%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU577^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:24:35 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 143 ( 11 ~; 10 |; 4 &; 99 @)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
powersetE: $o ).
thf(decl_26,type,
subset: $i > $i > $o ).
thf(decl_27,type,
subsetI1: $o ).
thf(decl_28,type,
esk1_2: $i > $i > $i ).
thf(decl_29,type,
esk2_0: $i ).
thf(decl_30,type,
esk3_0: $i ).
thf(powersetE1,conjecture,
( powersetE
=> ( subsetI1
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qWiDO12PGw/E---3.1_1089824.p',powersetE1) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qWiDO12PGw/E---3.1_1089824.p',powersetE) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qWiDO12PGw/E---3.1_1089824.p',subsetI1) ).
thf(c_0_3,negated_conjecture,
~ ( powersetE
=> ( subsetI1
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[powersetE1]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X12: $i,X13: $i,X14: $i] :
( ( in @ X13 @ ( powerset @ X12 ) )
=> ( ( in @ X14 @ X13 )
=> ( in @ X14 @ X12 ) ) )
=> ( ! [X15: $i,X16: $i] :
( ! [X17: $i] :
( ( in @ X17 @ X15 )
=> ( in @ X17 @ X16 ) )
=> ( subset @ X15 @ X16 ) )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ X1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,powersetE]),subsetI1]) ).
thf(c_0_5,negated_conjecture,
! [X18: $i,X19: $i,X20: $i,X21: $i,X22: $i] :
( ( ~ ( in @ X19 @ ( powerset @ X18 ) )
| ~ ( in @ X20 @ X19 )
| ( in @ X20 @ X18 ) )
& ( ( in @ ( esk1_2 @ X21 @ X22 ) @ X21 )
| ( subset @ X21 @ X22 ) )
& ( ~ ( in @ ( esk1_2 @ X21 @ X22 ) @ X22 )
| ( subset @ X21 @ X22 ) )
& ( in @ esk3_0 @ ( powerset @ esk2_0 ) )
& ~ ( subset @ esk3_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_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
in @ esk3_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk2_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 )
| ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk1_2 @ esk3_0 @ X1 ) @ esk2_0 )
| ( subset @ esk3_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
~ ( subset @ esk3_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU577^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n020.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 13:52:34 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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.qWiDO12PGw/E---3.1_1089824.p
% 0.09/0.24 % Version: 3.5.1-ho
% 0.09/0.24 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.09/0.24 % Starting post_as_ho8 with 300s (1) cores
% 0.09/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.24 % Starting post_as_ho2 with 300s (1) cores
% 0.09/0.24 % post_as_ho2 with pid 1089840 completed with status 0
% 0.09/0.24 % Result found by post_as_ho2
% 0.09/0.24 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.09/0.24 % Starting post_as_ho8 with 300s (1) cores
% 0.09/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.24 % Starting post_as_ho2 with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HGUNF-FFSF21-SFFFMFNN
% 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 1089841 completed with status 0
% 0.09/0.24 % Result found by SubtermCWHack
% 0.09/0.24 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.09/0.24 % Starting post_as_ho8 with 300s (1) cores
% 0.09/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.24 % Starting post_as_ho2 with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.24 % No SInE strategy applied
% 0.09/0.24 % Search class: HGUNF-FFSF21-SFFFMFNN
% 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 : 8
% 0.09/0.24 % Removed by relevancy pruning/SinE : 0
% 0.09/0.24 % Initial clauses : 10
% 0.09/0.24 % Removed in clause preprocessing : 5
% 0.09/0.24 % Initial clauses in saturation : 5
% 0.09/0.24 % Processed clauses : 8
% 0.09/0.24 % ...of these trivial : 0
% 0.09/0.24 % ...subsumed : 0
% 0.09/0.24 % ...remaining for further processing : 8
% 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 : 5
% 0.09/0.24 % ...of the previous two non-redundant : 4
% 0.09/0.24 % ...aggressively subsumed : 0
% 0.09/0.24 % Contextual simplify-reflections : 0
% 0.09/0.24 % Paramodulations : 5
% 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 : 0
% 0.09/0.24 % ...of those cached : 0
% 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 : 8
% 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 : 5
% 0.09/0.24 % Current number of unprocessed clauses: 1
% 0.09/0.24 % ...number of literals in the above : 3
% 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) : 3
% 0.09/0.24 % Rec. Clause-clause subsumption calls : 3
% 0.09/0.24 % Non-unit clause-clause subsumptions : 0
% 0.09/0.24 % Unit Clause-clause subsumption calls : 2
% 0.09/0.24 % Rewrite failures with RHS unbound : 0
% 0.09/0.24 % BW rewrite match attempts : 2
% 0.09/0.24 % BW rewrite match successes : 0
% 0.09/0.24 % Condensation attempts : 0
% 0.09/0.24 % Condensation successes : 0
% 0.09/0.24 % Termbank termtop insertions : 698
% 0.09/0.24 % Search garbage collected termcells : 214
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.003 s
% 0.09/0.24 % System time : 0.001 s
% 0.09/0.24 % Total time : 0.004 s
% 0.09/0.24 % Maximum resident set size: 3632 pages
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.005 s
% 0.09/0.24 % System time : 0.005 s
% 0.09/0.24 % Total time : 0.010 s
% 0.09/0.24 % Maximum resident set size: 4864 pages
% 0.09/0.24 % E exiting
%------------------------------------------------------------------------------