TSTP Solution File: SEU325+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU325+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 09:19:00 EDT 2022
% Result : Theorem 0.30s 1.47s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 64 ( 22 unt; 0 def)
% Number of atoms : 136 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 50 ~; 40 |; 17 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 65 ( 5 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_tops_2,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( is_a_cover_of_carrier(X1,X2)
& X2 = empty_set ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t5_tops_2) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t6_boole) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t8_boole) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rc1_xboole_0) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_xboole_1) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rc2_subset_1) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_pre_topc) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_subset) ).
fof(d8_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ( is_a_cover_of_carrier(X1,X2)
<=> cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d8_pre_topc) ).
fof(dt_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k5_setfam_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k5_setfam_1) ).
fof(d1_struct_0,axiom,
! [X1] :
( one_sorted_str(X1)
=> ( empty_carrier(X1)
<=> empty(the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_struct_0) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,powerset(powerset(the_carrier(X1))))
=> ~ ( is_a_cover_of_carrier(X1,X2)
& X2 = empty_set ) ) ),
inference(assume_negation,[status(cth)],[t5_tops_2]) ).
fof(c_0_14,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_15,negated_conjecture,
( ~ empty_carrier(esk1_0)
& one_sorted_str(esk1_0)
& element(esk2_0,powerset(powerset(the_carrier(esk1_0))))
& is_a_cover_of_carrier(esk1_0,esk2_0)
& esk2_0 = empty_set ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_13])])])])])]) ).
fof(c_0_16,plain,
! [X3,X4] :
( ~ empty(X3)
| X3 = X4
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_17,plain,
( empty(esk14_0)
& relation(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
cnf(c_0_18,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
esk2_0 = empty_set,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
empty(esk16_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(c_0_21,lemma,
! [X2] :
( ~ subset(X2,empty_set)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
cnf(c_0_22,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
empty(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( X1 = esk2_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
empty(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X3] :
( element(esk19_1(X3),powerset(X3))
& empty(esk19_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_27,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( X1 = esk14_0
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
is_a_cover_of_carrier(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_30,plain,
esk2_0 = esk14_0,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
fof(c_0_31,plain,
! [X2] :
( ~ one_sorted_str(X2)
| cast_as_carrier_subset(X2) = the_carrier(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
cnf(c_0_32,plain,
( X1 = esk16_0
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_33,plain,
empty(esk19_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,lemma,
( X1 = esk2_0
| ~ subset(X1,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_19]),c_0_19]) ).
cnf(c_0_35,plain,
esk14_0 = esk16_0,
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
fof(c_0_36,plain,
! [X3,X4,X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])])]) ).
fof(c_0_37,plain,
! [X3,X4] :
( ( ~ is_a_cover_of_carrier(X3,X4)
| cast_as_carrier_subset(X3) = union_of_subsets(the_carrier(X3),X4)
| ~ element(X4,powerset(powerset(the_carrier(X3))))
| ~ one_sorted_str(X3) )
& ( cast_as_carrier_subset(X3) != union_of_subsets(the_carrier(X3),X4)
| is_a_cover_of_carrier(X3,X4)
| ~ element(X4,powerset(powerset(the_carrier(X3))))
| ~ one_sorted_str(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_pre_topc])])])])])]) ).
cnf(c_0_38,negated_conjecture,
is_a_cover_of_carrier(esk1_0,esk14_0),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,negated_conjecture,
one_sorted_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,plain,
element(esk19_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_42,plain,
esk19_1(X1) = esk16_0,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,lemma,
( X1 = esk16_0
| ~ subset(X1,esk16_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_30]),c_0_30]),c_0_35]),c_0_35]) ).
cnf(c_0_44,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_45,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(union_of_subsets(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
fof(c_0_46,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| union_of_subsets(X3,X4) = union(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
cnf(c_0_47,plain,
( cast_as_carrier_subset(X1) = union_of_subsets(the_carrier(X1),X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ is_a_cover_of_carrier(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_48,negated_conjecture,
is_a_cover_of_carrier(esk1_0,esk16_0),
inference(rw,[status(thm)],[c_0_38,c_0_35]) ).
cnf(c_0_49,negated_conjecture,
cast_as_carrier_subset(esk1_0) = the_carrier(esk1_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_50,plain,
element(esk16_0,powerset(X1)),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,lemma,
( X1 = esk16_0
| ~ element(X1,powerset(esk16_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
( element(union_of_subsets(X1,X2),powerset(X1))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_53,plain,
! [X2] :
( ( ~ empty_carrier(X2)
| empty(the_carrier(X2))
| ~ one_sorted_str(X2) )
& ( ~ empty(the_carrier(X2))
| empty_carrier(X2)
| ~ one_sorted_str(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_struct_0])])]) ).
cnf(c_0_54,plain,
( union_of_subsets(X1,X2) = union(X2)
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,negated_conjecture,
union_of_subsets(the_carrier(esk1_0),esk16_0) = the_carrier(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_40])]),c_0_50])]) ).
cnf(c_0_56,lemma,
( union_of_subsets(esk16_0,X1) = esk16_0
| ~ element(X1,powerset(powerset(esk16_0))) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
~ empty_carrier(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_58,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,negated_conjecture,
union(esk16_0) = the_carrier(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_50])]) ).
cnf(c_0_60,lemma,
( union(X1) = esk16_0
| ~ element(X1,powerset(powerset(esk16_0))) ),
inference(spm,[status(thm)],[c_0_54,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
~ empty(the_carrier(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_40])]) ).
cnf(c_0_62,negated_conjecture,
the_carrier(esk1_0) = esk16_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_50])]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU325+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : run_ET %s %d
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 18:23:03 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.30/1.47 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.30/1.47 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.30/1.47 # Preprocessing time : 0.053 s
% 0.30/1.47
% 0.30/1.47 # Proof found!
% 0.30/1.47 # SZS status Theorem
% 0.30/1.47 # SZS output start CNFRefutation
% See solution above
% 0.30/1.47 # Proof object total steps : 64
% 0.30/1.47 # Proof object clause steps : 37
% 0.30/1.47 # Proof object formula steps : 27
% 0.30/1.47 # Proof object conjectures : 15
% 0.30/1.47 # Proof object clause conjectures : 12
% 0.30/1.47 # Proof object formula conjectures : 3
% 0.30/1.47 # Proof object initial clauses used : 17
% 0.30/1.47 # Proof object initial formulas used : 13
% 0.30/1.47 # Proof object generating inferences : 13
% 0.30/1.47 # Proof object simplifying inferences : 24
% 0.30/1.47 # Training examples: 0 positive, 0 negative
% 0.30/1.47 # Parsed axioms : 538
% 0.30/1.47 # Removed by relevancy pruning/SinE : 437
% 0.30/1.47 # Initial clauses : 410
% 0.30/1.47 # Removed in clause preprocessing : 2
% 0.30/1.47 # Initial clauses in saturation : 408
% 0.30/1.47 # Processed clauses : 519
% 0.30/1.47 # ...of these trivial : 2
% 0.30/1.47 # ...subsumed : 47
% 0.30/1.47 # ...remaining for further processing : 470
% 0.30/1.47 # Other redundant clauses eliminated : 75
% 0.30/1.47 # Clauses deleted for lack of memory : 0
% 0.30/1.47 # Backward-subsumed : 0
% 0.30/1.47 # Backward-rewritten : 55
% 0.30/1.47 # Generated clauses : 3676
% 0.30/1.47 # ...of the previous two non-trivial : 3486
% 0.30/1.47 # Contextual simplify-reflections : 42
% 0.30/1.47 # Paramodulations : 3603
% 0.30/1.47 # Factorizations : 4
% 0.30/1.47 # Equation resolutions : 80
% 0.30/1.47 # Current number of processed clauses : 359
% 0.30/1.47 # Positive orientable unit clauses : 35
% 0.30/1.47 # Positive unorientable unit clauses: 0
% 0.30/1.47 # Negative unit clauses : 13
% 0.30/1.47 # Non-unit-clauses : 311
% 0.30/1.47 # Current number of unprocessed clauses: 2905
% 0.30/1.47 # ...number of literals in the above : 18385
% 0.30/1.47 # Current number of archived formulas : 0
% 0.30/1.47 # Current number of archived clauses : 55
% 0.30/1.47 # Clause-clause subsumption calls (NU) : 63981
% 0.30/1.47 # Rec. Clause-clause subsumption calls : 6431
% 0.30/1.47 # Non-unit clause-clause subsumptions : 77
% 0.30/1.47 # Unit Clause-clause subsumption calls : 3217
% 0.30/1.47 # Rewrite failures with RHS unbound : 0
% 0.30/1.47 # BW rewrite match attempts : 49
% 0.30/1.47 # BW rewrite match successes : 14
% 0.30/1.47 # Condensation attempts : 0
% 0.30/1.47 # Condensation successes : 0
% 0.30/1.47 # Termbank termtop insertions : 109500
% 0.30/1.47
% 0.30/1.47 # -------------------------------------------------
% 0.30/1.47 # User time : 0.172 s
% 0.30/1.47 # System time : 0.006 s
% 0.30/1.47 # Total time : 0.178 s
% 0.30/1.47 # Maximum resident set size: 7860 pages
%------------------------------------------------------------------------------