%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET583^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 08:21:58 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 17 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 290 ( 53 ~; 33 |; 6 &; 192 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 46 ^; 16 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_23,type,
qmltpeq: mu > mu > $i > $o ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_34,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_37,type,
exists_in_world: mu > $i > $o ).
thf(decl_38,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_51,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_59,type,
subset: mu > mu > $i > $o ).
thf(decl_62,type,
esk3_0: $i ).
thf(decl_63,type,
esk4_0: mu ).
thf(decl_64,type,
esk5_0: mu ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3PxVM9dXjC/E---3.1_600532.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3PxVM9dXjC/E---3.1_600532.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3PxVM9dXjC/E---3.1_600532.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3PxVM9dXjC/E---3.1_600532.p',mimplies) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mand @ ( mimplies @ X4 @ X5 ) @ ( mimplies @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3PxVM9dXjC/E---3.1_600532.p',mequiv) ).
thf(prove_extensionality,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X27: mu] :
( mforall_ind
@ ^ [X28: mu] : ( mimplies @ ( mand @ ( subset @ X27 @ X28 ) @ ( subset @ X28 @ X27 ) ) @ ( qmltpeq @ X27 @ X28 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3PxVM9dXjC/E---3.1_600532.p',prove_extensionality) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X11: mu > $i > $o,X3: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ X3 )
=> ( X11 @ X12 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3PxVM9dXjC/E---3.1_600532.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3PxVM9dXjC/E---3.1_600532.p',mvalid) ).
thf(equal_defn,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X27: mu] :
( mforall_ind
@ ^ [X28: mu] : ( mequiv @ ( qmltpeq @ X27 @ X28 ) @ ( mand @ ( subset @ X27 @ X28 ) @ ( subset @ X28 @ X27 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3PxVM9dXjC/E---3.1_600532.p',equal_defn) ).
thf(c_0_9,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
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,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_13,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv]) ).
thf(c_0_14,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_9,c_0_10]),c_0_11]) ).
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_12,c_0_10]),c_0_11]) ).
thf(c_0_16,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X27: mu] :
( mforall_ind
@ ^ [X28: mu] : ( mimplies @ ( mand @ ( subset @ X27 @ X28 ) @ ( subset @ X28 @ X27 ) ) @ ( qmltpeq @ X27 @ X28 ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_extensionality]) ).
thf(c_0_17,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ Z1 )
=> ( Z0 @ X12 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_18,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_19,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_20,negated_conjecture,
~ ! [X79: $i,X78: mu] :
( ( exists_in_world @ X78 @ X79 )
=> ! [X77: mu] :
( ( exists_in_world @ X77 @ X79 )
=> ( ~ ~ ( ~ ( subset @ X78 @ X77 @ X79 )
| ~ ( subset @ X77 @ X78 @ X79 ) )
| ( qmltpeq @ X78 @ X77 @ X79 ) ) ) ),
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(fof_simplification,[status(thm)],[c_0_16]),c_0_14]),c_0_15]),c_0_17]),c_0_18])]) ).
thf(c_0_21,plain,
! [X70: $i,X69: mu] :
( ( exists_in_world @ X69 @ X70 )
=> ! [X68: mu] :
( ( exists_in_world @ X68 @ X70 )
=> ~ ( ~ ( ~ ( qmltpeq @ X69 @ X68 @ X70 )
| ~ ( ~ ( subset @ X69 @ X68 @ X70 )
| ~ ( subset @ X68 @ X69 @ X70 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ X69 @ X68 @ X70 )
| ~ ( subset @ X68 @ X69 @ X70 ) )
| ( qmltpeq @ X69 @ X68 @ X70 ) ) ) ) ),
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(fof_simplification,[status(thm)],[equal_defn]),c_0_14]),c_0_19]),c_0_17]),c_0_18])]) ).
thf(c_0_22,negated_conjecture,
( ( exists_in_world @ esk4_0 @ esk3_0 )
& ( exists_in_world @ esk5_0 @ esk3_0 )
& ( subset @ esk4_0 @ esk5_0 @ esk3_0 )
& ( subset @ esk5_0 @ esk4_0 @ esk3_0 )
& ~ ( qmltpeq @ esk4_0 @ esk5_0 @ esk3_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
thf(c_0_23,plain,
! [X114: $i,X115: mu,X116: mu] :
( ( ( subset @ X115 @ X116 @ X114 )
| ~ ( qmltpeq @ X115 @ X116 @ X114 )
| ~ ( exists_in_world @ X116 @ X114 )
| ~ ( exists_in_world @ X115 @ X114 ) )
& ( ( subset @ X116 @ X115 @ X114 )
| ~ ( qmltpeq @ X115 @ X116 @ X114 )
| ~ ( exists_in_world @ X116 @ X114 )
| ~ ( exists_in_world @ X115 @ X114 ) )
& ( ~ ( subset @ X115 @ X116 @ X114 )
| ~ ( subset @ X116 @ X115 @ X114 )
| ( qmltpeq @ X115 @ X116 @ X114 )
| ~ ( exists_in_world @ X116 @ X114 )
| ~ ( exists_in_world @ X115 @ X114 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
thf(c_0_24,negated_conjecture,
~ ( qmltpeq @ esk4_0 @ esk5_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_25,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( qmltpeq @ X10 @ X12 @ X3 )
| ~ ( subset @ X10 @ X12 @ X3 )
| ~ ( subset @ X12 @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_26,negated_conjecture,
subset @ esk5_0 @ esk4_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_27,negated_conjecture,
subset @ esk4_0 @ esk5_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,negated_conjecture,
exists_in_world @ esk5_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_29,negated_conjecture,
exists_in_world @ esk4_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET583^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n026.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 13:40:42 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.3PxVM9dXjC/E---3.1_600532.p
% 0.21/0.26 % Version: 3.5.1-ho
% 0.21/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.21/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.21/0.26 % Starting new_ho_12 with 300s (1) cores
% 0.21/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.26 % post_as_ho3 with pid 600546 completed with status 0
% 0.21/0.26 % Result found by post_as_ho3
% 0.21/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.21/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.21/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.26 % No SInE strategy applied
% 0.21/0.26 % Search class: HGUNS-FFMS32-SHSSMFNN
% 0.21/0.26 % partial match(1): HGUNS-FFMF32-SHSSMFNN
% 0.21/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.26 % SubtermCWHack with pid 600552 completed with status 0
% 0.21/0.26 % Result found by SubtermCWHack
% 0.21/0.26 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.21/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.26 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.21/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.21/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.26 % No SInE strategy applied
% 0.21/0.26 % Search class: HGUNS-FFMS32-SHSSMFNN
% 0.21/0.26 % partial match(1): HGUNS-FFMF32-SHSSMFNN
% 0.21/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.26 % Preprocessing time : 0.001 s
% 0.21/0.26
% 0.21/0.26 % Proof found!
% 0.21/0.26 % SZS status Theorem
% 0.21/0.26 % SZS output start CNFRefutation
% See solution above
% 0.21/0.26 % Parsed axioms : 85
% 0.21/0.26 % Removed by relevancy pruning/SinE : 0
% 0.21/0.26 % Initial clauses : 62
% 0.21/0.26 % Removed in clause preprocessing : 38
% 0.21/0.26 % Initial clauses in saturation : 24
% 0.21/0.26 % Processed clauses : 22
% 0.21/0.26 % ...of these trivial : 0
% 0.21/0.26 % ...subsumed : 4
% 0.21/0.26 % ...remaining for further processing : 18
% 0.21/0.26 % Other redundant clauses eliminated : 0
% 0.21/0.26 % Clauses deleted for lack of memory : 0
% 0.21/0.26 % Backward-subsumed : 0
% 0.21/0.26 % Backward-rewritten : 0
% 0.21/0.26 % Generated clauses : 10
% 0.21/0.26 % ...of the previous two non-redundant : 4
% 0.21/0.26 % ...aggressively subsumed : 0
% 0.21/0.26 % Contextual simplify-reflections : 0
% 0.21/0.26 % Paramodulations : 10
% 0.21/0.26 % Factorizations : 0
% 0.21/0.26 % NegExts : 0
% 0.21/0.26 % Equation resolutions : 0
% 0.21/0.26 % Disequality decompositions : 0
% 0.21/0.26 % Total rewrite steps : 4
% 0.21/0.26 % ...of those cached : 0
% 0.21/0.26 % Propositional unsat checks : 0
% 0.21/0.26 % Propositional check models : 0
% 0.21/0.26 % Propositional check unsatisfiable : 0
% 0.21/0.26 % Propositional clauses : 0
% 0.21/0.26 % Propositional clauses after purity: 0
% 0.21/0.26 % Propositional unsat core size : 0
% 0.21/0.26 % Propositional preprocessing time : 0.000
% 0.21/0.26 % Propositional encoding time : 0.000
% 0.21/0.26 % Propositional solver time : 0.000
% 0.21/0.26 % Success case prop preproc time : 0.000
% 0.21/0.26 % Success case prop encoding time : 0.000
% 0.21/0.26 % Success case prop solver time : 0.000
% 0.21/0.26 % Current number of processed clauses : 18
% 0.21/0.26 % Positive orientable unit clauses : 6
% 0.21/0.26 % Positive unorientable unit clauses: 0
% 0.21/0.26 % Negative unit clauses : 1
% 0.21/0.26 % Non-unit-clauses : 11
% 0.21/0.26 % Current number of unprocessed clauses: 6
% 0.21/0.26 % ...number of literals in the above : 36
% 0.21/0.26 % Current number of archived formulas : 0
% 0.21/0.26 % Current number of archived clauses : 0
% 0.21/0.26 % Clause-clause subsumption calls (NU) : 40
% 0.21/0.26 % Rec. Clause-clause subsumption calls : 23
% 0.21/0.26 % Non-unit clause-clause subsumptions : 4
% 0.21/0.26 % Unit Clause-clause subsumption calls : 0
% 0.21/0.26 % Rewrite failures with RHS unbound : 0
% 0.21/0.26 % BW rewrite match attempts : 0
% 0.21/0.26 % BW rewrite match successes : 0
% 0.21/0.26 % Condensation attempts : 0
% 0.21/0.26 % Condensation successes : 0
% 0.21/0.26 % Termbank termtop insertions : 7163
% 0.21/0.26 % Search garbage collected termcells : 2786
% 0.21/0.26
% 0.21/0.26 % -------------------------------------------------
% 0.21/0.26 % User time : 0.006 s
% 0.21/0.26 % System time : 0.005 s
% 0.21/0.26 % Total time : 0.010 s
% 0.21/0.26 % Maximum resident set size: 4232 pages
% 0.21/0.26
% 0.21/0.26 % -------------------------------------------------
% 0.21/0.26 % User time : 0.008 s
% 0.21/0.26 % System time : 0.009 s
% 0.21/0.26 % Total time : 0.017 s
% 0.21/0.26 % Maximum resident set size: 4864 pages
% 0.21/0.26 % E exiting
%------------------------------------------------------------------------------