%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL707^1 : TPTP v9.3.1. Bugfixed v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:13:03 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 27 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 268 ( 39 ~; 41 |; 11 &; 171 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 80 ( 44 ^; 36 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mand: ( $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_48,type,
mweakly_connected: ( $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_0: $i ).
thf(decl_56,type,
epred2_0: $i > $o ).
thf(decl_57,type,
epred3_0: $i > $o ).
thf(decl_58,type,
esk2_0: $i ).
thf(decl_59,type,
esk3_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UjEqxJSOZ3/E---3.1_370439.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UjEqxJSOZ3/E---3.1_370439.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UjEqxJSOZ3/E---3.1_370439.p',mor) ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UjEqxJSOZ3/E---3.1_370439.p',mand) ).
thf(conj,conjecture,
! [X13: $i > $i > $o] :
( ( mweakly_connected @ X13 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] :
( mforall_prop
@ ^ [X19: $i > $o] : ( mor @ ( mbox @ X13 @ ( mimplies @ ( mand @ X18 @ ( mbox @ X13 @ X18 ) ) @ X19 ) ) @ ( mbox @ X13 @ ( mimplies @ ( mand @ X19 @ ( mbox @ X13 @ X19 ) ) @ X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UjEqxJSOZ3/E---3.1_370439.p',conj) ).
thf(mweakly_connected,axiom,
( mweakly_connected
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( X13 @ X15 @ X16 )
& ( X13 @ X15 @ X17 ) )
=> ( ( X13 @ X16 @ X17 )
| ( X16 = X17 )
| ( X13 @ X17 @ X16 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UjEqxJSOZ3/E---3.1_370439.p',mweakly_connected) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UjEqxJSOZ3/E---3.1_370439.p',mbox) ).
thf(mforall_prop,axiom,
( mforall_prop
= ( ^ [X9: ( $i > $o ) > $i > $o,X3: $i] :
! [X10: $i > $o] : ( X9 @ X10 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UjEqxJSOZ3/E---3.1_370439.p',mforall_prop) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UjEqxJSOZ3/E---3.1_370439.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,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_13,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( ( mweakly_connected @ X13 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] :
( mforall_prop
@ ^ [X19: $i > $o] : ( mor @ ( mbox @ X13 @ ( mimplies @ ( mand @ X18 @ ( mbox @ X13 @ X18 ) ) @ X19 ) ) @ ( mbox @ X13 @ ( mimplies @ ( mand @ X19 @ ( mbox @ X13 @ X19 ) ) @ X18 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_14,plain,
( mweakly_connected
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( Z0 @ X15 @ X16 )
& ( Z0 @ X15 @ X17 ) )
=> ( ( Z0 @ X16 @ X17 )
| ( X16 = X17 )
| ( Z0 @ X17 @ X16 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mweakly_connected]) ).
thf(c_0_15,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_16,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_17,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_10]),c_0_11]) ).
thf(c_0_18,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_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] :
( ! [X23: $i,X24: $i,X25: $i] :
( ( ( X13 @ X23 @ X24 )
& ( X13 @ X23 @ X25 ) )
=> ( ( X13 @ X24 @ X25 )
| ( X24 = X25 )
| ( X13 @ X25 @ X24 ) ) )
=> ! [X32: $i,X31: $i > $o,X30: $i > $o] :
( ! [X27: $i] :
( ~ ( X13 @ X32 @ X27 )
| ~ ~ ( ~ ( X31 @ X27 )
| ~ ! [X26: $i] :
( ~ ( X13 @ X27 @ X26 )
| ( X31 @ X26 ) ) )
| ( X30 @ X27 ) )
| ! [X29: $i] :
( ~ ( X13 @ X32 @ X29 )
| ~ ~ ( ~ ( X30 @ X29 )
| ~ ! [X28: $i] :
( ~ ( X13 @ X29 @ X28 )
| ( X30 @ X28 ) ) )
| ( 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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_13]),c_0_14]),c_0_15]),c_0_16]),c_0_17]),c_0_11]),c_0_18]),c_0_19]) ).
thf(c_0_21,negated_conjecture,
! [X34: $i,X35: $i,X36: $i,X41: $i,X43: $i] :
( ( ~ ( epred1_0 @ X34 @ X35 )
| ~ ( epred1_0 @ X34 @ X36 )
| ( epred1_0 @ X35 @ X36 )
| ( X35 = X36 )
| ( epred1_0 @ X36 @ X35 ) )
& ( epred1_0 @ esk1_0 @ esk2_0 )
& ( epred2_0 @ esk2_0 )
& ( ~ ( epred1_0 @ esk2_0 @ X41 )
| ( epred2_0 @ X41 ) )
& ~ ( epred3_0 @ esk2_0 )
& ( epred1_0 @ esk1_0 @ esk3_0 )
& ( epred3_0 @ esk3_0 )
& ( ~ ( epred1_0 @ esk3_0 @ X43 )
| ( epred3_0 @ X43 ) )
& ~ ( epred2_0 @ esk3_0 ) ),
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,X14: $i,X15: $i] :
( ( epred1_0 @ X14 @ X15 )
| ( X14 = X15 )
| ( epred1_0 @ X15 @ X14 )
| ~ ( epred1_0 @ X3 @ X14 )
| ~ ( epred1_0 @ X3 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_23,negated_conjecture,
epred1_0 @ esk1_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X3: $i] :
( ( X3 = esk3_0 )
| ( epred1_0 @ esk3_0 @ X3 )
| ( epred1_0 @ X3 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_25,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ X3 )
| ~ ( epred1_0 @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
( ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_28,negated_conjecture,
~ ( epred2_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i] :
( ( epred3_0 @ X3 )
| ~ ( epred1_0 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_30,negated_conjecture,
( ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_31,negated_conjecture,
~ ( epred3_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_32,negated_conjecture,
esk2_0 = esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
thf(c_0_33,negated_conjecture,
epred3_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL707^1 : TPTP v9.3.1. Bugfixed v5.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 09:49:12 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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.UjEqxJSOZ3/E---3.1_370439.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.22/0.27 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.22/0.27 % Starting sh5l with 300s (1) cores
% 0.22/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.27 % sh5l with pid 370454 completed with status 0
% 0.22/0.27 % Result found by sh5l
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.22/0.27 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.22/0.27 % Starting sh5l with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.22/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.22/0.27 % Search class: HGUSF-FFSS00-SHHSMFNN
% 0.22/0.27 % partial match(3): HGHNF-FFSS00-SHSSMFNN
% 0.22/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 370456 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.22/0.27 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.22/0.27 % Starting sh5l with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.22/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.22/0.27 % Search class: HGUSF-FFSS00-SHHSMFNN
% 0.22/0.27 % partial match(3): HGHNF-FFSS00-SHSSMFNN
% 0.22/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.27 % Parsed axioms : 64
% 0.22/0.27 % Removed by relevancy pruning/SinE : 50
% 0.22/0.27 % Initial clauses : 9
% 0.22/0.27 % Removed in clause preprocessing : 0
% 0.22/0.27 % Initial clauses in saturation : 9
% 0.22/0.27 % Processed clauses : 14
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 0
% 0.22/0.27 % ...remaining for further processing : 14
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 1
% 0.22/0.27 % Backward-rewritten : 6
% 0.22/0.27 % Generated clauses : 8
% 0.22/0.27 % ...of the previous two non-redundant : 8
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 0
% 0.22/0.27 % Paramodulations : 8
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 2
% 0.22/0.27 % ...of those cached : 0
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 7
% 0.22/0.27 % Positive orientable unit clauses : 3
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 1
% 0.22/0.27 % Non-unit-clauses : 3
% 0.22/0.27 % Current number of unprocessed clauses: 3
% 0.22/0.27 % ...number of literals in the above : 14
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 7
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 1
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 1
% 0.22/0.27 % Non-unit clause-clause subsumptions : 1
% 0.22/0.27 % Unit Clause-clause subsumption calls : 0
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 1
% 0.22/0.27 % BW rewrite match successes : 1
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 2488
% 0.22/0.27 % Search garbage collected termcells : 1049
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.003 s
% 0.22/0.27 % System time : 0.003 s
% 0.22/0.28 % Total time : 0.007 s
% 0.22/0.28 % Maximum resident set size: 3900 pages
% 0.22/0.28
% 0.22/0.28 % -------------------------------------------------
% 0.22/0.28 % User time : 0.004 s
% 0.22/0.28 % System time : 0.010 s
% 0.22/0.28 % Total time : 0.014 s
% 0.22/0.28 % Maximum resident set size: 4864 pages
% 0.22/0.28 % E exiting
%------------------------------------------------------------------------------