union @ ( setminus @ X22 @ X24 ) @ ( setminus @ 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,
( setminus
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setminus]) ).
thf(c_0_6,negated_conjecture,
~ ! [X22: $i > $o,X23: $i > $o,X24: $i > $o,X28: $i] :
( ( ( ( X22 @ X28 )
| ( X23 @ X28 ) )
& ~ ( X24 @ X28 ) )
<=> ( ( ( X22 @ X28 )
& ~ ( X24 @ X28 ) )
| ( ( X23 @ X28 )
& ~ ( X24 @ X28 ) ) ) ),
inference(fof_simplification,[status(thm)],[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,
( ( ~ ( epred1_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) )
& ( ~ ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) )
& ( ~ ( epred1_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) )
& ( ~ ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 ) )
& ( ( epred2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) )
& ( ~ ( epred3_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) )
& ( ( epred2_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) )
& ( ~ ( epred3_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) )
& ( ( epred2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 ) )
& ( ~ ( epred3_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 ) )
& ( ( epred2_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 ) )
& ( ~ ( epred3_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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,
( ( epred3_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
( ~ ( epred3_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 )
| ~ ( epred3_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
( ( epred2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
( ( epred3_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
~ ( epred3_0 @ esk1_0 ),
inference(cn,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
( ( epred3_0 @ esk1_0 )
| ( epred3_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
( ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
~ ( epred1_0 @ esk1_0 ),
inference(sr,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
( ( epred3_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
epred2_0 @ esk1_0,
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET615^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n010.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 13:39:48 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 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.tUZfUlZup8/E---3.1_2864481.p
% 0.09/0.22 % Version: 3.5.1-ho
% 0.09/0.22 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.09/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.22 % Starting new_ho_9 with 1500s (5) cores
% 0.09/0.22 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.22 % Starting sh1l with 300s (1) cores
% 0.09/0.22 % Starting post_as_ho10 with 300s (1) cores
% 0.09/0.22 % post_as_ho1 with pid 2864511 completed with status 0
% 0.09/0.22 % Result found by post_as_ho1
% 0.09/0.22 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.09/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.22 % Starting new_ho_9 with 1500s (5) cores
% 0.09/0.22 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.22 % No SInE strategy applied
% 0.09/0.22 % Search class: HGUNF-FFSF00-SHSSMFNN
% 0.09/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.22 % SubtermCWHack with pid 2864519 completed with status 0
% 0.09/0.22 % Result found by SubtermCWHack
% 0.09/0.22 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.09/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.22 % Starting new_ho_9 with 1500s (5) cores
% 0.09/0.22 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.22 % No SInE strategy applied
% 0.09/0.22 % Search class: HGUNF-FFSF00-SHSSMFNN
% 0.09/0.22 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.22 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.22 % Preprocessing time : 0.001 s
% 0.09/0.22
% 0.09/0.22 % Proof found!
% 0.09/0.22 % SZS status Theorem
% 0.09/0.22 % SZS output start CNFRefutation
% See solution above
% 0.09/0.22 % Parsed axioms : 29
% 0.09/0.22 % Removed by relevancy pruning/SinE : 0
% 0.09/0.22 % Initial clauses : 26
% 0.09/0.22 % Removed in clause preprocessing : 14
% 0.09/0.22 % Initial clauses in saturation : 12
% 0.09/0.22 % Processed clauses : 7
% 0.09/0.22 % ...of these trivial : 0
% 0.09/0.22 % ...subsumed : 2
% 0.09/0.22 % ...remaining for further processing : 4
% 0.09/0.22 % Other redundant clauses eliminated : 0
% 0.09/0.22 % Clauses deleted for lack of memory : 0
% 0.09/0.22 % Backward-subsumed : 0
% 0.09/0.22 % Backward-rewritten : 0
% 0.09/0.22 % Generated clauses : 1
% 0.09/0.22 % ...of the previous two non-redundant : 1
% 0.09/0.22 % ...aggressively subsumed : 0
% 0.09/0.22 % Contextual simplify-reflections : 0
% 0.09/0.22 % Paramodulations : 0
% 0.09/0.22 % Factorizations : 0
% 0.09/0.22 % NegExts : 0
% 0.09/0.22 % Equation resolutions : 0
% 0.09/0.22 % Disequality decompositions : 0
% 0.09/0.22 % Total rewrite steps : 1
% 0.09/0.22 % ...of those cached : 0
% 0.09/0.22 % Propositional unsat checks : 0
% 0.09/0.22 % Propositional check models : 0
% 0.09/0.22 % Propositional check unsatisfiable : 0
% 0.09/0.22 % Propositional clauses : 0
% 0.09/0.22 % Propositional clauses after purity: 0
% 0.09/0.22 % Propositional unsat core size : 0
% 0.09/0.22 % Propositional preprocessing time : 0.000
% 0.09/0.22 % Propositional encoding time : 0.000
% 0.09/0.22 % Propositional solver time : 0.000
% 0.09/0.22 % Success case prop preproc time : 0.000
% 0.09/0.22 % Success case prop encoding time : 0.000
% 0.09/0.22 % Success case prop solver time : 0.000
% 0.09/0.22 % Current number of processed clauses : 3
% 0.09/0.22 % Positive orientable unit clauses : 1
% 0.09/0.22 % Positive unorientable unit clauses: 0
% 0.09/0.22 % Negative unit clauses : 2
% 0.09/0.22 % Non-unit-clauses : 0
% 0.09/0.22 % Current number of unprocessed clauses: 6
% 0.09/0.22 % ...number of literals in the above : 18
% 0.09/0.22 % Current number of archived formulas : 0
% 0.09/0.22 % Current number of archived clauses : 1
% 0.09/0.22 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.22 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.22 % Non-unit clause-clause subsumptions : 0
% 0.09/0.22 % Unit Clause-clause subsumption calls : 0
% 0.09/0.22 % Rewrite failures with RHS unbound : 0
% 0.09/0.22 % BW rewrite match attempts : 0
% 0.09/0.22 % BW rewrite match successes : 0
% 0.09/0.22 % Condensation attempts : 0
% 0.09/0.22 % Condensation successes : 0
% 0.09/0.22 % Termbank termtop insertions : 1384
% 0.09/0.22 % Search garbage collected termcells : 242
% 0.09/0.22
% 0.09/0.22 % -------------------------------------------------
% 0.09/0.22 % User time : 0.002 s
% 0.09/0.22 % System time : 0.003 s
% 0.09/0.22 % Total time : 0.005 s
% 0.09/0.22 % Maximum resident set size: 3612 pages
% 0.09/0.22
% 0.09/0.22 % -------------------------------------------------
% 0.09/0.22 % User time : 0.003 s
% 0.09/0.22 % System time : 0.005 s
% 0.09/0.22 % Total time : 0.008 s
% 0.09/0.22 % Maximum resident set size: 4864 pages
% 0.09/0.22 % E exiting
%------------------------------------------------------------------------------