TSTP Solution File: SET906+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.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 00:55:20 EDT 2022
% Result : Theorem 0.25s 1.44s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 92 ( 34 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 101 ( 36 ~; 44 |; 13 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 71 ( 15 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t47_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(set_union2(unordered_pair(X1,X2),X3),X3)
=> in(X1,X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t47_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_tarski) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(set_union2(unordered_pair(X1,X2),X3),X3)
=> in(X1,X3) ),
inference(assume_negation,[status(cth)],[t47_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
( subset(set_union2(unordered_pair(esk1_0,esk2_0),esk3_0),esk3_0)
& ~ in(esk1_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_9,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_10,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk5_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk5_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[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)],[d3_tarski])])])])])])]) ).
cnf(c_0_11,negated_conjecture,
subset(set_union2(unordered_pair(esk1_0,esk2_0),esk3_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X5,X6,X7,X8,X8,X5,X6,X7] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X6)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk4_3(X5,X6,X7),X5)
| ~ in(esk4_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk4_3(X5,X6,X7),X6)
| ~ in(esk4_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk4_3(X5,X6,X7),X7)
| in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[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)],[d2_xboole_0])])])])])])]) ).
fof(c_0_15,plain,
! [X5,X6,X7,X8,X8,X5,X6,X7] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk6_3(X5,X6,X7) != X5
| ~ in(esk6_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk6_3(X5,X6,X7) != X6
| ~ in(esk6_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| esk6_3(X5,X6,X7) = X5
| esk6_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[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)],[d2_tarski])])])])])])]) ).
cnf(c_0_16,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
subset(set_union2(esk3_0,unordered_pair(esk2_0,esk1_0)),esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_18,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X1,set_union2(esk3_0,unordered_pair(esk2_0,esk1_0))) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( in(X1,X2)
| X2 != unordered_pair(X3,X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( in(X1,esk3_0)
| ~ in(X1,unordered_pair(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ in(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : run_ET %s %d
% 0.14/0.35 % Computer : n026.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 22:56:12 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.25/1.44 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.25/1.44 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.25/1.44 # Preprocessing time : 0.015 s
% 0.25/1.44
% 0.25/1.44 # Proof found!
% 0.25/1.44 # SZS status Theorem
% 0.25/1.44 # SZS output start CNFRefutation
% See solution above
% 0.25/1.44 # Proof object total steps : 27
% 0.25/1.44 # Proof object clause steps : 14
% 0.25/1.44 # Proof object formula steps : 13
% 0.25/1.44 # Proof object conjectures : 9
% 0.25/1.44 # Proof object clause conjectures : 6
% 0.25/1.44 # Proof object formula conjectures : 3
% 0.25/1.44 # Proof object initial clauses used : 7
% 0.25/1.44 # Proof object initial formulas used : 6
% 0.25/1.44 # Proof object generating inferences : 5
% 0.25/1.44 # Proof object simplifying inferences : 4
% 0.25/1.44 # Training examples: 0 positive, 0 negative
% 0.25/1.44 # Parsed axioms : 13
% 0.25/1.44 # Removed by relevancy pruning/SinE : 4
% 0.25/1.44 # Initial clauses : 22
% 0.25/1.44 # Removed in clause preprocessing : 0
% 0.25/1.44 # Initial clauses in saturation : 22
% 0.25/1.44 # Processed clauses : 47
% 0.25/1.44 # ...of these trivial : 1
% 0.25/1.44 # ...subsumed : 10
% 0.25/1.44 # ...remaining for further processing : 36
% 0.25/1.44 # Other redundant clauses eliminated : 5
% 0.25/1.44 # Clauses deleted for lack of memory : 0
% 0.25/1.44 # Backward-subsumed : 0
% 0.25/1.44 # Backward-rewritten : 1
% 0.25/1.44 # Generated clauses : 89
% 0.25/1.44 # ...of the previous two non-trivial : 69
% 0.25/1.44 # Contextual simplify-reflections : 0
% 0.25/1.44 # Paramodulations : 72
% 0.25/1.44 # Factorizations : 6
% 0.25/1.44 # Equation resolutions : 11
% 0.25/1.44 # Current number of processed clauses : 33
% 0.25/1.44 # Positive orientable unit clauses : 5
% 0.25/1.44 # Positive unorientable unit clauses: 2
% 0.25/1.44 # Negative unit clauses : 3
% 0.25/1.44 # Non-unit-clauses : 23
% 0.25/1.44 # Current number of unprocessed clauses: 44
% 0.25/1.44 # ...number of literals in the above : 136
% 0.25/1.44 # Current number of archived formulas : 0
% 0.25/1.44 # Current number of archived clauses : 1
% 0.25/1.44 # Clause-clause subsumption calls (NU) : 87
% 0.25/1.44 # Rec. Clause-clause subsumption calls : 85
% 0.25/1.44 # Non-unit clause-clause subsumptions : 10
% 0.25/1.44 # Unit Clause-clause subsumption calls : 24
% 0.25/1.44 # Rewrite failures with RHS unbound : 0
% 0.25/1.44 # BW rewrite match attempts : 8
% 0.25/1.44 # BW rewrite match successes : 4
% 0.25/1.44 # Condensation attempts : 0
% 0.25/1.44 # Condensation successes : 0
% 0.25/1.44 # Termbank termtop insertions : 1998
% 0.25/1.44
% 0.25/1.44 # -------------------------------------------------
% 0.25/1.44 # User time : 0.017 s
% 0.25/1.44 # System time : 0.001 s
% 0.25/1.44 # Total time : 0.018 s
% 0.25/1.44 # Maximum resident set size: 2780 pages
%------------------------------------------------------------------------------