%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU458^1 : 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 : n011.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 08:26:04 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 6 equ; 0 cnn)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 160 ( 24 ~; 27 |; 8 &; 100 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 13 ( 8 ^; 5 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(decl_34,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_52,type,
epred1_0: $i > $i > $o ).
thf(decl_53,type,
esk1_0: $i ).
thf(decl_54,type,
esk2_0: $i ).
thf(symmetric_closure_op_is_idempotent,conjecture,
idem @ sc,
file('/export/starexec/sandbox2/tmp/tmp.V3jkPtZct9/E---3.1_111958.p',symmetric_closure_op_is_idempotent) ).
thf(idempotent,axiom,
( idem
= ( ^ [X5: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o] :
( ( X5 @ ( X5 @ X1 ) )
= ( X5 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.V3jkPtZct9/E---3.1_111958.p',idempotent) ).
thf(symmetric_closure,axiom,
( sc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
( ( X1 @ X4 @ X3 )
| ( X1 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.V3jkPtZct9/E---3.1_111958.p',symmetric_closure) ).
thf(c_0_3,negated_conjecture,
~ ( idem @ sc ),
inference(assume_negation,[status(cth)],[symmetric_closure_op_is_idempotent]) ).
thf(c_0_4,plain,
( idem
= ( ^ [Z0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o] :
( ( Z0 @ ( Z0 @ X1 ) )
= ( Z0 @ X1 ) ) ) ),
inference(fof_simplification,[status(thm)],[idempotent]) ).
thf(c_0_5,plain,
( sc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( ( Z0 @ Z2 @ Z1 )
| ( Z0 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[symmetric_closure]) ).
thf(c_0_6,negated_conjecture,
~ ! [X157: $i > $i > $o,X158: $i,X159: $i] :
( ( ( X157 @ X158 @ X159 )
| ( X157 @ X159 @ X158 )
| ( X157 @ X159 @ X158 )
| ( X157 @ X158 @ X159 ) )
<=> ( ( X157 @ X159 @ X158 )
| ( X157 @ X158 @ X159 ) ) ),
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 @ esk2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred1_0 @ esk2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) )
& ( ~ ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) )
& ( ~ ( epred1_0 @ esk2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) )
& ( ~ ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) )
& ( ~ ( epred1_0 @ esk2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 @ esk1_0 )
| ( epred1_0 @ esk2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 @ esk2_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,
( ( epred1_0 @ esk1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 @ esk1_0 )
| ( epred1_0 @ esk2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
( ~ ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
( ~ ( epred1_0 @ esk2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
~ ( epred1_0 @ esk1_0 @ esk2_0 ),
inference(cn,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
~ ( epred1_0 @ esk2_0 @ esk1_0 ),
inference(cn,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU458^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n011.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:41:46 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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.V3jkPtZct9/E---3.1_111958.p
% 0.10/0.26 % Version: 3.5.1-ho
% 0.10/0.26 % Preprocessing class: HSSSSMSSMLSNHHN.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.10/0.26 % Starting post_as_ho11 with 300s (1) cores
% 0.10/0.26 % Starting ho_unfolding_1 with 300s (1) cores
% 0.10/0.26 % ho_unfolding_1 with pid 111975 completed with status 0
% 0.10/0.26 % Result found by ho_unfolding_1
% 0.10/0.26 % Preprocessing class: HSSSSMSSMLSNHHN.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.10/0.26 % Starting post_as_ho11 with 300s (1) cores
% 0.10/0.26 % Starting ho_unfolding_1 with 300s (1) cores
% 0.10/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.26 % No SInE strategy applied
% 0.10/0.26 % Search class: HGHNF-FFSF00-SHHSMFNN
% 0.10/0.26 % partial match(1): HGHNF-FFSF00-SHSSMFNN
% 0.10/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.26 % SubtermCWHack with pid 111976 completed with status 0
% 0.10/0.26 % Result found by SubtermCWHack
% 0.10/0.26 % Preprocessing class: HSSSSMSSMLSNHHN.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.10/0.26 % Starting post_as_ho11 with 300s (1) cores
% 0.10/0.26 % Starting ho_unfolding_1 with 300s (1) cores
% 0.10/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.26 % No SInE strategy applied
% 0.10/0.26 % Search class: HGHNF-FFSF00-SHHSMFNN
% 0.10/0.26 % partial match(1): HGHNF-FFSF00-SHSSMFNN
% 0.10/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.26 % Preprocessing time : 0.001 s
% 0.10/0.26
% 0.10/0.26 % Proof found!
% 0.10/0.26 % SZS status Theorem
% 0.10/0.26 % SZS output start CNFRefutation
% See solution above
% 0.10/0.27 % Parsed axioms : 59
% 0.10/0.27 % Removed by relevancy pruning/SinE : 0
% 0.10/0.27 % Initial clauses : 38
% 0.10/0.27 % Removed in clause preprocessing : 29
% 0.10/0.27 % Initial clauses in saturation : 9
% 0.10/0.27 % Processed clauses : 5
% 0.10/0.27 % ...of these trivial : 0
% 0.10/0.27 % ...subsumed : 2
% 0.10/0.27 % ...remaining for further processing : 2
% 0.10/0.27 % Other redundant clauses eliminated : 0
% 0.10/0.27 % Clauses deleted for lack of memory : 0
% 0.10/0.27 % Backward-subsumed : 0
% 0.10/0.27 % Backward-rewritten : 0
% 0.10/0.27 % Generated clauses : 0
% 0.10/0.27 % ...of the previous two non-redundant : 0
% 0.10/0.27 % ...aggressively subsumed : 0
% 0.10/0.27 % Contextual simplify-reflections : 0
% 0.10/0.27 % Paramodulations : 0
% 0.10/0.27 % Factorizations : 0
% 0.10/0.27 % NegExts : 0
% 0.10/0.27 % Equation resolutions : 0
% 0.10/0.27 % Disequality decompositions : 0
% 0.10/0.27 % Total rewrite steps : 0
% 0.10/0.27 % ...of those cached : 0
% 0.10/0.27 % Propositional unsat checks : 0
% 0.10/0.27 % Propositional check models : 0
% 0.10/0.27 % Propositional check unsatisfiable : 0
% 0.10/0.27 % Propositional clauses : 0
% 0.10/0.27 % Propositional clauses after purity: 0
% 0.10/0.27 % Propositional unsat core size : 0
% 0.10/0.27 % Propositional preprocessing time : 0.000
% 0.10/0.27 % Propositional encoding time : 0.000
% 0.10/0.27 % Propositional solver time : 0.000
% 0.10/0.27 % Success case prop preproc time : 0.000
% 0.10/0.27 % Success case prop encoding time : 0.000
% 0.10/0.27 % Success case prop solver time : 0.000
% 0.10/0.27 % Current number of processed clauses : 2
% 0.10/0.27 % Positive orientable unit clauses : 0
% 0.10/0.27 % Positive unorientable unit clauses: 0
% 0.10/0.27 % Negative unit clauses : 2
% 0.10/0.27 % Non-unit-clauses : 0
% 0.10/0.27 % Current number of unprocessed clauses: 4
% 0.10/0.27 % ...number of literals in the above : 8
% 0.10/0.27 % Current number of archived formulas : 0
% 0.10/0.27 % Current number of archived clauses : 0
% 0.10/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.27 % Non-unit clause-clause subsumptions : 0
% 0.10/0.27 % Unit Clause-clause subsumption calls : 1
% 0.10/0.27 % Rewrite failures with RHS unbound : 0
% 0.10/0.27 % BW rewrite match attempts : 0
% 0.10/0.27 % BW rewrite match successes : 0
% 0.10/0.27 % Condensation attempts : 0
% 0.10/0.27 % Condensation successes : 0
% 0.10/0.27 % Termbank termtop insertions : 3196
% 0.10/0.27 % Search garbage collected termcells : 676
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.004 s
% 0.10/0.27 % System time : 0.002 s
% 0.10/0.27 % Total time : 0.006 s
% 0.10/0.27 % Maximum resident set size: 3940 pages
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.007 s
% 0.10/0.27 % System time : 0.006 s
% 0.10/0.27 % Total time : 0.012 s
% 0.10/0.27 % Maximum resident set size: 4864 pages
% 0.10/0.27 % E exiting
%------------------------------------------------------------------------------