%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL713^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:12:04 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 22 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 244 ( 42 ~; 30 |; 7 &; 159 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 88 ( 44 ^; 44 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_33,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_44,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
epred1_0: $i > $i > $o ).
thf(decl_55,type,
esk1_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_56,type,
esk2_0: $i ).
thf(decl_57,type,
esk3_0: $i ).
thf(decl_58,type,
esk4_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.V1qD5Jn2oX/E---3.1_2461106.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.V1qD5Jn2oX/E---3.1_2461106.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.V1qD5Jn2oX/E---3.1_2461106.p',mor) ).
thf(mdia,axiom,
( mdia
= ( ^ [X13: $i > $i > $o,X6: $i > $o] : ( mnot @ ( mbox @ X13 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.V1qD5Jn2oX/E---3.1_2461106.p',mdia) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.V1qD5Jn2oX/E---3.1_2461106.p',mbox) ).
thf(conj,conjecture,
! [X13: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] : ( mimplies @ ( mdia @ X13 @ X18 ) @ ( mbox @ X13 @ ( mdia @ X13 @ X18 ) ) ) ) )
=> ( meuclidean @ X13 ) ),
file('/export/starexec/sandbox/tmp/tmp.V1qD5Jn2oX/E---3.1_2461106.p',conj) ).
thf(mforall_prop,axiom,
( mforall_prop
= ( ^ [X9: ( $i > $o ) > $i > $o,X3: $i] :
! [X10: $i > $o] : ( X9 @ X10 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.V1qD5Jn2oX/E---3.1_2461106.p',mforall_prop) ).
thf(meuclidean,axiom,
( meuclidean
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( X13 @ X15 @ X16 )
& ( X13 @ X15 @ X17 ) )
=> ( X13 @ X16 @ X17 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.V1qD5Jn2oX/E---3.1_2461106.p',meuclidean) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.V1qD5Jn2oX/E---3.1_2461106.p',mvalid) ).
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,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X22: $i] :
( ~ ( Z0 @ Z2 @ X22 )
| ~ ( Z1 @ X22 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia]) ).
thf(c_0_13,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X14: $i] :
( ~ ( Z0 @ Z2 @ X14 )
| ( Z1 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_14,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] : ( mimplies @ ( mdia @ X13 @ X18 ) @ ( mbox @ X13 @ ( mdia @ X13 @ X18 ) ) ) ) )
=> ( meuclidean @ X13 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_15,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_16,plain,
( mforall_prop
= ( ^ [Z0: ( $i > $o ) > $i > $o,Z1: $i] :
! [X10: $i > $o] : ( Z0 @ X10 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_prop]) ).
thf(c_0_17,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X22: $i] :
( ~ ( Z0 @ Z2 @ X22 )
| ~ ( Z1 @ X22 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_10]),c_0_13]) ).
thf(c_0_18,plain,
( meuclidean
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( Z0 @ X15 @ X16 )
& ( Z0 @ X15 @ X17 ) )
=> ( Z0 @ X16 @ X17 ) ) ) ),
inference(fof_simplification,[status(thm)],[meuclidean]) ).
thf(c_0_19,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_20,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( ! [X27: $i,X26: $i > $o] :
( ~ ~ ! [X23: $i] :
( ~ ( X13 @ X27 @ X23 )
| ~ ( X26 @ X23 ) )
| ! [X25: $i] :
( ~ ( X13 @ X27 @ X25 )
| ~ ! [X24: $i] :
( ~ ( X13 @ X25 @ X24 )
| ~ ( X26 @ X24 ) ) ) )
=> ! [X28: $i,X29: $i,X30: $i] :
( ( ( X13 @ X28 @ X29 )
& ( X13 @ X28 @ X30 ) )
=> ( X13 @ X29 @ X30 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_14]),c_0_15]),c_0_16]),c_0_13]),c_0_17]),c_0_18]),c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X32: $i,X33: $i > $o,X34: $i,X35: $i] :
( ( ( epred1_0 @ X35 @ ( esk1_3 @ X32 @ X33 @ X35 ) )
| ~ ( epred1_0 @ X32 @ X35 )
| ~ ( epred1_0 @ X32 @ X34 )
| ~ ( X33 @ X34 ) )
& ( ( X33 @ ( esk1_3 @ X32 @ X33 @ X35 ) )
| ~ ( epred1_0 @ X32 @ X35 )
| ~ ( epred1_0 @ X32 @ X34 )
| ~ ( X33 @ X34 ) )
& ( epred1_0 @ esk2_0 @ esk3_0 )
& ( epred1_0 @ esk2_0 @ esk4_0 )
& ~ ( epred1_0 @ esk3_0 @ esk4_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_20])])])])])]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i,X4: $i > $o,X14: $i,X15: $i] :
( ( epred1_0 @ X3 @ ( esk1_3 @ X14 @ X4 @ X3 ) )
| ~ ( epred1_0 @ X14 @ X3 )
| ~ ( epred1_0 @ X14 @ X15 )
| ~ ( X4 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_23,negated_conjecture,
epred1_0 @ esk2_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X3: $i,X4: $i > $o,X14: $i,X15: $i] :
( ( X4 @ ( esk1_3 @ X3 @ X4 @ X14 ) )
| ~ ( epred1_0 @ X3 @ X14 )
| ~ ( epred1_0 @ X3 @ X15 )
| ~ ( X4 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X3: $i,X4: $i > $o] :
( ( epred1_0 @ X3 @ ( esk1_3 @ esk2_0 @ X4 @ X3 ) )
| ~ ( epred1_0 @ esk2_0 @ X3 )
| ~ ( X4 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_26,negated_conjecture,
epred1_0 @ esk2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
! [X3: $i,X14: $i,X15: $i] :
( ( ( esk1_3 @ X3
@ ^ [Z0: $i] : ( Z0 = X14 )
@ X15 )
= X14 )
| ~ ( epred1_0 @ X3 @ X14 )
| ~ ( epred1_0 @ X3 @ X15 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_24]) ).
thf(c_0_28,negated_conjecture,
! [X4: $i > $o] :
( ( epred1_0 @ esk3_0 @ ( esk1_3 @ esk2_0 @ X4 @ esk3_0 ) )
| ~ ( X4 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i] :
( ( ( esk1_3 @ esk2_0
@ ^ [Z0: $i] : ( Z0 = esk4_0 )
@ X3 )
= esk4_0 )
| ~ ( epred1_0 @ esk2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
thf(c_0_30,negated_conjecture,
~ ( epred1_0 @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29])])]),c_0_26])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL713^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n014.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 09:48:15 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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.V1qD5Jn2oX/E---3.1_2461106.p
% 0.20/0.28 % Version: 3.5.1-ho
% 0.20/0.28 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.20/0.28 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting ho_unfolding_6 with 300s (1) cores
% 0.20/0.28 % ehoh_best2_full_lfho with pid 2461135 completed with status 0
% 0.20/0.28 % Result found by ehoh_best2_full_lfho
% 0.20/0.28 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.28 % No SInE strategy applied
% 0.20/0.28 % Search class: HHUNF-FFSF33-SHHSMSBN
% 0.20/0.28 % partial match(2): HGHNF-FFSF33-SHHSMSBN
% 0.20/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.28 % Starting ehoh_best2_full_lfho with 151s (1) cores
% 0.20/0.28 % Starting sh5l with 136s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 136s (1) cores
% 0.20/0.28 % Starting new_bool_2 with 136s (1) cores
% 0.20/0.28 % sh5l with pid 2461145 completed with status 0
% 0.20/0.28 % Result found by sh5l
% 0.20/0.28 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.28 % No SInE strategy applied
% 0.20/0.28 % Search class: HHUNF-FFSF33-SHHSMSBN
% 0.20/0.28 % partial match(2): HGHNF-FFSF33-SHHSMSBN
% 0.20/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.28 % Starting ehoh_best2_full_lfho with 151s (1) cores
% 0.20/0.28 % Starting sh5l with 136s (1) cores
% 0.20/0.28 % Preprocessing time : 0.001 s
% 0.20/0.28 % Presaturation interreduction done
% 0.20/0.28
% 0.20/0.28 % Proof found!
% 0.20/0.28 % SZS status Theorem
% 0.20/0.28 % SZS output start CNFRefutation
% See solution above
% 0.20/0.28 % Parsed axioms : 64
% 0.20/0.28 % Removed by relevancy pruning/SinE : 0
% 0.20/0.28 % Initial clauses : 37
% 0.20/0.28 % Removed in clause preprocessing : 32
% 0.20/0.28 % Initial clauses in saturation : 5
% 0.20/0.28 % Processed clauses : 215
% 0.20/0.28 % ...of these trivial : 0
% 0.20/0.28 % ...subsumed : 67
% 0.20/0.28 % ...remaining for further processing : 148
% 0.20/0.28 % Other redundant clauses eliminated : 0
% 0.20/0.28 % Clauses deleted for lack of memory : 0
% 0.20/0.28 % Backward-subsumed : 18
% 0.20/0.28 % Backward-rewritten : 0
% 0.20/0.28 % Generated clauses : 1308
% 0.20/0.28 % ...of the previous two non-redundant : 1256
% 0.20/0.28 % ...aggressively subsumed : 0
% 0.20/0.28 % Contextual simplify-reflections : 0
% 0.20/0.28 % Paramodulations : 1307
% 0.20/0.28 % Factorizations : 0
% 0.20/0.28 % NegExts : 0
% 0.20/0.28 % Equation resolutions : 0
% 0.20/0.28 % Disequality decompositions : 0
% 0.20/0.28 % Total rewrite steps : 481
% 0.20/0.28 % ...of those cached : 479
% 0.20/0.28 % Propositional unsat checks : 0
% 0.20/0.28 % Propositional check models : 0
% 0.20/0.28 % Propositional check unsatisfiable : 0
% 0.20/0.28 % Propositional clauses : 0
% 0.20/0.28 % Propositional clauses after purity: 0
% 0.20/0.28 % Propositional unsat core size : 0
% 0.20/0.28 % Propositional preprocessing time : 0.000
% 0.20/0.28 % Propositional encoding time : 0.000
% 0.20/0.28 % Propositional solver time : 0.000
% 0.20/0.28 % Success case prop preproc time : 0.000
% 0.20/0.28 % Success case prop encoding time : 0.000
% 0.20/0.28 % Success case prop solver time : 0.000
% 0.20/0.28 % Current number of processed clauses : 125
% 0.20/0.28 % Positive orientable unit clauses : 2
% 0.20/0.28 % Positive unorientable unit clauses: 0
% 0.20/0.28 % Negative unit clauses : 1
% 0.20/0.28 % Non-unit-clauses : 122
% 0.20/0.28 % Current number of unprocessed clauses: 1048
% 0.20/0.28 % ...number of literals in the above : 3302
% 0.20/0.28 % Current number of archived formulas : 0
% 0.20/0.28 % Current number of archived clauses : 23
% 0.20/0.28 % Clause-clause subsumption calls (NU) : 1698
% 0.20/0.28 % Rec. Clause-clause subsumption calls : 1489
% 0.20/0.28 % Non-unit clause-clause subsumptions : 104
% 0.20/0.28 % Unit Clause-clause subsumption calls : 0
% 0.20/0.28 % Rewrite failures with RHS unbound : 0
% 0.20/0.28 % BW rewrite match attempts : 0
% 0.20/0.28 % BW rewrite match successes : 0
% 0.20/0.28 % Condensation attempts : 215
% 0.20/0.28 % Condensation successes : 33
% 0.20/0.28 % Termbank termtop insertions : 60936
% 0.20/0.28 % Search garbage collected termcells : 642
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.025 s
% 0.20/0.28 % System time : 0.004 s
% 0.20/0.28 % Total time : 0.029 s
% 0.20/0.28 % Maximum resident set size: 3692 pages
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.090 s
% 0.20/0.28 % System time : 0.019 s
% 0.20/0.28 % Total time : 0.109 s
% 0.20/0.28 % Maximum resident set size: 4864 pages
% 0.20/0.28 % E exiting
%------------------------------------------------------------------------------