%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO066^4.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:42:17 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 11 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 5 ~; 5 |; 3 &; 56 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 36 ( 22 ^; 14 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
irel: $i > $i > $o ).
thf(decl_25,type,
mor: ( $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_34,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_43,type,
o11: $i > $o ).
thf(decl_44,type,
o21: $i > $o ).
thf(decl_45,type,
esk1_0: $i ).
thf(decl_46,type,
esk2_0: $i ).
thf(decl_47,type,
esk3_0: $i ).
thf(ior,axiom,
( ior
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mor @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5PrtodxWoB/E---3.1_1503688.p',ior) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5PrtodxWoB/E---3.1_1503688.p',mor) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5PrtodxWoB/E---3.1_1503688.p',mbox_s4) ).
thf(con,conjecture,
ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o21 ) ),
file('/export/starexec/sandbox2/tmp/tmp.5PrtodxWoB/E---3.1_1503688.p',con) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox2/tmp/tmp.5PrtodxWoB/E---3.1_1503688.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5PrtodxWoB/E---3.1_1503688.p',ivalid) ).
thf(axiom1,axiom,
ivalid @ ( iatom @ o11 ),
file('/export/starexec/sandbox2/tmp/tmp.5PrtodxWoB/E---3.1_1503688.p',axiom1) ).
thf(c_0_7,plain,
( ior
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ! [X22: $i] :
( ( irel @ Z2 @ X22 )
=> ( Z0 @ X22 ) )
| ! [X23: $i] :
( ( irel @ Z2 @ X23 )
=> ( Z1 @ X23 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ior]) ).
thf(c_0_8,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_9,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_10,negated_conjecture,
~ ( ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_11,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_12,plain,
( ior
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ! [X22: $i] :
( ( irel @ Z2 @ X22 )
=> ( Z0 @ X22 ) )
| ! [X23: $i] :
( ( irel @ Z2 @ X23 )
=> ( Z1 @ X23 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
thf(c_0_13,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_14,negated_conjecture,
~ ! [X41: $i] :
( ! [X39: $i] :
( ( irel @ X41 @ X39 )
=> ( o11 @ X39 ) )
| ! [X40: $i] :
( ( irel @ X41 @ X40 )
=> ( o21 @ X40 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]) ).
thf(c_0_15,plain,
! [X37: $i] : ( o11 @ X37 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_11]),c_0_13]) ).
thf(c_0_16,negated_conjecture,
( ( irel @ esk1_0 @ esk2_0 )
& ~ ( o11 @ esk2_0 )
& ( irel @ esk1_0 @ esk3_0 )
& ~ ( o21 @ esk3_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_17,plain,
! [X46: $i] : ( o11 @ X46 ),
inference(variable_rename,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
~ ( o11 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,plain,
! [X1: $i] : ( o11 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO066^4.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n002.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 16:30:46 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 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.5PrtodxWoB/E---3.1_1503688.p
% 0.08/0.23 % Version: 3.5.1-ho
% 0.08/0.23 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.23 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.23 % Starting post_as_ho11 with 300s (1) cores
% 0.08/0.23 % Starting full_lambda_8 with 300s (1) cores
% 0.08/0.23 % post_as_ho3 with pid 1503709 completed with status 0
% 0.08/0.23 % Result found by post_as_ho3
% 0.08/0.23 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.23 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.23 % No SInE strategy applied
% 0.08/0.23 % Search class: HHUNS-FFSF00-SHSSMFNN
% 0.08/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.23 % SubtermCWHack with pid 1503715 completed with status 0
% 0.08/0.23 % Result found by SubtermCWHack
% 0.08/0.23 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.08/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.23 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.08/0.23 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.23 % No SInE strategy applied
% 0.08/0.23 % Search class: HHUNS-FFSF00-SHSSMFNN
% 0.08/0.23 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.23 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.23 % Preprocessing time : 0.001 s
% 0.08/0.23
% 0.08/0.23 % Proof found!
% 0.08/0.23 % SZS status Theorem
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23 % Parsed axioms : 46
% 0.08/0.23 % Removed by relevancy pruning/SinE : 0
% 0.08/0.23 % Initial clauses : 30
% 0.08/0.23 % Removed in clause preprocessing : 22
% 0.08/0.23 % Initial clauses in saturation : 8
% 0.08/0.23 % Processed clauses : 3
% 0.08/0.23 % ...of these trivial : 0
% 0.08/0.23 % ...subsumed : 0
% 0.08/0.23 % ...remaining for further processing : 2
% 0.08/0.23 % Other redundant clauses eliminated : 0
% 0.08/0.23 % Clauses deleted for lack of memory : 0
% 0.08/0.23 % Backward-subsumed : 0
% 0.08/0.23 % Backward-rewritten : 0
% 0.08/0.23 % Generated clauses : 0
% 0.08/0.23 % ...of the previous two non-redundant : 0
% 0.08/0.23 % ...aggressively subsumed : 0
% 0.08/0.23 % Contextual simplify-reflections : 0
% 0.08/0.23 % Paramodulations : 0
% 0.08/0.23 % Factorizations : 0
% 0.08/0.23 % NegExts : 0
% 0.08/0.23 % Equation resolutions : 0
% 0.08/0.23 % Disequality decompositions : 0
% 0.08/0.23 % Total rewrite steps : 1
% 0.08/0.23 % ...of those cached : 0
% 0.08/0.23 % Propositional unsat checks : 0
% 0.08/0.23 % Propositional check models : 0
% 0.08/0.23 % Propositional check unsatisfiable : 0
% 0.08/0.23 % Propositional clauses : 0
% 0.08/0.23 % Propositional clauses after purity: 0
% 0.08/0.23 % Propositional unsat core size : 0
% 0.08/0.23 % Propositional preprocessing time : 0.000
% 0.08/0.23 % Propositional encoding time : 0.000
% 0.08/0.23 % Propositional solver time : 0.000
% 0.08/0.23 % Success case prop preproc time : 0.000
% 0.08/0.23 % Success case prop encoding time : 0.000
% 0.08/0.23 % Success case prop solver time : 0.000
% 0.08/0.23 % Current number of processed clauses : 2
% 0.08/0.23 % Positive orientable unit clauses : 2
% 0.08/0.23 % Positive unorientable unit clauses: 0
% 0.08/0.23 % Negative unit clauses : 0
% 0.08/0.23 % Non-unit-clauses : 0
% 0.08/0.23 % Current number of unprocessed clauses: 5
% 0.08/0.24 % ...number of literals in the above : 7
% 0.08/0.24 % Current number of archived formulas : 0
% 0.08/0.24 % Current number of archived clauses : 0
% 0.08/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.24 % Non-unit clause-clause subsumptions : 0
% 0.08/0.24 % Unit Clause-clause subsumption calls : 0
% 0.08/0.24 % Rewrite failures with RHS unbound : 0
% 0.08/0.24 % BW rewrite match attempts : 0
% 0.08/0.24 % BW rewrite match successes : 0
% 0.08/0.24 % Condensation attempts : 0
% 0.08/0.24 % Condensation successes : 0
% 0.08/0.24 % Termbank termtop insertions : 1606
% 0.08/0.24 % Search garbage collected termcells : 431
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.004 s
% 0.08/0.24 % System time : 0.002 s
% 0.08/0.24 % Total time : 0.006 s
% 0.08/0.24 % Maximum resident set size: 3664 pages
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.007 s
% 0.08/0.24 % System time : 0.004 s
% 0.08/0.24 % Total time : 0.010 s
% 0.08/0.24 % Maximum resident set size: 4864 pages
% 0.08/0.24 % E exiting
%------------------------------------------------------------------------------