%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO061^4 : 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 : n002.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 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 16 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 167 ( 23 ~; 21 |; 3 &; 110 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 59 ( 34 ^; 25 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
irel: $i > $i > $o ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mimplies: ( $i > $o ) > ( $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_35,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_43,type,
a: $i > $o ).
thf(decl_44,type,
b: $i > $o ).
thf(decl_45,type,
esk1_1: $i > $i ).
thf(decl_46,type,
esk2_0: $i ).
thf(decl_47,type,
esk3_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y8mUp6buak/E---3.1_1501394.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y8mUp6buak/E---3.1_1501394.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y8mUp6buak/E---3.1_1501394.p',mor) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y8mUp6buak/E---3.1_1501394.p',iimplies) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y8mUp6buak/E---3.1_1501394.p',mbox_s4) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.y8mUp6buak/E---3.1_1501394.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y8mUp6buak/E---3.1_1501394.p',ivalid) ).
thf(con,conjecture,
ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox/tmp/tmp.y8mUp6buak/E---3.1_1501394.p',con) ).
thf(axiom1,axiom,
ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox/tmp/tmp.y8mUp6buak/E---3.1_1501394.p',axiom1) ).
thf(c_0_9,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_10,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_11,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_12,plain,
( iimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ! [X24: $i] :
( ( irel @ Z2 @ X24 )
=> ( Z0 @ X24 ) )
| ! [X25: $i] :
( ( irel @ Z2 @ X25 )
=> ( Z1 @ X25 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iimplies]) ).
thf(c_0_13,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
thf(c_0_14,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_15,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_16,plain,
( iimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ! [X24: $i] :
( ( irel @ Z2 @ X24 )
=> ( Z0 @ X24 ) )
| ! [X25: $i] :
( ( irel @ Z2 @ X25 )
=> ( Z1 @ X25 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_17,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_18,negated_conjecture,
~ ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_19,plain,
! [X39: $i] :
( ~ ! [X37: $i] :
( ( irel @ X39 @ X37 )
=> ( a @ X37 ) )
| ! [X38: $i] :
( ( irel @ X39 @ X38 )
=> ( b @ X38 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_15]),c_0_16]),c_0_17]) ).
thf(c_0_20,negated_conjecture,
~ ! [X42: $i] :
( ~ ! [X40: $i] :
( ( irel @ X42 @ X40 )
=> ( a @ X40 ) )
| ! [X41: $i] :
( ( irel @ X42 @ X41 )
=> ( b @ X41 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_15]),c_0_16]),c_0_17]) ).
thf(c_0_21,plain,
! [X47: $i,X49: $i] :
( ( ( irel @ X47 @ ( esk1_1 @ X47 ) )
| ~ ( irel @ X47 @ X49 )
| ( b @ X49 ) )
& ( ~ ( a @ ( esk1_1 @ X47 ) )
| ~ ( irel @ X47 @ X49 )
| ( b @ X49 ) ) ),
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_19])])])])])]) ).
thf(c_0_22,negated_conjecture,
! [X51: $i] :
( ( ~ ( irel @ esk2_0 @ X51 )
| ( a @ X51 ) )
& ( irel @ esk2_0 @ esk3_0 )
& ~ ( b @ esk3_0 ) ),
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_20])])])])]) ).
thf(c_0_23,plain,
! [X1: $i,X2: $i] :
( ( b @ X2 )
| ~ ( a @ ( esk1_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( a @ X1 )
| ~ ( irel @ esk2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_25,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk1_1 @ X1 ) )
| ( b @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
irel @ esk2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_27,negated_conjecture,
~ ( b @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,negated_conjecture,
! [X2: $i,X1: $i] :
( ( b @ X1 )
| ~ ( irel @ esk2_0 @ ( esk1_1 @ X2 ) )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_29,negated_conjecture,
irel @ esk2_0 @ ( esk1_1 @ esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i] :
( ( b @ X1 )
| ~ ( irel @ esk2_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO061^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:28:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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.y8mUp6buak/E---3.1_1501394.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.22/0.27 % Starting post_as_ho11 with 300s (1) cores
% 0.22/0.27 % Starting full_lambda_8 with 300s (1) cores
% 0.22/0.27 % new_ho_10_cnf2 with pid 1501409 completed with status 0
% 0.22/0.27 % Result found by new_ho_10_cnf2
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGUNF-FFSF11-SHSSMFNN
% 0.22/0.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.27 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.27 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.22/0.27 % Starting post_as_ho11 with 136s (1) cores
% 0.22/0.27 % Starting post_as_ho1 with 136s (1) cores
% 0.22/0.27 % Starting lpo5_fix with 136s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 1501413 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGUNF-FFSF11-SHSSMFNN
% 0.22/0.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.27 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.27 % Parsed axioms : 45
% 0.22/0.27 % Removed by relevancy pruning/SinE : 0
% 0.22/0.27 % Initial clauses : 29
% 0.22/0.27 % Removed in clause preprocessing : 22
% 0.22/0.27 % Initial clauses in saturation : 7
% 0.22/0.27 % Processed clauses : 12
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 0
% 0.22/0.27 % ...remaining for further processing : 12
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 0
% 0.22/0.27 % Backward-rewritten : 0
% 0.22/0.27 % Generated clauses : 14
% 0.22/0.27 % ...of the previous two non-redundant : 11
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 0
% 0.22/0.27 % Paramodulations : 14
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 2
% 0.22/0.27 % ...of those cached : 0
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 12
% 0.22/0.27 % Positive orientable unit clauses : 3
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 1
% 0.22/0.27 % Non-unit-clauses : 8
% 0.22/0.27 % Current number of unprocessed clauses: 6
% 0.22/0.27 % ...number of literals in the above : 16
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 0
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 4
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 4
% 0.22/0.27 % Non-unit clause-clause subsumptions : 0
% 0.22/0.27 % Unit Clause-clause subsumption calls : 0
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 1
% 0.22/0.27 % BW rewrite match successes : 0
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 1958
% 0.22/0.27 % Search garbage collected termcells : 508
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.002 s
% 0.22/0.27 % System time : 0.005 s
% 0.22/0.27 % Total time : 0.006 s
% 0.22/0.27 % Maximum resident set size: 3664 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.012 s
% 0.22/0.27 % System time : 0.013 s
% 0.22/0.27 % Total time : 0.024 s
% 0.22/0.27 % Maximum resident set size: 4864 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------