%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO059^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:42:15 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 11 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 81 ( 14 ~; 3 |; 1 &; 57 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 17 ^; 18 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
irel: $i > $i > $o ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_29,type,
iatom: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
inot: ( $i > $o ) > $i > $o ).
thf(decl_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_43,type,
a: $i > $o ).
thf(decl_44,type,
esk1_0: $i ).
thf(decl_45,type,
esk2_1: $i > $i ).
thf(inot,axiom,
( inot
= ( ^ [X12: $i > $o] : ( mnot @ ( mbox_s4 @ X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7n7QxU3jHb/E---3.1_14300.p',inot) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7n7QxU3jHb/E---3.1_14300.p',mnot) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7n7QxU3jHb/E---3.1_14300.p',mbox_s4) ).
thf(con,conjecture,
ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7n7QxU3jHb/E---3.1_14300.p',con) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.7n7QxU3jHb/E---3.1_14300.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7n7QxU3jHb/E---3.1_14300.p',ivalid) ).
thf(axiom1,axiom,
ivalid @ ( iatom @ a ),
file('/export/starexec/sandbox/tmp/tmp.7n7QxU3jHb/E---3.1_14300.p',axiom1) ).
thf(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.7n7QxU3jHb/E---3.1_14300.p',refl_axiom) ).
thf(c_0_8,plain,
( inot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X20: $i] :
( ( irel @ Z1 @ X20 )
=> ( Z0 @ X20 ) ) ) ),
inference(fof_simplification,[status(thm)],[inot]) ).
thf(c_0_9,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_10,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X2: $i] :
( ( irel @ Z1 @ X2 )
=> ( Z0 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_11,negated_conjecture,
~ ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_12,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_13,plain,
( inot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X20: $i] :
( ( irel @ Z1 @ X20 )
=> ( Z0 @ X20 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_14,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_15,negated_conjecture,
~ ! [X40: $i] :
~ ! [X39: $i] :
( ( irel @ X40 @ X39 )
=> ~ ! [X38: $i] :
( ( irel @ X39 @ X38 )
=> ( a @ X38 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]) ).
thf(c_0_16,plain,
! [X37: $i] : ( a @ X37 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_12]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X47: $i] :
( ( ( irel @ X47 @ ( esk2_1 @ X47 ) )
| ~ ( irel @ esk1_0 @ X47 ) )
& ( ~ ( a @ ( esk2_1 @ X47 ) )
| ~ ( irel @ esk1_0 @ X47 ) ) ),
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_15])])])])]) ).
thf(c_0_18,plain,
! [X45: $i] : ( a @ X45 ),
inference(variable_rename,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ~ ( a @ ( esk2_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
! [X1: $i] : ( a @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,plain,
! [X41: $i] : ( irel @ X41 @ X41 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i] :
~ ( irel @ esk1_0 @ X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
thf(c_0_23,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_22,c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO059^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:26:15 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.7n7QxU3jHb/E---3.1_14300.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_9 with 1500s (5) cores
% 0.08/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.26 % Starting sh1l with 300s (1) cores
% 0.08/0.26 % Starting post_as_ho10 with 300s (1) cores
% 0.08/0.26 % post_as_ho1 with pid 14314 completed with status 0
% 0.08/0.26 % Result found by post_as_ho1
% 0.08/0.26 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_9 with 1500s (5) cores
% 0.08/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HHHNS-FFSF11-SHSSMFNN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 14318 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_9 with 1500s (5) cores
% 0.08/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HHHNS-FFSF11-SHSSMFNN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26 % Parsed axioms : 44
% 0.08/0.26 % Removed by relevancy pruning/SinE : 0
% 0.08/0.26 % Initial clauses : 26
% 0.08/0.26 % Removed in clause preprocessing : 21
% 0.08/0.26 % Initial clauses in saturation : 5
% 0.08/0.26 % Processed clauses : 3
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 3
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 0
% 0.08/0.26 % Backward-rewritten : 0
% 0.08/0.26 % Generated clauses : 1
% 0.08/0.26 % ...of the previous two non-redundant : 0
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 1
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 1
% 0.08/0.26 % ...of those cached : 0
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 3
% 0.08/0.26 % Positive orientable unit clauses : 2
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 1
% 0.08/0.26 % Non-unit-clauses : 0
% 0.08/0.26 % Current number of unprocessed clauses: 2
% 0.08/0.26 % ...number of literals in the above : 5
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 0
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.26 % Non-unit clause-clause subsumptions : 0
% 0.08/0.26 % Unit Clause-clause subsumption calls : 0
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 0
% 0.08/0.26 % BW rewrite match successes : 0
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 1562
% 0.08/0.26 % Search garbage collected termcells : 428
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.003 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.005 s
% 0.08/0.26 % Maximum resident set size: 3664 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.006 s
% 0.08/0.26 % System time : 0.005 s
% 0.08/0.26 % Total time : 0.012 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------