%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET753^4 : 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 : n002.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 08:22:19 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 18 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 93 ( 12 ~; 7 |; 12 &; 59 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 16 ^; 17 !; 5 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_30,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_37,type,
fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(decl_45,type,
epred1_0: $i > $o ).
thf(decl_46,type,
epred2_0: $i > $o ).
thf(decl_47,type,
esk1_0: $i > $i ).
thf(decl_48,type,
esk2_0: $i ).
thf(decl_49,type,
esk3_0: $i ).
thf(thm,conjecture,
! [X27: $i > $o,X28: $i > $o,X22: $i > $i] : ( subset @ ( fun_image @ X22 @ ( intersection @ X27 @ X28 ) ) @ ( intersection @ ( fun_image @ X22 @ X27 ) @ ( fun_image @ X22 @ X28 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Wu84tzmRpL/E---3.1_1300322.p',thm) ).
thf(intersection,axiom,
( intersection
= ( ^ [X9: $i > $o,X10: $i > $o,X4: $i] :
( ( X9 @ X4 )
& ( X10 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Wu84tzmRpL/E---3.1_1300322.p',intersection) ).
thf(subset,axiom,
( subset
= ( ^ [X16: $i > $o,X17: $i > $o] :
! [X4: $i] :
( ( X16 @ X4 )
=> ( X17 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Wu84tzmRpL/E---3.1_1300322.p',subset) ).
thf(fun_image,axiom,
( fun_image
= ( ^ [X22: $i > $i,X23: $i > $o,X3: $i] :
? [X1: $i] :
( ( X23 @ X1 )
& ( X3
= ( X22 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Wu84tzmRpL/E---3.1_1300322.p',fun_image) ).
thf(c_0_4,negated_conjecture,
~ ! [X27: $i > $o,X28: $i > $o,X22: $i > $i] : ( subset @ ( fun_image @ X22 @ ( intersection @ X27 @ X28 ) ) @ ( intersection @ ( fun_image @ X22 @ X27 ) @ ( fun_image @ X22 @ X28 ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_5,plain,
( intersection
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[intersection]) ).
thf(c_0_6,plain,
( subset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_7,plain,
( fun_image
= ( ^ [Z0: $i > $i,Z1: $i > $o,Z2: $i] :
? [X1: $i] :
( ( Z1 @ X1 )
& ( Z2
= ( Z0 @ X1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fun_image]) ).
thf(c_0_8,negated_conjecture,
~ ! [X27: $i > $o,X28: $i > $o,X22: $i > $i,X39: $i] :
( ? [X36: $i] :
( ( X27 @ X36 )
& ( X28 @ X36 )
& ( X39
= ( X22 @ X36 ) ) )
=> ( ? [X37: $i] :
( ( X27 @ X37 )
& ( X39
= ( X22 @ X37 ) ) )
& ? [X38: $i] :
( ( X28 @ X38 )
& ( X39
= ( X22 @ X38 ) ) ) ) ),
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,
! [X51: $i,X52: $i] :
( ( epred1_0 @ esk3_0 )
& ( epred2_0 @ esk3_0 )
& ( esk2_0
= ( esk1_0 @ esk3_0 ) )
& ( ~ ( epred1_0 @ X51 )
| ( esk2_0
!= ( esk1_0 @ X51 ) )
| ~ ( epred2_0 @ X52 )
| ( esk2_0
!= ( esk1_0 @ X52 ) ) ) ),
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,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ X1 )
| ( esk2_0
!= ( esk1_0 @ X1 ) )
| ~ ( epred2_0 @ X3 )
| ( esk2_0
!= ( esk1_0 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
epred1_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
( esk2_0
= ( esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] :
( ( ( esk1_0 @ X1 )
!= esk2_0 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
thf(c_0_14,negated_conjecture,
epred2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET753^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:43:37 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.Wu84tzmRpL/E---3.1_1300322.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_9 with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.25 % Starting sh1l with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho10 with 300s (1) cores
% 0.08/0.25 % post_as_ho1 with pid 1300353 completed with status 0
% 0.08/0.25 % Result found by post_as_ho1
% 0.08/0.25 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_9 with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HUHSF-FFSS33-SHSSMSNN
% 0.08/0.25 % partial match(4): HGHNF-FFSS33-SHHSMSBN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 1300357 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_9 with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HUHSF-FFSS33-SHSSMSNN
% 0.08/0.25 % partial match(4): HGHNF-FFSS33-SHHSMSBN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 45
% 0.08/0.25 % Removed by relevancy pruning/SinE : 0
% 0.08/0.25 % Initial clauses : 27
% 0.08/0.25 % Removed in clause preprocessing : 22
% 0.08/0.25 % Initial clauses in saturation : 5
% 0.08/0.25 % Processed clauses : 6
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 6
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 1
% 0.08/0.25 % Backward-rewritten : 0
% 0.08/0.25 % Generated clauses : 2
% 0.08/0.25 % ...of the previous two non-redundant : 1
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 2
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 2
% 0.08/0.25 % ...of those cached : 1
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 5
% 0.08/0.25 % Positive orientable unit clauses : 4
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 0
% 0.08/0.25 % Non-unit-clauses : 1
% 0.08/0.25 % Current number of unprocessed clauses: 0
% 0.08/0.25 % ...number of literals in the above : 0
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 1
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 1
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 1
% 0.08/0.25 % Non-unit clause-clause subsumptions : 1
% 0.08/0.25 % Unit Clause-clause subsumption calls : 0
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 0
% 0.08/0.25 % BW rewrite match successes : 0
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 1490
% 0.08/0.25 % Search garbage collected termcells : 277
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.004 s
% 0.08/0.25 % System time : 0.002 s
% 0.08/0.25 % Total time : 0.006 s
% 0.08/0.25 % Maximum resident set size: 3680 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.006 s
% 0.08/0.25 % System time : 0.006 s
% 0.08/0.25 % Total time : 0.012 s
% 0.08/0.25 % Maximum resident set size: 4608 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------