%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU309+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n022.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 09:18:51 EDT 2022
% Result : Theorem 0.23s 1.42s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 90 ( 32 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 86 ( 39 ~; 31 |; 5 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t22_pre_topc,conjecture,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t22_pre_topc) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k6_subset_1) ).
fof(dt_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> element(subset_difference(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k6_subset_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k3_xboole_0) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t48_xboole_1) ).
fof(t15_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t15_pre_topc) ).
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(dt_k2_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> element(cast_as_carrier_subset(X1),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k2_pre_topc) ).
fof(redefinition_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k5_subset_1) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2)) = X2 ) ),
inference(assume_negation,[status(cth)],[t22_pre_topc]) ).
fof(c_0_10,negated_conjecture,
( one_sorted_str(esk1_0)
& element(esk2_0,powerset(the_carrier(esk1_0)))
& subset_difference(the_carrier(esk1_0),cast_as_carrier_subset(esk1_0),subset_difference(the_carrier(esk1_0),cast_as_carrier_subset(esk1_0),esk2_0)) != esk2_0 ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
fof(c_0_11,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_difference(X4,X5,X6) = set_difference(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
cnf(c_0_12,negated_conjecture,
subset_difference(the_carrier(esk1_0),cast_as_carrier_subset(esk1_0),subset_difference(the_carrier(esk1_0),cast_as_carrier_subset(esk1_0),esk2_0)) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( subset_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| element(subset_difference(X4,X5,X6),powerset(X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])]) ).
fof(c_0_15,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_16,plain,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_17,plain,
! [X3,X4] :
( ~ one_sorted_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| subset_intersection2(the_carrier(X3),X4,cast_as_carrier_subset(X3)) = X4 ),
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)],[t15_pre_topc])])])])]) ).
fof(c_0_18,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])]) ).
fof(c_0_19,plain,
! [X2] :
( ~ one_sorted_str(X2)
| element(cast_as_carrier_subset(X2),powerset(the_carrier(X2))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_pre_topc])]) ).
cnf(c_0_20,negated_conjecture,
( set_difference(cast_as_carrier_subset(esk1_0),subset_difference(the_carrier(esk1_0),cast_as_carrier_subset(esk1_0),esk2_0)) != esk2_0
| ~ element(subset_difference(the_carrier(esk1_0),cast_as_carrier_subset(esk1_0),esk2_0),powerset(the_carrier(esk1_0)))
| ~ element(cast_as_carrier_subset(esk1_0),powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,plain,
( element(subset_difference(X1,X2,X3),powerset(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
element(esk2_0,powerset(the_carrier(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_intersection2(X4,X5,X6) = set_intersection2(X5,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1])]) ).
cnf(c_0_26,plain,
( subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2
| ~ element(X2,powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
( element(cast_as_carrier_subset(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( set_difference(cast_as_carrier_subset(esk1_0),subset_difference(the_carrier(esk1_0),cast_as_carrier_subset(esk1_0),esk2_0)) != esk2_0
| ~ element(cast_as_carrier_subset(esk1_0),powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_30,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
cnf(c_0_31,plain,
( subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( subset_intersection2(the_carrier(X1),X2,the_carrier(X1)) = X2
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
one_sorted_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_34,plain,
( element(the_carrier(X1),powerset(the_carrier(X1)))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( set_difference(esk2_0,set_difference(esk2_0,cast_as_carrier_subset(esk1_0))) != esk2_0
| ~ element(cast_as_carrier_subset(esk1_0),powerset(the_carrier(esk1_0))) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_13]),c_0_22])]),c_0_30]) ).
cnf(c_0_36,plain,
( subset_intersection2(X1,X2,X3) = set_difference(X2,set_difference(X2,X3))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(rw,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_37,negated_conjecture,
( subset_intersection2(the_carrier(esk1_0),X1,the_carrier(esk1_0)) = X1
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
element(the_carrier(esk1_0),powerset(the_carrier(esk1_0))),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
set_difference(esk2_0,set_difference(esk2_0,cast_as_carrier_subset(esk1_0))) != esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_33])]) ).
cnf(c_0_40,negated_conjecture,
( set_difference(X1,set_difference(X1,the_carrier(esk1_0))) = X1
| ~ element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
set_difference(esk2_0,set_difference(esk2_0,the_carrier(esk1_0))) != esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_27]),c_0_33])]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_22]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU309+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 13:57:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.23/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.42 # Preprocessing time : 0.019 s
% 0.23/1.42
% 0.23/1.42 # Proof found!
% 0.23/1.42 # SZS status Theorem
% 0.23/1.42 # SZS output start CNFRefutation
% See solution above
% 0.23/1.42 # Proof object total steps : 43
% 0.23/1.42 # Proof object clause steps : 24
% 0.23/1.42 # Proof object formula steps : 19
% 0.23/1.42 # Proof object conjectures : 15
% 0.23/1.42 # Proof object clause conjectures : 12
% 0.23/1.42 # Proof object formula conjectures : 3
% 0.23/1.42 # Proof object initial clauses used : 11
% 0.23/1.42 # Proof object initial formulas used : 9
% 0.23/1.42 # Proof object generating inferences : 11
% 0.23/1.42 # Proof object simplifying inferences : 15
% 0.23/1.42 # Training examples: 0 positive, 0 negative
% 0.23/1.42 # Parsed axioms : 70
% 0.23/1.42 # Removed by relevancy pruning/SinE : 25
% 0.23/1.42 # Initial clauses : 98
% 0.23/1.42 # Removed in clause preprocessing : 1
% 0.23/1.42 # Initial clauses in saturation : 97
% 0.23/1.42 # Processed clauses : 323
% 0.23/1.42 # ...of these trivial : 13
% 0.23/1.42 # ...subsumed : 102
% 0.23/1.42 # ...remaining for further processing : 208
% 0.23/1.42 # Other redundant clauses eliminated : 0
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 1
% 0.23/1.42 # Backward-rewritten : 9
% 0.23/1.42 # Generated clauses : 672
% 0.23/1.42 # ...of the previous two non-trivial : 558
% 0.23/1.42 # Contextual simplify-reflections : 7
% 0.23/1.42 # Paramodulations : 672
% 0.23/1.42 # Factorizations : 0
% 0.23/1.42 # Equation resolutions : 0
% 0.23/1.42 # Current number of processed clauses : 198
% 0.23/1.42 # Positive orientable unit clauses : 33
% 0.23/1.42 # Positive unorientable unit clauses: 2
% 0.23/1.42 # Negative unit clauses : 6
% 0.23/1.42 # Non-unit-clauses : 157
% 0.23/1.42 # Current number of unprocessed clauses: 311
% 0.23/1.42 # ...number of literals in the above : 706
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 11
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 4021
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 3884
% 0.23/1.42 # Non-unit clause-clause subsumptions : 95
% 0.23/1.42 # Unit Clause-clause subsumption calls : 173
% 0.23/1.42 # Rewrite failures with RHS unbound : 10
% 0.23/1.42 # BW rewrite match attempts : 16
% 0.23/1.42 # BW rewrite match successes : 11
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 11865
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.031 s
% 0.23/1.42 # System time : 0.004 s
% 0.23/1.42 # Total time : 0.035 s
% 0.23/1.42 # Maximum resident set size: 3676 pages
%------------------------------------------------------------------------------