%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET606^3 : 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 08:22:10 AM UTC 2026
% Result : Theorem 0.11s 0.27s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 6 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 115 ( 24 ~; 20 |; 12 &; 58 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 19 ( 12 ^; 7 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_30,type,
intersection: ( $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,
esk1_0: $i ).
thf(thm,conjecture,
! [X22: $i > $o,X23: $i > $o] :
( ( setminus @ X22 @ ( intersection @ X22 @ X23 ) )
= ( setminus @ X22 @ X23 ) ),
file('/export/starexec/sandbox2/tmp/tmp.lD8I8pVHzW/E---3.1_2667470.p',thm) ).
thf(intersection,axiom,
( intersection
= ( ^ [X9: $i > $o,X10: $i > $o,X4: $i] :
( ( X9 @ X4 )
& ( X10 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lD8I8pVHzW/E---3.1_2667470.p',intersection) ).
thf(setminus,axiom,
( setminus
= ( ^ [X11: $i > $o,X12: $i > $o,X4: $i] :
( ( X11 @ X4 )
& ~ ( X12 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lD8I8pVHzW/E---3.1_2667470.p',setminus) ).
thf(c_0_3,negated_conjecture,
~ ! [X22: $i > $o,X23: $i > $o] :
( ( setminus @ X22 @ ( intersection @ X22 @ X23 ) )
= ( setminus @ X22 @ X23 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_4,plain,
( intersection
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[intersection]) ).
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,X26: $i] :
( ( ( X22 @ X26 )
& ~ ( ( X22 @ X26 )
& ( X23 @ X26 ) ) )
<=> ( ( X22 @ X26 )
& ~ ( X23 @ X26 ) ) ),
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 )
| ~ ( epred1_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) )
& ( ( epred2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk1_0 ) )
& ( ( epred1_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 ) )
& ( ~ ( epred2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 ) )
& ( ( epred1_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 ) )
& ( ~ ( epred2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 )
| ~ ( epred2_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,
( ( epred2_0 @ esk1_0 )
| ( epred2_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,
( ( epred1_0 @ esk1_0 )
| ( epred1_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 )
| ~ ( epred2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
( ( epred2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
epred1_0 @ esk1_0,
inference(cn,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
( ~ ( epred1_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
epred2_0 @ esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET606^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n014.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 13:38:45 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.11/0.25 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.lD8I8pVHzW/E---3.1_2667470.p
% 0.11/0.27 % Version: 3.5.1-ho
% 0.11/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.11/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.11/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.11/0.27 % Starting sh1l with 300s (1) cores
% 0.11/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.11/0.27 % post_as_ho10 with pid 2667487 completed with status 0
% 0.11/0.27 % Result found by post_as_ho10
% 0.11/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.11/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.11/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.11/0.27 % Starting sh1l with 300s (1) cores
% 0.11/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.11/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.27 % No SInE strategy applied
% 0.11/0.27 % Search class: HHHNF-FFSF00-SHSSMFNN
% 0.11/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.27 % SubtermCWHack with pid 2667488 completed with status 0
% 0.11/0.27 % Result found by SubtermCWHack
% 0.11/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.11/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.11/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.11/0.27 % Starting sh1l with 300s (1) cores
% 0.11/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.11/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.27 % No SInE strategy applied
% 0.11/0.27 % Search class: HHHNF-FFSF00-SHSSMFNN
% 0.11/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.27 % Preprocessing time : 0.001 s
% 0.11/0.27
% 0.11/0.27 % Proof found!
% 0.11/0.27 % SZS status Theorem
% 0.11/0.27 % SZS output start CNFRefutation
% See solution above
% 0.11/0.27 % Parsed axioms : 29
% 0.11/0.27 % Removed by relevancy pruning/SinE : 0
% 0.11/0.27 % Initial clauses : 20
% 0.11/0.27 % Removed in clause preprocessing : 16
% 0.11/0.27 % Initial clauses in saturation : 4
% 0.11/0.27 % Processed clauses : 4
% 0.11/0.27 % ...of these trivial : 1
% 0.11/0.27 % ...subsumed : 0
% 0.11/0.27 % ...remaining for further processing : 2
% 0.11/0.27 % Other redundant clauses eliminated : 0
% 0.11/0.27 % Clauses deleted for lack of memory : 0
% 0.11/0.27 % Backward-subsumed : 0
% 0.11/0.27 % Backward-rewritten : 0
% 0.11/0.27 % Generated clauses : 0
% 0.11/0.27 % ...of the previous two non-redundant : 0
% 0.11/0.27 % ...aggressively subsumed : 0
% 0.11/0.27 % Contextual simplify-reflections : 0
% 0.11/0.27 % Paramodulations : 0
% 0.11/0.27 % Factorizations : 0
% 0.11/0.27 % NegExts : 0
% 0.11/0.27 % Equation resolutions : 0
% 0.11/0.27 % Disequality decompositions : 0
% 0.11/0.27 % Total rewrite steps : 4
% 0.11/0.27 % ...of those cached : 2
% 0.11/0.27 % Propositional unsat checks : 0
% 0.11/0.27 % Propositional check models : 0
% 0.11/0.27 % Propositional check unsatisfiable : 0
% 0.11/0.27 % Propositional clauses : 0
% 0.11/0.27 % Propositional clauses after purity: 0
% 0.11/0.27 % Propositional unsat core size : 0
% 0.11/0.27 % Propositional preprocessing time : 0.000
% 0.11/0.27 % Propositional encoding time : 0.000
% 0.11/0.27 % Propositional solver time : 0.000
% 0.11/0.27 % Success case prop preproc time : 0.000
% 0.11/0.27 % Success case prop encoding time : 0.000
% 0.11/0.27 % Success case prop solver time : 0.000
% 0.11/0.27 % Current number of processed clauses : 2
% 0.11/0.27 % Positive orientable unit clauses : 2
% 0.11/0.27 % Positive unorientable unit clauses: 0
% 0.11/0.27 % Negative unit clauses : 0
% 0.11/0.27 % Non-unit-clauses : 0
% 0.11/0.27 % Current number of unprocessed clauses: 0
% 0.11/0.27 % ...number of literals in the above : 0
% 0.11/0.27 % Current number of archived formulas : 0
% 0.11/0.27 % Current number of archived clauses : 0
% 0.11/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.27 % Non-unit clause-clause subsumptions : 0
% 0.11/0.27 % Unit Clause-clause subsumption calls : 0
% 0.11/0.27 % Rewrite failures with RHS unbound : 0
% 0.11/0.27 % BW rewrite match attempts : 0
% 0.11/0.27 % BW rewrite match successes : 0
% 0.11/0.27 % Condensation attempts : 0
% 0.11/0.27 % Condensation successes : 0
% 0.11/0.27 % Termbank termtop insertions : 1043
% 0.11/0.27 % Search garbage collected termcells : 161
% 0.11/0.27
% 0.11/0.27 % -------------------------------------------------
% 0.11/0.27 % User time : 0.002 s
% 0.11/0.27 % System time : 0.002 s
% 0.11/0.27 % Total time : 0.004 s
% 0.11/0.27 % Maximum resident set size: 3656 pages
% 0.11/0.27
% 0.11/0.27 % -------------------------------------------------
% 0.11/0.27 % User time : 0.005 s
% 0.11/0.27 % System time : 0.005 s
% 0.11/0.27 % Total time : 0.011 s
% 0.11/0.27 % Maximum resident set size: 4864 pages
% 0.11/0.27 % E exiting
%------------------------------------------------------------------------------