%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU737^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:25:25 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 0 equ; 0 cnn)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 463 ( 40 ~; 38 |; 8 &; 334 @)
% ( 3 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
subset: $i > $i > $o ).
thf(decl_26,type,
setminus: $i > $i > $i ).
thf(decl_27,type,
complementT_lem: $o ).
thf(decl_28,type,
subsetTI: $o ).
thf(decl_29,type,
contraSubsetComplement: $o ).
thf(decl_30,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(complementTcontraSubset,conjecture,
( complementT_lem
=> ( subsetTI
=> ( contraSubsetComplement
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
=> ( subset @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WMePiXXsdx/E---3.1_148217.p',complementTcontraSubset) ).
thf(complementT_lem,axiom,
( complementT_lem
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WMePiXXsdx/E---3.1_148217.p',complementT_lem) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X3 ) ) )
=> ( subset @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WMePiXXsdx/E---3.1_148217.p',subsetTI) ).
thf(contraSubsetComplement,axiom,
( contraSubsetComplement
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X3 )
=> ( in @ X4 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WMePiXXsdx/E---3.1_148217.p',contraSubsetComplement) ).
thf(c_0_4,negated_conjecture,
~ ( complementT_lem
=> ( subsetTI
=> ( contraSubsetComplement
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
=> ( subset @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[complementTcontraSubset]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X18: $i,X19: $i] :
( ( in @ X19 @ ( powerset @ X18 ) )
=> ( in @ ( setminus @ X18 @ X19 ) @ ( powerset @ X18 ) ) )
=> ( ! [X20: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X20 ) )
=> ! [X22: $i] :
( ( in @ X22 @ ( powerset @ X20 ) )
=> ( ! [X23: $i] :
( ( in @ X23 @ X20 )
=> ( ( in @ X23 @ X21 )
=> ( in @ X23 @ X22 ) ) )
=> ( subset @ X21 @ X22 ) ) ) )
=> ( ! [X24: $i,X25: $i] :
( ( in @ X25 @ ( powerset @ X24 ) )
=> ! [X26: $i] :
( ( in @ X26 @ ( powerset @ X24 ) )
=> ( ( subset @ X25 @ ( setminus @ X24 @ X26 ) )
=> ! [X27: $i] :
( ( in @ X27 @ X24 )
=> ( ( in @ X27 @ X26 )
=> ( in @ X27 @ ( setminus @ X24 @ X25 ) ) ) ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
=> ( subset @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,complementT_lem]),subsetTI]),contraSubsetComplement]) ).
thf(c_0_6,negated_conjecture,
! [X28: $i,X29: $i,X30: $i,X31: $i,X32: $i,X34: $i,X35: $i,X36: $i,X37: $i] :
( ( ~ ( in @ X29 @ ( powerset @ X28 ) )
| ( in @ ( setminus @ X28 @ X29 ) @ ( powerset @ X28 ) ) )
& ( ( in @ ( esk1_3 @ X30 @ X31 @ X32 ) @ X30 )
| ( subset @ X31 @ X32 )
| ~ ( in @ X32 @ ( powerset @ X30 ) )
| ~ ( in @ X31 @ ( powerset @ X30 ) ) )
& ( ( in @ ( esk1_3 @ X30 @ X31 @ X32 ) @ X31 )
| ( subset @ X31 @ X32 )
| ~ ( in @ X32 @ ( powerset @ X30 ) )
| ~ ( in @ X31 @ ( powerset @ X30 ) ) )
& ( ~ ( in @ ( esk1_3 @ X30 @ X31 @ X32 ) @ X32 )
| ( subset @ X31 @ X32 )
| ~ ( in @ X32 @ ( powerset @ X30 ) )
| ~ ( in @ X31 @ ( powerset @ X30 ) ) )
& ( ~ ( in @ X35 @ ( powerset @ X34 ) )
| ~ ( in @ X36 @ ( powerset @ X34 ) )
| ~ ( subset @ X35 @ ( setminus @ X34 @ X36 ) )
| ~ ( in @ X37 @ X34 )
| ~ ( in @ X37 @ X36 )
| ( in @ X37 @ ( setminus @ X34 @ X35 ) ) )
& ( in @ esk3_0 @ ( powerset @ esk2_0 ) )
& ( in @ esk4_0 @ ( powerset @ esk2_0 ) )
& ( subset @ esk3_0 @ ( setminus @ esk2_0 @ esk4_0 ) )
& ~ ( subset @ esk4_0 @ ( setminus @ esk2_0 @ esk3_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_5])])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ X4 @ ( setminus @ X2 @ X1 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( subset @ X1 @ ( setminus @ X2 @ X3 ) )
| ~ ( in @ X4 @ X2 )
| ~ ( in @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
subset @ esk3_0 @ ( setminus @ esk2_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
in @ esk4_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
in @ esk3_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ ( setminus @ esk2_0 @ esk3_0 ) )
| ~ ( in @ X1 @ esk4_0 )
| ~ ( in @ X1 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10])]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ ( setminus @ esk2_0 @ esk3_0 ) )
| ~ ( in @ ( esk1_3 @ X2 @ X1 @ ( setminus @ esk2_0 @ esk3_0 ) ) @ esk4_0 )
| ~ ( in @ ( esk1_3 @ X2 @ X1 @ ( setminus @ esk2_0 @ esk3_0 ) ) @ esk2_0 )
| ~ ( in @ ( setminus @ esk2_0 @ esk3_0 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_15,negated_conjecture,
~ ( subset @ esk4_0 @ ( setminus @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ~ ( in @ ( esk1_3 @ X1 @ esk4_0 @ ( setminus @ esk2_0 @ esk3_0 ) ) @ esk2_0 )
| ~ ( in @ ( setminus @ esk2_0 @ esk3_0 ) @ ( powerset @ X1 ) )
| ~ ( in @ esk4_0 @ ( powerset @ X1 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ( subset @ X2 @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_18,negated_conjecture,
~ ( in @ ( setminus @ esk2_0 @ esk3_0 ) @ ( powerset @ esk2_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_9])]),c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU737^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.15 % Computer : n018.cluster.edu
% 0.08/0.15 % Model : x86_64 x86_64
% 0.08/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.15 % Memory : 8046.5625MB
% 0.08/0.15 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 14:21:11 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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.WMePiXXsdx/E---3.1_148217.p
% 0.08/0.23 % Version: 3.5.1-ho
% 0.08/0.23 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.23 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.23 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.23 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.23 % post_as_ho2 with pid 148252 completed with status 0
% 0.08/0.23 % Result found by post_as_ho2
% 0.08/0.23 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.23 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.23 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.23 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.23 % No SInE strategy applied
% 0.08/0.23 % Search class: HGUNF-FFSS32-SFFFMFNN
% 0.08/0.23 % partial match(1): HGUNF-FFSF32-SFFFMFNN
% 0.08/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.23 % SubtermCWHack with pid 148257 completed with status 0
% 0.08/0.23 % Result found by SubtermCWHack
% 0.08/0.23 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.23 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.23 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.23 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.23 % No SInE strategy applied
% 0.08/0.23 % Search class: HGUNF-FFSS32-SFFFMFNN
% 0.08/0.23 % partial match(1): HGUNF-FFSF32-SFFFMFNN
% 0.08/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.23 % Preprocessing time : 0.001 s
% 0.08/0.23
% 0.08/0.23 % Proof found!
% 0.08/0.23 % SZS status Theorem
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23 % Parsed axioms : 11
% 0.08/0.23 % Removed by relevancy pruning/SinE : 0
% 0.08/0.23 % Initial clauses : 16
% 0.08/0.23 % Removed in clause preprocessing : 7
% 0.08/0.23 % Initial clauses in saturation : 9
% 0.08/0.23 % Processed clauses : 21
% 0.08/0.23 % ...of these trivial : 0
% 0.08/0.23 % ...subsumed : 0
% 0.08/0.23 % ...remaining for further processing : 21
% 0.08/0.23 % Other redundant clauses eliminated : 0
% 0.08/0.23 % Clauses deleted for lack of memory : 0
% 0.08/0.23 % Backward-subsumed : 0
% 0.08/0.23 % Backward-rewritten : 0
% 0.08/0.23 % Generated clauses : 15
% 0.08/0.23 % ...of the previous two non-redundant : 14
% 0.08/0.23 % ...aggressively subsumed : 0
% 0.08/0.23 % Contextual simplify-reflections : 1
% 0.08/0.23 % Paramodulations : 15
% 0.08/0.23 % Factorizations : 0
% 0.08/0.23 % NegExts : 0
% 0.08/0.23 % Equation resolutions : 0
% 0.08/0.23 % Disequality decompositions : 0
% 0.08/0.23 % Total rewrite steps : 4
% 0.08/0.23 % ...of those cached : 2
% 0.08/0.23 % Propositional unsat checks : 0
% 0.08/0.23 % Propositional check models : 0
% 0.08/0.23 % Propositional check unsatisfiable : 0
% 0.08/0.23 % Propositional clauses : 0
% 0.08/0.23 % Propositional clauses after purity: 0
% 0.08/0.23 % Propositional unsat core size : 0
% 0.08/0.23 % Propositional preprocessing time : 0.000
% 0.08/0.23 % Propositional encoding time : 0.000
% 0.08/0.23 % Propositional solver time : 0.000
% 0.08/0.23 % Success case prop preproc time : 0.000
% 0.08/0.23 % Success case prop encoding time : 0.000
% 0.08/0.23 % Success case prop solver time : 0.000
% 0.08/0.23 % Current number of processed clauses : 21
% 0.08/0.23 % Positive orientable unit clauses : 5
% 0.08/0.23 % Positive unorientable unit clauses: 0
% 0.08/0.23 % Negative unit clauses : 2
% 0.08/0.23 % Non-unit-clauses : 14
% 0.08/0.23 % Current number of unprocessed clauses: 2
% 0.08/0.23 % ...number of literals in the above : 10
% 0.08/0.23 % Current number of archived formulas : 0
% 0.08/0.23 % Current number of archived clauses : 0
% 0.08/0.23 % Clause-clause subsumption calls (NU) : 66
% 0.08/0.23 % Rec. Clause-clause subsumption calls : 26
% 0.08/0.23 % Non-unit clause-clause subsumptions : 1
% 0.08/0.23 % Unit Clause-clause subsumption calls : 3
% 0.08/0.23 % Rewrite failures with RHS unbound : 0
% 0.08/0.23 % BW rewrite match attempts : 0
% 0.08/0.23 % BW rewrite match successes : 0
% 0.08/0.23 % Condensation attempts : 0
% 0.08/0.23 % Condensation successes : 0
% 0.08/0.23 % Termbank termtop insertions : 1904
% 0.08/0.23 % Search garbage collected termcells : 453
% 0.08/0.23
% 0.08/0.23 % -------------------------------------------------
% 0.08/0.23 % User time : 0.005 s
% 0.08/0.23 % System time : 0.001 s
% 0.08/0.23 % Total time : 0.006 s
% 0.08/0.23 % Maximum resident set size: 3580 pages
% 0.08/0.23
% 0.08/0.23 % -------------------------------------------------
% 0.08/0.23 % User time : 0.005 s
% 0.08/0.23 % System time : 0.004 s
% 0.08/0.23 % Total time : 0.009 s
% 0.08/0.23 % Maximum resident set size: 4864 pages
% 0.08/0.23 % E exiting
%------------------------------------------------------------------------------