%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET002^7 : 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 : 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 08:21:50 AM UTC 2026
% Result : Theorem 0.24s 0.28s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 11 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 163 ( 18 ~; 13 |; 1 &; 125 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 29 ^; 21 !; 0 ?; 50 :)
% 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_32,type,
mimplies: ( $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_58,type,
subset: mu > mu > $i > $o ).
thf(decl_60,type,
union: mu > mu > mu ).
thf(decl_64,type,
esk4_0: $i ).
thf(decl_65,type,
esk5_0: mu ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v1ftnVHI8w/E---3.1_2656182.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v1ftnVHI8w/E---3.1_2656182.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v1ftnVHI8w/E---3.1_2656182.p',mor) ).
thf(prove_idempotency_of_union,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X29: mu] : ( qmltpeq @ ( union @ X29 @ X29 ) @ X29 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v1ftnVHI8w/E---3.1_2656182.p',prove_idempotency_of_union) ).
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.v1ftnVHI8w/E---3.1_2656182.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v1ftnVHI8w/E---3.1_2656182.p',mvalid) ).
thf(subset_union,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X29: mu] :
( mforall_ind
@ ^ [X30: mu] : ( mimplies @ ( subset @ X29 @ X30 ) @ ( qmltpeq @ ( union @ X29 @ X30 ) @ X30 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v1ftnVHI8w/E---3.1_2656182.p',subset_union) ).
thf(reflexivity_of_subset,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X29: mu] : ( subset @ X29 @ X29 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v1ftnVHI8w/E---3.1_2656182.p',reflexivity_of_subset) ).
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,
~ ( mvalid
@ ( mforall_ind
@ ^ [X29: mu] : ( qmltpeq @ ( union @ X29 @ X29 ) @ X29 ) ) ),
inference(assume_negation,[status(cth)],[prove_idempotency_of_union]) ).
thf(c_0_12,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_13,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_14,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_15,negated_conjecture,
~ ! [X105: $i,X104: mu] :
( ( exists_in_world @ X104 @ X105 )
=> ( qmltpeq @ ( union @ X104 @ X104 ) @ X104 @ X105 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_11]),c_0_12]),c_0_13]) ).
thf(c_0_16,plain,
! [X83: $i,X82: mu] :
( ( exists_in_world @ X82 @ X83 )
=> ! [X81: mu] :
( ( exists_in_world @ X81 @ X83 )
=> ( ~ ( subset @ X82 @ X81 @ X83 )
| ( qmltpeq @ ( union @ X82 @ X81 ) @ X81 @ X83 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[subset_union]),c_0_14]),c_0_12]),c_0_13])]) ).
thf(c_0_17,negated_conjecture,
( ( exists_in_world @ esk5_0 @ esk4_0 )
& ~ ( qmltpeq @ ( union @ esk5_0 @ esk5_0 ) @ esk5_0 @ esk4_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
thf(c_0_18,plain,
! [X151: $i,X152: mu,X153: mu] :
( ~ ( exists_in_world @ X152 @ X151 )
| ~ ( exists_in_world @ X153 @ X151 )
| ~ ( subset @ X152 @ X153 @ X151 )
| ( qmltpeq @ ( union @ X152 @ X153 ) @ X153 @ X151 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
thf(c_0_19,plain,
! [X99: $i,X98: mu] :
( ( exists_in_world @ X98 @ X99 )
=> ( subset @ X98 @ X98 @ X99 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_of_subset]),c_0_12]),c_0_13]) ).
thf(c_0_20,negated_conjecture,
~ ( qmltpeq @ ( union @ esk5_0 @ esk5_0 ) @ esk5_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( qmltpeq @ ( union @ X10 @ X12 ) @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( subset @ X10 @ X12 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
exists_in_world @ esk5_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
! [X169: $i,X170: mu] :
( ~ ( exists_in_world @ X170 @ X169 )
| ( subset @ X170 @ X170 @ X169 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
thf(c_0_24,negated_conjecture,
~ ( subset @ esk5_0 @ esk5_0 @ esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
thf(c_0_25,plain,
! [X10: mu,X3: $i] :
( ( subset @ X10 @ X10 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.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
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:35:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.v1ftnVHI8w/E---3.1_2656182.p
% 0.24/0.28 % Version: 3.5.1-ho
% 0.24/0.28 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.28 % Starting post_as_ho3 with 300s (1) cores
% 0.24/0.28 % Starting new_ho_12 with 300s (1) cores
% 0.24/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.24/0.28 % post_as_ho3 with pid 2656196 completed with status 0
% 0.24/0.28 % Result found by post_as_ho3
% 0.24/0.28 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.28 % Starting post_as_ho3 with 300s (1) cores
% 0.24/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.28 % No SInE strategy applied
% 0.24/0.28 % Search class: HGUNS-FFMF32-SHSSMFNN
% 0.24/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.28 % SubtermCWHack with pid 2656201 completed with status 0
% 0.24/0.28 % Result found by SubtermCWHack
% 0.24/0.28 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.24/0.28 % Starting post_as_ho3 with 300s (1) cores
% 0.24/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.28 % No SInE strategy applied
% 0.24/0.28 % Search class: HGUNS-FFMF32-SHSSMFNN
% 0.24/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.28 % Preprocessing time : 0.001 s
% 0.24/0.28
% 0.24/0.28 % Proof found!
% 0.24/0.28 % SZS status Theorem
% 0.24/0.28 % SZS output start CNFRefutation
% See solution above
% 0.24/0.28 % Parsed axioms : 93
% 0.24/0.28 % Removed by relevancy pruning/SinE : 0
% 0.24/0.28 % Initial clauses : 75
% 0.24/0.28 % Removed in clause preprocessing : 41
% 0.24/0.28 % Initial clauses in saturation : 34
% 0.24/0.28 % Processed clauses : 17
% 0.24/0.28 % ...of these trivial : 0
% 0.24/0.28 % ...subsumed : 2
% 0.24/0.28 % ...remaining for further processing : 15
% 0.24/0.28 % Other redundant clauses eliminated : 0
% 0.24/0.28 % Clauses deleted for lack of memory : 0
% 0.24/0.28 % Backward-subsumed : 0
% 0.24/0.28 % Backward-rewritten : 0
% 0.24/0.28 % Generated clauses : 9
% 0.24/0.28 % ...of the previous two non-redundant : 6
% 0.24/0.28 % ...aggressively subsumed : 0
% 0.24/0.28 % Contextual simplify-reflections : 0
% 0.24/0.28 % Paramodulations : 9
% 0.24/0.28 % Factorizations : 0
% 0.24/0.28 % NegExts : 0
% 0.24/0.28 % Equation resolutions : 0
% 0.24/0.28 % Disequality decompositions : 0
% 0.24/0.28 % Total rewrite steps : 7
% 0.24/0.28 % ...of those cached : 4
% 0.24/0.28 % Propositional unsat checks : 0
% 0.24/0.28 % Propositional check models : 0
% 0.24/0.28 % Propositional check unsatisfiable : 0
% 0.24/0.28 % Propositional clauses : 0
% 0.24/0.28 % Propositional clauses after purity: 0
% 0.24/0.28 % Propositional unsat core size : 0
% 0.24/0.28 % Propositional preprocessing time : 0.000
% 0.24/0.28 % Propositional encoding time : 0.000
% 0.24/0.28 % Propositional solver time : 0.000
% 0.24/0.28 % Success case prop preproc time : 0.000
% 0.24/0.28 % Success case prop encoding time : 0.000
% 0.24/0.28 % Success case prop solver time : 0.000
% 0.24/0.28 % Current number of processed clauses : 15
% 0.24/0.28 % Positive orientable unit clauses : 4
% 0.24/0.28 % Positive unorientable unit clauses: 0
% 0.24/0.28 % Negative unit clauses : 2
% 0.24/0.28 % Non-unit-clauses : 9
% 0.24/0.28 % Current number of unprocessed clauses: 21
% 0.24/0.28 % ...number of literals in the above : 109
% 0.24/0.28 % Current number of archived formulas : 0
% 0.24/0.28 % Current number of archived clauses : 0
% 0.24/0.28 % Clause-clause subsumption calls (NU) : 27
% 0.24/0.28 % Rec. Clause-clause subsumption calls : 23
% 0.24/0.28 % Non-unit clause-clause subsumptions : 2
% 0.24/0.28 % Unit Clause-clause subsumption calls : 0
% 0.24/0.28 % Rewrite failures with RHS unbound : 0
% 0.24/0.28 % BW rewrite match attempts : 0
% 0.24/0.28 % BW rewrite match successes : 0
% 0.24/0.28 % Condensation attempts : 0
% 0.24/0.28 % Condensation successes : 0
% 0.24/0.28 % Termbank termtop insertions : 10067
% 0.24/0.28 % Search garbage collected termcells : 4150
% 0.24/0.28
% 0.24/0.28 % -------------------------------------------------
% 0.24/0.28 % User time : 0.008 s
% 0.24/0.28 % System time : 0.005 s
% 0.24/0.28 % Total time : 0.013 s
% 0.24/0.28 % Maximum resident set size: 4248 pages
% 0.24/0.28
% 0.24/0.28 % -------------------------------------------------
% 0.24/0.28 % User time : 0.010 s
% 0.24/0.28 % System time : 0.008 s
% 0.24/0.28 % Total time : 0.018 s
% 0.24/0.28 % Maximum resident set size: 4864 pages
% 0.24/0.28 % E exiting
%------------------------------------------------------------------------------