%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL716^1 : 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 : n008.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 0.29s 0.37s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 21 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 225 ( 30 ~; 27 |; 7 &; 155 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 38 ^; 41 !; 3 ?; 82 :)
% 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_47,type,
mweakly_dense: ( $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_2: $i > ( $i > $o ) > $i ).
thf(decl_56,type,
esk2_2: $i > ( $i > $o ) > $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.QmuhpYtzbx/E---3.1_2937400.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QmuhpYtzbx/E---3.1_2937400.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QmuhpYtzbx/E---3.1_2937400.p',mor) ).
thf(conj,conjecture,
! [X13: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] : ( mimplies @ ( mbox @ X13 @ ( mbox @ X13 @ X18 ) ) @ ( mbox @ X13 @ X18 ) ) ) )
=> ( mweakly_dense @ X13 ) ),
file('/export/starexec/sandbox/tmp/tmp.QmuhpYtzbx/E---3.1_2937400.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.QmuhpYtzbx/E---3.1_2937400.p',mforall_prop) ).
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.QmuhpYtzbx/E---3.1_2937400.p',mbox) ).
thf(mweakly_dense,axiom,
( mweakly_dense
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( X13 @ X15 @ X16 )
=> ? [X17: $i] :
( ( X13 @ X15 @ X17 )
& ( X13 @ X17 @ X16 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QmuhpYtzbx/E---3.1_2937400.p',mweakly_dense) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QmuhpYtzbx/E---3.1_2937400.p',mvalid) ).
thf(c_0_8,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_9,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_10,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_11,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] : ( mimplies @ ( mbox @ X13 @ ( mbox @ X13 @ X18 ) ) @ ( mbox @ X13 @ X18 ) ) ) )
=> ( mweakly_dense @ X13 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_12,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_8,c_0_9]),c_0_10]) ).
thf(c_0_13,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_14,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_15,plain,
( mweakly_dense
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( Z0 @ X15 @ X16 )
=> ? [X17: $i] :
( ( Z0 @ X15 @ X17 )
& ( Z0 @ X17 @ X16 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mweakly_dense]) ).
thf(c_0_16,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_17,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( ! [X27: $i,X26: $i > $o] :
( ~ ! [X24: $i] :
( ~ ( X13 @ X27 @ X24 )
| ! [X23: $i] :
( ~ ( X13 @ X24 @ X23 )
| ( X26 @ X23 ) ) )
| ! [X25: $i] :
( ~ ( X13 @ X27 @ X25 )
| ( X26 @ X25 ) ) )
=> ! [X28: $i,X29: $i,X30: $i] :
( ( X13 @ X28 @ X29 )
=> ? [X31: $i] :
( ( X13 @ X28 @ X31 )
& ( X13 @ X31 @ X29 ) ) ) ),
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_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16]) ).
thf(c_0_18,negated_conjecture,
! [X33: $i,X34: $i > $o,X37: $i,X40: $i] :
( ( ( epred1_0 @ X33 @ ( esk1_2 @ X33 @ X34 ) )
| ~ ( epred1_0 @ X33 @ X37 )
| ( X34 @ X37 ) )
& ( ( epred1_0 @ ( esk1_2 @ X33 @ X34 ) @ ( esk2_2 @ X33 @ X34 ) )
| ~ ( epred1_0 @ X33 @ X37 )
| ( X34 @ X37 ) )
& ( ~ ( X34 @ ( esk2_2 @ X33 @ X34 ) )
| ~ ( epred1_0 @ X33 @ X37 )
| ( X34 @ X37 ) )
& ( epred1_0 @ esk3_0 @ esk4_0 )
& ( ~ ( epred1_0 @ esk3_0 @ X40 )
| ~ ( epred1_0 @ X40 @ 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)],[inference(fof_simplification,[status(thm)],[c_0_17])])])])])])]) ).
thf(c_0_19,negated_conjecture,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ X14 )
| ~ ( X4 @ ( esk2_2 @ X3 @ X4 ) )
| ~ ( epred1_0 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_20,negated_conjecture,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( epred1_0 @ ( esk1_2 @ X3 @ X4 ) @ ( esk2_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( epred1_0 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
epred1_0 @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i,X14: $i] :
( ( ( esk2_2 @ X3
@ ^ [Z0: $i] : ( Z0 != X14 ) )
= X14 )
| ~ ( epred1_0 @ X3 @ X14 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_19]) ).
thf(c_0_23,negated_conjecture,
! [X4: $i > $o] :
( ( epred1_0 @ ( esk1_2 @ esk3_0 @ X4 ) @ ( esk2_2 @ esk3_0 @ X4 ) )
| ( X4 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,negated_conjecture,
( ( esk2_2 @ esk3_0
@ ^ [Z0: $i] : ( Z0 != esk4_0 ) )
= esk4_0 ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X3: $i] :
( ~ ( epred1_0 @ esk3_0 @ X3 )
| ~ ( epred1_0 @ X3 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,negated_conjecture,
( epred1_0
@ ( esk1_2 @ esk3_0
@ ^ [Z0: $i] : ( Z0 != esk4_0 ) )
@ esk4_0 ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24])])]) ).
thf(c_0_27,negated_conjecture,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( epred1_0 @ X3 @ ( esk1_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( epred1_0 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_28,negated_conjecture,
~ ( epred1_0 @ esk3_0
@ ( esk1_2 @ esk3_0
@ ^ [Z0: $i] : ( Z0 != esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_29,negated_conjecture,
! [X4: $i > $o] :
( ( epred1_0 @ esk3_0 @ ( esk1_2 @ esk3_0 @ X4 ) )
| ( X4 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
thf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29])])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL716^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n008.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 09:53:24 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.30 Running higher-order theorem proving
% 0.29/0.33 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.QmuhpYtzbx/E---3.1_2937400.p
% 0.29/0.37 % Version: 3.5.1-ho
% 0.29/0.37 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.29/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.37 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.29/0.37 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.29/0.37 % Starting sh5l with 300s (1) cores
% 0.29/0.37 % Starting ho_unfolding_6 with 300s (1) cores
% 0.29/0.37 % ehoh_best2_full_lfho with pid 2937413 completed with status 0
% 0.29/0.37 % Result found by ehoh_best2_full_lfho
% 0.29/0.37 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.29/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.37 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.29/0.37 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.37 % No SInE strategy applied
% 0.29/0.37 % Search class: HGHNF-FFSF22-SHHSMMBN
% 0.29/0.37 % partial match(1): HGUNF-FFSF22-SHHSMMBN
% 0.29/0.37 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.37 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.37 % Starting ehoh_best2_full_lfho with 151s (1) cores
% 0.29/0.37 % Starting sh5l with 136s (1) cores
% 0.29/0.37 % Starting new_bool_1 with 136s (1) cores
% 0.29/0.37 % Starting new_bool_2 with 136s (1) cores
% 0.29/0.37 % ehoh_best2_full_lfho with pid 2937420 completed with status 0
% 0.29/0.37 % Result found by ehoh_best2_full_lfho
% 0.29/0.37 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.29/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.37 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.29/0.37 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.37 % No SInE strategy applied
% 0.29/0.37 % Search class: HGHNF-FFSF22-SHHSMMBN
% 0.29/0.37 % partial match(1): HGUNF-FFSF22-SHHSMMBN
% 0.29/0.37 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.37 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.37 % Starting ehoh_best2_full_lfho with 151s (1) cores
% 0.29/0.37 % Preprocessing time : 0.002 s
% 0.29/0.37
% 0.29/0.37 % Proof found!
% 0.29/0.37 % SZS status Theorem
% 0.29/0.37 % SZS output start CNFRefutation
% See solution above
% 0.29/0.37 % Parsed axioms : 64
% 0.29/0.37 % Removed by relevancy pruning/SinE : 0
% 0.29/0.37 % Initial clauses : 37
% 0.29/0.37 % Removed in clause preprocessing : 32
% 0.29/0.37 % Initial clauses in saturation : 5
% 0.29/0.37 % Processed clauses : 19
% 0.29/0.37 % ...of these trivial : 0
% 0.29/0.37 % ...subsumed : 1
% 0.29/0.37 % ...remaining for further processing : 18
% 0.29/0.37 % Other redundant clauses eliminated : 2
% 0.29/0.37 % Clauses deleted for lack of memory : 0
% 0.29/0.37 % Backward-subsumed : 0
% 0.29/0.37 % Backward-rewritten : 0
% 0.29/0.37 % Generated clauses : 101
% 0.29/0.37 % ...of the previous two non-redundant : 81
% 0.29/0.37 % ...aggressively subsumed : 0
% 0.29/0.37 % Contextual simplify-reflections : 0
% 0.29/0.37 % Paramodulations : 51
% 0.29/0.37 % Factorizations : 2
% 0.29/0.37 % NegExts : 0
% 0.29/0.37 % Equation resolutions : 2
% 0.29/0.37 % Disequality decompositions : 0
% 0.29/0.37 % Total rewrite steps : 6
% 0.29/0.37 % ...of those cached : 4
% 0.29/0.37 % Propositional unsat checks : 0
% 0.29/0.37 % Propositional check models : 0
% 0.29/0.37 % Propositional check unsatisfiable : 0
% 0.29/0.37 % Propositional clauses : 0
% 0.29/0.37 % Propositional clauses after purity: 0
% 0.29/0.37 % Propositional unsat core size : 0
% 0.29/0.37 % Propositional preprocessing time : 0.000
% 0.29/0.37 % Propositional encoding time : 0.000
% 0.29/0.37 % Propositional solver time : 0.000
% 0.29/0.37 % Success case prop preproc time : 0.000
% 0.29/0.37 % Success case prop encoding time : 0.000
% 0.29/0.37 % Success case prop solver time : 0.000
% 0.29/0.37 % Current number of processed clauses : 18
% 0.29/0.37 % Positive orientable unit clauses : 4
% 0.29/0.37 % Positive unorientable unit clauses: 0
% 0.29/0.37 % Negative unit clauses : 2
% 0.29/0.37 % Non-unit-clauses : 12
% 0.29/0.37 % Current number of unprocessed clauses: 66
% 0.29/0.37 % ...number of literals in the above : 174
% 0.29/0.37 % Current number of archived formulas : 0
% 0.29/0.37 % Current number of archived clauses : 0
% 0.29/0.37 % Clause-clause subsumption calls (NU) : 8
% 0.29/0.37 % Rec. Clause-clause subsumption calls : 8
% 0.29/0.37 % Non-unit clause-clause subsumptions : 1
% 0.29/0.37 % Unit Clause-clause subsumption calls : 0
% 0.29/0.37 % Rewrite failures with RHS unbound : 0
% 0.29/0.37 % BW rewrite match attempts : 0
% 0.29/0.37 % BW rewrite match successes : 0
% 0.29/0.37 % Condensation attempts : 0
% 0.29/0.37 % Condensation successes : 0
% 0.29/0.37 % Termbank termtop insertions : 4442
% 0.29/0.37 % Search garbage collected termcells : 604
% 0.29/0.37
% 0.29/0.37 % -------------------------------------------------
% 0.29/0.37 % User time : 0.013 s
% 0.29/0.37 % System time : 0.004 s
% 0.29/0.37 % Total time : 0.017 s
% 0.29/0.37 % Maximum resident set size: 3652 pages
% 0.29/0.37
% 0.29/0.37 % -------------------------------------------------
% 0.29/0.37 % User time : 0.056 s
% 0.29/0.37 % System time : 0.016 s
% 0.29/0.37 % Total time : 0.072 s
% 0.29/0.37 % Maximum resident set size: 4608 pages
% 0.29/0.37 % E exiting
%------------------------------------------------------------------------------