%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU464^1 : 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 : n008.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 08:23:52 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 4 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 336 ( 23 ~; 34 |; 21 &; 244 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 6 ^; 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(decl_35,type,
trans: ( $i > $i > $o ) > $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(decl_55,type,
epred2_0: $i > $i > $o ).
thf(decl_56,type,
esk3_1: ( $i > $i > $o ) > $i ).
thf(decl_57,type,
esk4_1: ( $i > $i > $o ) > $i ).
thf(decl_58,type,
esk5_1: ( $i > $i > $o ) > $i ).
thf(decl_59,type,
esk6_1: ( $i > $i > $o ) > $i ).
thf(decl_60,type,
esk7_1: ( $i > $i > $o ) > $i ).
thf(transitive_closure_is_transitive4,conjecture,
! [X1: $i > $i > $o,X3: $i,X4: $i,X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 )
& ! [X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 ) )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ X3 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.UmUMScs61g/E---3.1_3172516.p',transitive_closure_is_transitive4) ).
thf(transitive,axiom,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X4 @ X6 ) )
=> ( X1 @ X3 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UmUMScs61g/E---3.1_3172516.p',transitive) ).
thf(subrel,axiom,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UmUMScs61g/E---3.1_3172516.p',subrel) ).
thf(c_0_3,negated_conjecture,
~ ! [X1: $i > $i > $o,X3: $i,X4: $i,X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 )
& ! [X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 ) )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ X3 @ X4 ) ),
inference(assume_negation,[status(cth)],[transitive_closure_is_transitive4]) ).
thf(c_0_4,plain,
( trans
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( Z0 @ X3 @ X4 )
& ( Z0 @ X4 @ X6 ) )
=> ( Z0 @ X3 @ X6 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive]) ).
thf(c_0_5,plain,
( subrel
= ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( Z0 @ X3 @ X4 )
=> ( Z1 @ X3 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subrel]) ).
thf(c_0_6,negated_conjecture,
~ ! [X1: $i > $i > $o,X3: $i,X4: $i,X2: $i > $i > $o] :
( ( ! [X43: $i,X44: $i,X45: $i] :
( ( ( X2 @ X43 @ X44 )
& ( X2 @ X44 @ X45 ) )
=> ( X2 @ X43 @ X45 ) )
& ! [X46: $i,X47: $i] :
( ( X1 @ X46 @ X47 )
=> ( X2 @ X46 @ X47 ) )
& ! [X2: $i > $i > $o] :
( ( ! [X48: $i,X49: $i,X50: $i] :
( ( ( X2 @ X48 @ X49 )
& ( X2 @ X49 @ X50 ) )
=> ( X2 @ X48 @ X50 ) )
& ! [X51: $i,X52: $i] :
( ( X1 @ X51 @ X52 )
=> ( X2 @ X51 @ X52 ) ) )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ X3 @ X4 ) ),
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,
! [X57: $i,X58: $i,X59: $i,X60: $i,X61: $i,X62: $i > $i > $o] :
( ( ~ ( epred2_0 @ X57 @ X58 )
| ~ ( epred2_0 @ X58 @ X59 )
| ( epred2_0 @ X57 @ X59 ) )
& ( ~ ( epred1_0 @ X60 @ X61 )
| ( epred2_0 @ X60 @ X61 ) )
& ( ( epred1_0 @ ( esk6_1 @ X62 ) @ ( esk7_1 @ X62 ) )
| ( X62 @ ( esk3_1 @ X62 ) @ ( esk4_1 @ X62 ) )
| ( X62 @ esk1_0 @ esk2_0 ) )
& ( ~ ( X62 @ ( esk6_1 @ X62 ) @ ( esk7_1 @ X62 ) )
| ( X62 @ ( esk3_1 @ X62 ) @ ( esk4_1 @ X62 ) )
| ( X62 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ ( esk6_1 @ X62 ) @ ( esk7_1 @ X62 ) )
| ( X62 @ ( esk4_1 @ X62 ) @ ( esk5_1 @ X62 ) )
| ( X62 @ esk1_0 @ esk2_0 ) )
& ( ~ ( X62 @ ( esk6_1 @ X62 ) @ ( esk7_1 @ X62 ) )
| ( X62 @ ( esk4_1 @ X62 ) @ ( esk5_1 @ X62 ) )
| ( X62 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ ( esk6_1 @ X62 ) @ ( esk7_1 @ X62 ) )
| ~ ( X62 @ ( esk3_1 @ X62 ) @ ( esk5_1 @ X62 ) )
| ( X62 @ esk1_0 @ esk2_0 ) )
& ( ~ ( X62 @ ( esk6_1 @ X62 ) @ ( esk7_1 @ X62 ) )
| ~ ( X62 @ ( esk3_1 @ X62 ) @ ( esk5_1 @ X62 ) )
| ( X62 @ esk1_0 @ esk2_0 ) )
& ~ ( epred2_0 @ esk1_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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i,X4: $i,X6: $i] :
( ( epred2_0 @ X3 @ X6 )
| ~ ( epred2_0 @ X3 @ X4 )
| ~ ( epred2_0 @ X4 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) )
| ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ( epred2_0 @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk7_1 @ epred2_0 ) )
| ( epred2_0 @ X3 @ ( esk5_1 @ epred2_0 ) )
| ~ ( epred2_0 @ X3 @ ( esk4_1 @ epred2_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) )
| ( X1 @ ( esk3_1 @ X1 ) @ ( esk4_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ~ ( X1 @ ( esk3_1 @ X1 ) @ ( esk5_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
( ( epred2_0 @ ( esk3_1 @ epred2_0 ) @ ( esk5_1 @ epred2_0 ) )
| ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk7_1 @ epred2_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred2_0 @ X3 @ X4 )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_16,negated_conjecture,
epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk7_1 @ epred2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_10]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ~ ( X1 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_18,negated_conjecture,
epred2_0 @ ( esk6_1 @ epred2_0 ) @ ( esk7_1 @ epred2_0 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ esk1_0 @ esk2_0 )
| ~ ( X1 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) )
| ~ ( X1 @ ( esk3_1 @ X1 ) @ ( esk5_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ X3 @ ( esk5_1 @ epred2_0 ) )
| ~ ( epred2_0 @ X3 @ ( esk4_1 @ epred2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_17]),c_0_10]),c_0_18])]) ).
thf(c_0_21,negated_conjecture,
~ ( epred2_0 @ ( esk3_1 @ epred2_0 ) @ ( esk4_1 @ epred2_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18])]),c_0_10]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ ( esk3_1 @ X1 ) @ ( esk4_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ~ ( X1 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_18])]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU464^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n008.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 13:42:39 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.22 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.UmUMScs61g/E---3.1_3172516.p
% 0.11/0.25 % Version: 3.5.1-ho
% 0.11/0.25 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.25 % Starting sh5l with 300s (1) cores
% 0.11/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.11/0.25 % new_bool_1 with pid 3172547 completed with status 0
% 0.11/0.25 % Result found by new_bool_1
% 0.11/0.25 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.25 % Starting sh5l with 300s (1) cores
% 0.11/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.25 % Search class: HGUNF-FFSF11-SHSSMMBN
% 0.11/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.25 % SubtermCWHack with pid 3172549 completed with status 0
% 0.11/0.25 % Result found by SubtermCWHack
% 0.11/0.25 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.25 % Starting sh5l with 300s (1) cores
% 0.11/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.25 % Search class: HGUNF-FFSF11-SHSSMMBN
% 0.11/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.25 % Preprocessing time : 0.001 s
% 0.11/0.25
% 0.11/0.25 % Proof found!
% 0.11/0.25 % SZS status Theorem
% 0.11/0.25 % SZS output start CNFRefutation
% See solution above
% 0.11/0.25 % Parsed axioms : 59
% 0.11/0.25 % Removed by relevancy pruning/SinE : 51
% 0.11/0.25 % Initial clauses : 9
% 0.11/0.25 % Removed in clause preprocessing : 0
% 0.11/0.25 % Initial clauses in saturation : 9
% 0.11/0.25 % Processed clauses : 23
% 0.11/0.25 % ...of these trivial : 0
% 0.11/0.25 % ...subsumed : 0
% 0.11/0.25 % ...remaining for further processing : 23
% 0.11/0.25 % Other redundant clauses eliminated : 0
% 0.11/0.25 % Clauses deleted for lack of memory : 0
% 0.11/0.25 % Backward-subsumed : 1
% 0.11/0.25 % Backward-rewritten : 3
% 0.11/0.25 % Generated clauses : 26
% 0.11/0.25 % ...of the previous two non-redundant : 22
% 0.11/0.25 % ...aggressively subsumed : 0
% 0.11/0.25 % Contextual simplify-reflections : 1
% 0.11/0.25 % Paramodulations : 26
% 0.11/0.25 % Factorizations : 0
% 0.11/0.25 % NegExts : 0
% 0.11/0.25 % Equation resolutions : 0
% 0.11/0.25 % Disequality decompositions : 0
% 0.11/0.25 % Total rewrite steps : 9
% 0.11/0.25 % ...of those cached : 7
% 0.11/0.25 % Propositional unsat checks : 0
% 0.11/0.25 % Propositional check models : 0
% 0.11/0.25 % Propositional check unsatisfiable : 0
% 0.11/0.25 % Propositional clauses : 0
% 0.11/0.25 % Propositional clauses after purity: 0
% 0.11/0.25 % Propositional unsat core size : 0
% 0.11/0.25 % Propositional preprocessing time : 0.000
% 0.11/0.25 % Propositional encoding time : 0.000
% 0.11/0.25 % Propositional solver time : 0.000
% 0.11/0.25 % Success case prop preproc time : 0.000
% 0.11/0.25 % Success case prop encoding time : 0.000
% 0.11/0.25 % Success case prop solver time : 0.000
% 0.11/0.25 % Current number of processed clauses : 19
% 0.11/0.25 % Positive orientable unit clauses : 2
% 0.11/0.25 % Positive unorientable unit clauses: 0
% 0.11/0.25 % Negative unit clauses : 2
% 0.11/0.25 % Non-unit-clauses : 15
% 0.11/0.25 % Current number of unprocessed clauses: 7
% 0.11/0.25 % ...number of literals in the above : 23
% 0.11/0.25 % Current number of archived formulas : 0
% 0.11/0.25 % Current number of archived clauses : 4
% 0.11/0.25 % Clause-clause subsumption calls (NU) : 32
% 0.11/0.25 % Rec. Clause-clause subsumption calls : 29
% 0.11/0.25 % Non-unit clause-clause subsumptions : 2
% 0.11/0.25 % Unit Clause-clause subsumption calls : 1
% 0.11/0.25 % Rewrite failures with RHS unbound : 0
% 0.11/0.25 % BW rewrite match attempts : 1
% 0.11/0.25 % BW rewrite match successes : 1
% 0.11/0.25 % Condensation attempts : 0
% 0.11/0.25 % Condensation successes : 0
% 0.11/0.25 % Termbank termtop insertions : 2414
% 0.11/0.25 % Search garbage collected termcells : 746
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.005 s
% 0.11/0.25 % System time : 0.002 s
% 0.11/0.25 % Total time : 0.007 s
% 0.11/0.25 % Maximum resident set size: 3688 pages
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.006 s
% 0.11/0.25 % System time : 0.007 s
% 0.11/0.25 % Total time : 0.013 s
% 0.11/0.25 % Maximum resident set size: 4864 pages
% 0.11/0.25 % E exiting
%------------------------------------------------------------------------------