TSTP Solution File: SET980+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET980+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n008.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 00:55:51 EDT 2022
% Result : Theorem 0.26s 1.44s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 129 ( 57 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 135 ( 54 ~; 62 |; 12 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 83 ( 21 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t134_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t134_zfmisc_1) ).
fof(l55_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l55_zfmisc_1) ).
fof(t113_zfmisc_1,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t113_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
inference(assume_negation,[status(cth)],[t134_zfmisc_1]) ).
fof(c_0_6,plain,
! [X5,X6,X7,X8,X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X5,X7)
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])])])]) ).
fof(c_0_7,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0)
& esk1_0 != empty_set
& esk2_0 != empty_set
& ( esk1_0 != esk3_0
| esk2_0 != esk4_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X3,X4,X3,X4] :
( ( cartesian_product2(X3,X4) != empty_set
| X3 = empty_set
| X4 = empty_set )
& ( X3 != empty_set
| cartesian_product2(X3,X4) = empty_set )
& ( X4 != empty_set
| cartesian_product2(X3,X4) = empty_set ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])])])]) ).
cnf(c_0_9,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( X1 = empty_set
| X2 = empty_set
| cartesian_product2(X2,X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0))
| ~ in(X2,esk2_0)
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_16,plain,
! [X3,X4,X3] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk5_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[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)],[d1_xboole_0])])])])])])]) ).
cnf(c_0_17,negated_conjecture,
( in(X1,esk1_0)
| ~ in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_18,negated_conjecture,
cartesian_product2(esk3_0,esk4_0) != empty_set,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_13]),c_0_14]) ).
cnf(c_0_19,plain,
( cartesian_product2(X1,X2) = empty_set
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X2,esk2_0)
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_21,plain,
( X1 = empty_set
| in(esk5_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X4,X5] :
( ( ~ in(esk6_2(X4,X5),X4)
| ~ in(esk6_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk6_2(X4,X5),X4)
| in(esk6_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])])]) ).
cnf(c_0_23,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X2,esk4_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_9]) ).
cnf(c_0_24,negated_conjecture,
empty_set != esk4_0,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_13]) ).
cnf(c_0_26,plain,
( X1 = X2
| in(esk6_2(X1,X2),X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,plain,
( X1 = X2
| ~ in(esk6_2(X1,X2),X2)
| ~ in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X1,esk3_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( X1 = esk1_0
| in(esk6_2(X1,esk1_0),esk3_0)
| in(esk6_2(X1,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk2_0)
| ~ in(X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_32,negated_conjecture,
( X1 = esk1_0
| ~ in(esk6_2(X1,esk1_0),esk3_0)
| ~ in(esk6_2(X1,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( esk1_0 = esk3_0
| in(esk6_2(esk3_0,esk1_0),esk3_0) ),
inference(ef,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( esk2_0 = X1
| in(esk6_2(esk2_0,X1),esk4_0)
| in(esk6_2(esk2_0,X1),X1)
| ~ in(X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_35,negated_conjecture,
esk1_0 = esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_36,plain,
( cartesian_product2(X1,X2) = empty_set
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_37,negated_conjecture,
( esk2_0 = X1
| in(esk6_2(esk2_0,X1),esk4_0)
| in(esk6_2(esk2_0,X1),X1)
| ~ in(X2,esk3_0) ),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
empty_set != esk3_0,
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( esk2_0 != esk4_0
| esk1_0 != esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_40,negated_conjecture,
( esk2_0 = X1
| in(esk6_2(esk2_0,X1),esk4_0)
| in(esk6_2(esk2_0,X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_21]),c_0_38]) ).
cnf(c_0_41,negated_conjecture,
esk2_0 != esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_35])]) ).
cnf(c_0_42,negated_conjecture,
( in(X1,esk2_0)
| ~ in(ordered_pair(X2,X1),cartesian_product2(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_10]) ).
cnf(c_0_43,negated_conjecture,
in(esk6_2(esk2_0,esk4_0),esk4_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk4_0)
| ~ in(X2,esk3_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_9]) ).
cnf(c_0_45,negated_conjecture,
~ in(esk6_2(esk2_0,esk4_0),esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_43]),c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_21]),c_0_38]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET980+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.14 % Command : run_ET %s %d
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 20:08:38 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.26/1.44 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.26/1.44 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.26/1.44 # Preprocessing time : 0.016 s
% 0.26/1.44
% 0.26/1.44 # Proof found!
% 0.26/1.44 # SZS status Theorem
% 0.26/1.44 # SZS output start CNFRefutation
% See solution above
% 0.26/1.44 # Proof object total steps : 48
% 0.26/1.44 # Proof object clause steps : 37
% 0.26/1.44 # Proof object formula steps : 11
% 0.26/1.44 # Proof object conjectures : 31
% 0.26/1.44 # Proof object clause conjectures : 28
% 0.26/1.44 # Proof object formula conjectures : 3
% 0.26/1.44 # Proof object initial clauses used : 13
% 0.26/1.44 # Proof object initial formulas used : 5
% 0.26/1.44 # Proof object generating inferences : 22
% 0.26/1.44 # Proof object simplifying inferences : 14
% 0.26/1.44 # Training examples: 0 positive, 0 negative
% 0.26/1.44 # Parsed axioms : 12
% 0.26/1.44 # Removed by relevancy pruning/SinE : 2
% 0.26/1.44 # Initial clauses : 19
% 0.26/1.44 # Removed in clause preprocessing : 0
% 0.26/1.44 # Initial clauses in saturation : 19
% 0.26/1.44 # Processed clauses : 205
% 0.26/1.44 # ...of these trivial : 3
% 0.26/1.44 # ...subsumed : 96
% 0.26/1.44 # ...remaining for further processing : 106
% 0.26/1.44 # Other redundant clauses eliminated : 0
% 0.26/1.44 # Clauses deleted for lack of memory : 0
% 0.26/1.44 # Backward-subsumed : 9
% 0.26/1.44 # Backward-rewritten : 35
% 0.26/1.44 # Generated clauses : 294
% 0.26/1.44 # ...of the previous two non-trivial : 300
% 0.26/1.44 # Contextual simplify-reflections : 40
% 0.26/1.44 # Paramodulations : 284
% 0.26/1.44 # Factorizations : 8
% 0.26/1.44 # Equation resolutions : 2
% 0.26/1.44 # Current number of processed clauses : 62
% 0.26/1.44 # Positive orientable unit clauses : 7
% 0.26/1.44 # Positive unorientable unit clauses: 0
% 0.26/1.44 # Negative unit clauses : 13
% 0.26/1.44 # Non-unit-clauses : 42
% 0.26/1.44 # Current number of unprocessed clauses: 12
% 0.26/1.44 # ...number of literals in the above : 44
% 0.26/1.44 # Current number of archived formulas : 0
% 0.26/1.44 # Current number of archived clauses : 44
% 0.26/1.44 # Clause-clause subsumption calls (NU) : 2023
% 0.26/1.44 # Rec. Clause-clause subsumption calls : 1511
% 0.26/1.44 # Non-unit clause-clause subsumptions : 98
% 0.26/1.44 # Unit Clause-clause subsumption calls : 184
% 0.26/1.44 # Rewrite failures with RHS unbound : 0
% 0.26/1.44 # BW rewrite match attempts : 2
% 0.26/1.44 # BW rewrite match successes : 2
% 0.26/1.44 # Condensation attempts : 0
% 0.26/1.44 # Condensation successes : 0
% 0.26/1.44 # Termbank termtop insertions : 4583
% 0.26/1.44
% 0.26/1.44 # -------------------------------------------------
% 0.26/1.44 # User time : 0.027 s
% 0.26/1.44 # System time : 0.001 s
% 0.26/1.44 # Total time : 0.028 s
% 0.26/1.44 # Maximum resident set size: 3040 pages
%------------------------------------------------------------------------------