%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL604^1 : TPTP v9.3.1. Released v3.6.0.
% 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 08:11:59 AM UTC 2026
% Result : Theorem 0.29s 0.39s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 15 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 292 ( 40 ~; 40 |; 18 &; 182 @)
% ( 0 <=>; 10 =>; 2 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 76 ( 30 ^; 46 !; 0 ?; 76 :)
% 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_50,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(decl_53,type,
transitive: ( $i > $i > $o ) > $o ).
thf(decl_63,type,
epred1_0: $i > $i > $o ).
thf(decl_64,type,
epred2_0: $i > $o ).
thf(decl_65,type,
esk1_0: $i ).
thf(decl_66,type,
esk2_0: $i ).
thf(decl_67,type,
esk3_0: $i ).
thf(decl_68,type,
esk4_0: $i ).
thf(mimpl,axiom,
( mimpl
= ( ^ [X7: $i > $o,X8: $i > $o] : ( mor @ ( mnot @ X7 ) @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vBnohuRZnI/E---3.1_1033523.p',mimpl) ).
thf(mnot,axiom,
( mnot
= ( ^ [X2: $i > $o,X3: $i] :
~ ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vBnohuRZnI/E---3.1_1033523.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vBnohuRZnI/E---3.1_1033523.p',mor) ).
thf(thm,conjecture,
! [X10: $i > $i > $o] :
( ! [X28: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X10 @ X28 ) @ ( mbox @ X10 @ ( mbox @ X10 @ X28 ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ X10 @ X28 ) @ X28 ) ) )
<= ( ( reflexive @ X10 )
& ( transitive @ X10 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vBnohuRZnI/E---3.1_1033523.p',thm) ).
thf(mbox,axiom,
( mbox
= ( ^ [X10: $i > $i > $o,X11: $i > $o,X1: $i] :
! [X12: $i] :
( ( X10 @ X1 @ X12 )
=> ( X11 @ X12 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vBnohuRZnI/E---3.1_1033523.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X11: $i > $o] :
! [X15: $i] : ( X11 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vBnohuRZnI/E---3.1_1033523.p',mvalid) ).
thf(reflexive,axiom,
( reflexive
= ( ^ [X10: $i > $i > $o] :
! [X1: $i] : ( X10 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vBnohuRZnI/E---3.1_1033523.p',reflexive) ).
thf(transitive,axiom,
( transitive
= ( ^ [X10: $i > $i > $o] :
! [X1: $i,X36: $i,X33: $i] :
( ( ( X10 @ X1 @ X36 )
& ( X10 @ X36 @ X33 ) )
=> ( X10 @ X1 @ X33 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vBnohuRZnI/E---3.1_1033523.p',transitive) ).
thf(c_0_8,plain,
( mimpl
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimpl]) ).
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,
~ ! [X10: $i > $i > $o] :
( ! [X28: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X10 @ X28 ) @ ( mbox @ X10 @ ( mbox @ X10 @ X28 ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ X10 @ X28 ) @ X28 ) ) )
<= ( ( reflexive @ X10 )
& ( transitive @ X10 ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_12,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_8,c_0_9]),c_0_10]) ).
thf(c_0_13,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_14,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X15: $i] : ( Z0 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_15,plain,
( reflexive
= ( ^ [Z0: $i > $i > $o] :
! [X1: $i] : ( Z0 @ X1 @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[reflexive]) ).
thf(c_0_16,plain,
( transitive
= ( ^ [Z0: $i > $i > $o] :
! [X1: $i,X36: $i,X33: $i] :
( ( ( Z0 @ X1 @ X36 )
& ( Z0 @ X36 @ X33 ) )
=> ( Z0 @ X1 @ X33 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive]) ).
thf(c_0_17,negated_conjecture,
~ ! [X10: $i > $i > $o] :
( ( ! [X63: $i] : ( X10 @ X63 @ X63 )
& ! [X64: $i,X65: $i,X66: $i] :
( ( ( X10 @ X64 @ X65 )
& ( X10 @ X65 @ X66 ) )
=> ( X10 @ X64 @ X66 ) ) )
=> ! [X28: $i > $o] :
( ! [X60: $i] :
( ~ ! [X57: $i] :
( ( X10 @ X60 @ X57 )
=> ( X28 @ X57 ) )
| ! [X59: $i] :
( ( X10 @ X60 @ X59 )
=> ! [X58: $i] :
( ( X10 @ X59 @ X58 )
=> ( X28 @ X58 ) ) ) )
& ! [X62: $i] :
( ~ ! [X61: $i] :
( ( X10 @ X62 @ X61 )
=> ( X28 @ X61 ) )
| ( X28 @ X62 ) ) ) ),
inference(fof_simplification,[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)],[c_0_11,c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]) ).
thf(c_0_18,negated_conjecture,
! [X68: $i,X69: $i,X70: $i,X71: $i,X74: $i,X78: $i] :
( ( epred1_0 @ X68 @ X68 )
& ( ~ ( epred1_0 @ X69 @ X70 )
| ~ ( epred1_0 @ X70 @ X71 )
| ( epred1_0 @ X69 @ X71 ) )
& ( ~ ( epred1_0 @ esk4_0 @ X78 )
| ( epred2_0 @ X78 )
| ~ ( epred1_0 @ esk1_0 @ X74 )
| ( epred2_0 @ X74 ) )
& ( ~ ( epred2_0 @ esk4_0 )
| ~ ( epred1_0 @ esk1_0 @ X74 )
| ( epred2_0 @ X74 ) )
& ( ~ ( epred1_0 @ esk4_0 @ X78 )
| ( epred2_0 @ X78 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred2_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ X78 )
| ( epred2_0 @ X78 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) )
& ( ~ ( epred2_0 @ esk4_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ X78 )
| ( epred2_0 @ X78 )
| ~ ( epred2_0 @ esk3_0 ) )
& ( ~ ( epred2_0 @ esk4_0 )
| ~ ( epred2_0 @ esk3_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_17])])])])])]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk4_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] : ( epred1_0 @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
( ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred2_0 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X3: $i,X12: $i] :
( ( epred1_0 @ X1 @ X12 )
| ~ ( epred1_0 @ X1 @ X3 )
| ~ ( epred1_0 @ X3 @ X12 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
epred1_0 @ esk2_0 @ esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk4_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred2_0 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ esk4_0 @ X1 )
| ~ ( epred2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_27,negated_conjecture,
( ~ ( epred2_0 @ esk4_0 )
| ~ ( epred2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred2_0 @ X1 )
| ( epred2_0 @ X3 )
| ~ ( epred1_0 @ esk4_0 @ X1 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 @ esk3_0 )
| ~ ( epred1_0 @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_30,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20]),c_0_25]) ).
thf(c_0_31,negated_conjecture,
~ ( epred2_0 @ esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_27]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( epred2_0 @ esk4_0 )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ esk4_0 @ X1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),c_0_31]) ).
thf(c_0_34,negated_conjecture,
~ ( epred2_0 @ esk4_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_29]),c_0_30])]),c_0_31]) ).
thf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL604^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n002.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Tue Sep 29 09:20:22 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.33 Running higher-order theorem proving
% 0.29/0.36 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.vBnohuRZnI/E---3.1_1033523.p
% 0.29/0.39 % Version: 3.5.1-ho
% 0.29/0.39 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.29/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.39 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.29/0.39 % Starting post_as_ho3 with 300s (1) cores
% 0.29/0.39 % Starting post_as_ho11 with 300s (1) cores
% 0.29/0.39 % Starting full_lambda_8 with 300s (1) cores
% 0.29/0.39 % new_ho_10_cnf2 with pid 1033536 completed with status 0
% 0.29/0.39 % Result found by new_ho_10_cnf2
% 0.29/0.39 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.29/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.39 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.29/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.39 % No SInE strategy applied
% 0.29/0.39 % Search class: HGHNF-FFSF00-SHSSMFNN
% 0.29/0.39 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.39 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.39 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.29/0.39 % Starting sh5l with 136s (1) cores
% 0.29/0.39 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.29/0.39 % Starting lpo1_def_fix with 136s (1) cores
% 0.29/0.39 % SubtermCWHack with pid 1033541 completed with status 0
% 0.29/0.39 % Result found by SubtermCWHack
% 0.29/0.39 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.29/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.39 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.29/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.39 % No SInE strategy applied
% 0.29/0.39 % Search class: HGHNF-FFSF00-SHSSMFNN
% 0.29/0.39 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.39 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.39 % Preprocessing time : 0.001 s
% 0.29/0.39
% 0.29/0.39 % Proof found!
% 0.29/0.39 % SZS status Theorem
% 0.29/0.39 % SZS output start CNFRefutation
% See solution above
% 0.29/0.40 % Parsed axioms : 78
% 0.29/0.40 % Removed by relevancy pruning/SinE : 0
% 0.29/0.40 % Initial clauses : 51
% 0.29/0.40 % Removed in clause preprocessing : 41
% 0.29/0.40 % Initial clauses in saturation : 10
% 0.29/0.40 % Processed clauses : 23
% 0.29/0.40 % ...of these trivial : 0
% 0.29/0.40 % ...subsumed : 2
% 0.29/0.40 % ...remaining for further processing : 21
% 0.29/0.40 % Other redundant clauses eliminated : 0
% 0.29/0.40 % Clauses deleted for lack of memory : 0
% 0.29/0.40 % Backward-subsumed : 8
% 0.29/0.40 % Backward-rewritten : 2
% 0.29/0.40 % Generated clauses : 25
% 0.29/0.40 % ...of the previous two non-redundant : 23
% 0.29/0.40 % ...aggressively subsumed : 0
% 0.29/0.40 % Contextual simplify-reflections : 3
% 0.29/0.40 % Paramodulations : 25
% 0.29/0.40 % Factorizations : 0
% 0.29/0.40 % NegExts : 0
% 0.29/0.40 % Equation resolutions : 0
% 0.29/0.40 % Disequality decompositions : 0
% 0.29/0.40 % Total rewrite steps : 6
% 0.29/0.40 % ...of those cached : 3
% 0.29/0.40 % Propositional unsat checks : 0
% 0.29/0.40 % Propositional check models : 0
% 0.29/0.40 % Propositional check unsatisfiable : 0
% 0.29/0.40 % Propositional clauses : 0
% 0.29/0.40 % Propositional clauses after purity: 0
% 0.29/0.40 % Propositional unsat core size : 0
% 0.29/0.40 % Propositional preprocessing time : 0.000
% 0.29/0.40 % Propositional encoding time : 0.000
% 0.29/0.40 % Propositional solver time : 0.000
% 0.29/0.40 % Success case prop preproc time : 0.000
% 0.29/0.40 % Success case prop encoding time : 0.000
% 0.29/0.40 % Success case prop solver time : 0.000
% 0.29/0.40 % Current number of processed clauses : 11
% 0.29/0.40 % Positive orientable unit clauses : 3
% 0.29/0.40 % Positive unorientable unit clauses: 0
% 0.29/0.40 % Negative unit clauses : 2
% 0.29/0.40 % Non-unit-clauses : 6
% 0.29/0.40 % Current number of unprocessed clauses: 7
% 0.29/0.40 % ...number of literals in the above : 20
% 0.29/0.40 % Current number of archived formulas : 0
% 0.29/0.40 % Current number of archived clauses : 10
% 0.29/0.40 % Clause-clause subsumption calls (NU) : 14
% 0.29/0.40 % Rec. Clause-clause subsumption calls : 13
% 0.29/0.40 % Non-unit clause-clause subsumptions : 6
% 0.29/0.40 % Unit Clause-clause subsumption calls : 7
% 0.29/0.40 % Rewrite failures with RHS unbound : 0
% 0.29/0.40 % BW rewrite match attempts : 2
% 0.29/0.40 % BW rewrite match successes : 2
% 0.29/0.40 % Condensation attempts : 0
% 0.29/0.40 % Condensation successes : 0
% 0.29/0.40 % Termbank termtop insertions : 3052
% 0.29/0.40 % Search garbage collected termcells : 574
% 0.29/0.40
% 0.29/0.40 % -------------------------------------------------
% 0.29/0.40 % User time : 0.009 s
% 0.29/0.40 % System time : 0.003 s
% 0.29/0.40 % Total time : 0.012 s
% 0.29/0.40 % Maximum resident set size: 3720 pages
% 0.29/0.40
% 0.29/0.40 % -------------------------------------------------
% 0.29/0.40 % User time : 0.022 s
% 0.29/0.40 % System time : 0.013 s
% 0.29/0.40 % Total time : 0.035 s
% 0.29/0.40 % Maximum resident set size: 4864 pages
% 0.29/0.40 % E exiting
%------------------------------------------------------------------------------