%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV429^2 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:39:43 AM UTC 2026
% Result : Theorem 0.07s 0.28s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 19 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 81 ( 11 ~; 7 |; 2 &; 56 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 49 ( 39 ^; 10 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_29,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_42,type,
rel: $i > $i > $o ).
thf(decl_44,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(decl_51,type,
iclval: ( $i > $o ) > $o ).
thf(decl_52,type,
icl_impl_princ: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_53,type,
a: $i > $o ).
thf(decl_56,type,
esk3_0: $i ).
thf(decl_57,type,
esk4_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LyCsE4I2IO/E---3.1_268111.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LyCsE4I2IO/E---3.1_268111.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LyCsE4I2IO/E---3.1_268111.p',mor) ).
thf(icl_s4_valid,axiom,
( iclval
= ( ^ [X22: $i > $o] : ( mvalid @ X22 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LyCsE4I2IO/E---3.1_268111.p',icl_s4_valid) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LyCsE4I2IO/E---3.1_268111.p',mvalid) ).
thf(icl_impl_princ,axiom,
( icl_impl_princ
= ( ^ [X19: $i > $o,X20: $i > $o] : ( mbox @ rel @ ( mimpl @ X19 @ X20 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LyCsE4I2IO/E---3.1_268111.p',icl_impl_princ) ).
thf(mbox,axiom,
( mbox
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
! [X12: $i] :
( ( X10 @ X1 @ X12 )
=> ( X11 @ X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LyCsE4I2IO/E---3.1_268111.p',mbox) ).
thf(conj,conjecture,
iclval @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ a ) ),
file('/export/starexec/sandbox/tmp/tmp.LyCsE4I2IO/E---3.1_268111.p',conj) ).
thf(icl_princ,axiom,
( icl_princ
= ( ^ [X11: $i > $o] : X11 ) ),
file('/export/starexec/sandbox/tmp/tmp.LyCsE4I2IO/E---3.1_268111.p',icl_princ) ).
thf(c_0_9,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
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,
( iclval
= ( ^ [Z0: $i > $o] :
! [X28: $i] : ( Z0 @ X28 ) ) ),
inference(fof_simplification,[status(thm)],[icl_s4_valid]) ).
thf(c_0_13,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_14,plain,
( icl_impl_princ
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X29: $i] :
( ( rel @ Z2 @ X29 )
=> ( ~ ( Z0 @ X29 )
| ( Z1 @ X29 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[icl_impl_princ]) ).
thf(c_0_15,plain,
( mimpl
= ( ^ [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_16,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X12: $i] :
( ( Z0 @ Z2 @ X12 )
=> ( Z1 @ X12 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_17,negated_conjecture,
~ ( iclval @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ a ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_18,plain,
( icl_princ
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[icl_princ]) ).
thf(c_0_19,plain,
( iclval
= ( ^ [Z0: $i > $o] :
! [X28: $i] : ( Z0 @ X28 ) ) ),
inference(apply_def,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_20,plain,
( icl_impl_princ
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
! [X29: $i] :
( ( rel @ Z2 @ X29 )
=> ( ~ ( Z0 @ X29 )
| ( Z1 @ X29 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_21,negated_conjecture,
~ ! [X37: $i,X36: $i] :
( ( rel @ X37 @ X36 )
=> ( ~ ( a @ X36 )
| ( a @ X36 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
thf(c_0_22,negated_conjecture,
( ( rel @ esk3_0 @ esk4_0 )
& ( a @ esk4_0 )
& ~ ( a @ esk4_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
thf(c_0_23,negated_conjecture,
~ ( a @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_24,negated_conjecture,
a @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV429^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n018.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:05:03 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.07/0.25 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.LyCsE4I2IO/E---3.1_268111.p
% 0.07/0.28 % Version: 3.5.1-ho
% 0.07/0.28 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.07/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.28 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.28 % Starting post_as_ho11 with 300s (1) cores
% 0.07/0.28 % Starting full_lambda_8 with 300s (1) cores
% 0.07/0.28 % post_as_ho3 with pid 268125 completed with status 0
% 0.07/0.28 % Result found by post_as_ho3
% 0.07/0.28 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.07/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.28 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.28 % No SInE strategy applied
% 0.07/0.28 % Search class: HGUNF-FFSF22-SHSSMMBN
% 0.07/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.28 % SubtermCWHack with pid 268129 completed with status 0
% 0.07/0.28 % Result found by SubtermCWHack
% 0.07/0.28 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.07/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.28 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.28 % No SInE strategy applied
% 0.07/0.28 % Search class: HGUNF-FFSF22-SHSSMMBN
% 0.07/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.28 % Preprocessing time : 0.001 s
% 0.07/0.28
% 0.07/0.28 % Proof found!
% 0.07/0.28 % SZS status Theorem
% 0.07/0.28 % SZS output start CNFRefutation
% See solution above
% 0.07/0.28 % Parsed axioms : 60
% 0.07/0.28 % Removed by relevancy pruning/SinE : 0
% 0.07/0.28 % Initial clauses : 39
% 0.07/0.28 % Removed in clause preprocessing : 32
% 0.07/0.28 % Initial clauses in saturation : 7
% 0.07/0.28 % Processed clauses : 2
% 0.07/0.28 % ...of these trivial : 0
% 0.07/0.28 % ...subsumed : 0
% 0.07/0.28 % ...remaining for further processing : 1
% 0.07/0.28 % Other redundant clauses eliminated : 0
% 0.07/0.28 % Clauses deleted for lack of memory : 0
% 0.07/0.28 % Backward-subsumed : 0
% 0.07/0.28 % Backward-rewritten : 0
% 0.07/0.28 % Generated clauses : 0
% 0.07/0.28 % ...of the previous two non-redundant : 0
% 0.07/0.28 % ...aggressively subsumed : 0
% 0.07/0.28 % Contextual simplify-reflections : 0
% 0.07/0.28 % Paramodulations : 0
% 0.07/0.28 % Factorizations : 0
% 0.07/0.28 % NegExts : 0
% 0.07/0.28 % Equation resolutions : 0
% 0.07/0.28 % Disequality decompositions : 0
% 0.07/0.28 % Total rewrite steps : 1
% 0.07/0.28 % ...of those cached : 0
% 0.07/0.28 % Propositional unsat checks : 0
% 0.07/0.28 % Propositional check models : 0
% 0.07/0.28 % Propositional check unsatisfiable : 0
% 0.07/0.28 % Propositional clauses : 0
% 0.07/0.28 % Propositional clauses after purity: 0
% 0.07/0.28 % Propositional unsat core size : 0
% 0.07/0.28 % Propositional preprocessing time : 0.000
% 0.07/0.28 % Propositional encoding time : 0.000
% 0.07/0.28 % Propositional solver time : 0.000
% 0.07/0.28 % Success case prop preproc time : 0.000
% 0.07/0.28 % Success case prop encoding time : 0.000
% 0.07/0.28 % Success case prop solver time : 0.000
% 0.07/0.28 % Current number of processed clauses : 1
% 0.07/0.28 % Positive orientable unit clauses : 1
% 0.07/0.28 % Positive unorientable unit clauses: 0
% 0.07/0.28 % Negative unit clauses : 0
% 0.07/0.28 % Non-unit-clauses : 0
% 0.07/0.28 % Current number of unprocessed clauses: 5
% 0.07/0.28 % ...number of literals in the above : 13
% 0.07/0.28 % Current number of archived formulas : 0
% 0.07/0.28 % Current number of archived clauses : 0
% 0.07/0.28 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.28 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.28 % Non-unit clause-clause subsumptions : 0
% 0.07/0.28 % Unit Clause-clause subsumption calls : 0
% 0.07/0.28 % Rewrite failures with RHS unbound : 0
% 0.07/0.28 % BW rewrite match attempts : 0
% 0.07/0.28 % BW rewrite match successes : 0
% 0.07/0.28 % Condensation attempts : 0
% 0.07/0.28 % Condensation successes : 0
% 0.07/0.28 % Termbank termtop insertions : 1837
% 0.07/0.28 % Search garbage collected termcells : 455
% 0.07/0.28
% 0.07/0.28 % -------------------------------------------------
% 0.07/0.28 % User time : 0.004 s
% 0.07/0.28 % System time : 0.003 s
% 0.07/0.28 % Total time : 0.007 s
% 0.07/0.28 % Maximum resident set size: 3680 pages
% 0.07/0.28
% 0.07/0.28 % -------------------------------------------------
% 0.07/0.28 % User time : 0.010 s
% 0.07/0.28 % System time : 0.004 s
% 0.07/0.28 % Total time : 0.014 s
% 0.07/0.28 % Maximum resident set size: 4864 pages
% 0.07/0.28 % E exiting
%------------------------------------------------------------------------------