TSTP Solution File: SET908+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n023.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 00:55:21 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 93 ( 50 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 101 ( 44 ~; 43 |; 9 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 72 ( 22 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t49_zfmisc_1,conjecture,
! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t49_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_xboole_0) ).
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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
inference(assume_negation,[status(cth)],[t49_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
set_union2(singleton(esk1_0),esk2_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_8,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(esk5_3(X5,X6,X7),X5)
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk5_3(X5,X6,X7),X6)
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X5)
| in(esk5_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])])])])])])]) ).
cnf(c_0_9,negated_conjecture,
set_union2(singleton(esk1_0),esk2_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X3,X4,X3] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk3_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])])])])])])]) ).
fof(c_0_12,plain,
! [X4,X5,X6,X6,X4,X5] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
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)],[d1_tarski])])])])])])]) ).
cnf(c_0_13,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
set_union2(esk2_0,singleton(esk1_0)) = empty_set,
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( X1 != empty_set
| ~ in(X2,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
( X1 = empty_set
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( in(X1,X2)
| X2 != singleton(X1) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( empty_set = esk2_0
| X1 != empty_set ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_22,negated_conjecture,
empty_set = esk2_0,
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
singleton(X1) != empty_set,
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( X1 != esk2_0
| ~ in(X2,esk2_0) ),
inference(rw,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_25,plain,
( X1 = singleton(X2)
| esk4_2(X2,X1) = X2
| in(esk4_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,plain,
singleton(X1) != esk2_0,
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( esk4_2(X1,esk2_0) = X1
| X2 != esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,plain,
( X1 = singleton(X2)
| esk4_2(X2,X1) != X2
| ~ in(esk4_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
esk4_2(X1,esk2_0) = X1,
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_32,negated_conjecture,
set_union2(esk2_0,singleton(esk1_0)) = esk2_0,
inference(rw,[status(thm)],[c_0_14,c_0_22]) ).
cnf(c_0_33,negated_conjecture,
~ in(X1,esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_26]) ).
cnf(c_0_34,negated_conjecture,
~ in(X1,singleton(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_34,c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 19:39:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.23/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41 # Preprocessing time : 0.015 s
% 0.23/1.41
% 0.23/1.41 # Proof found!
% 0.23/1.41 # SZS status Theorem
% 0.23/1.41 # SZS output start CNFRefutation
% See solution above
% 0.23/1.41 # Proof object total steps : 36
% 0.23/1.41 # Proof object clause steps : 25
% 0.23/1.41 # Proof object formula steps : 11
% 0.23/1.41 # Proof object conjectures : 15
% 0.23/1.41 # Proof object clause conjectures : 12
% 0.23/1.41 # Proof object formula conjectures : 3
% 0.23/1.41 # Proof object initial clauses used : 9
% 0.23/1.41 # Proof object initial formulas used : 5
% 0.23/1.41 # Proof object generating inferences : 11
% 0.23/1.41 # Proof object simplifying inferences : 9
% 0.23/1.41 # Training examples: 0 positive, 0 negative
% 0.23/1.41 # Parsed axioms : 12
% 0.23/1.41 # Removed by relevancy pruning/SinE : 0
% 0.23/1.41 # Initial clauses : 21
% 0.23/1.41 # Removed in clause preprocessing : 0
% 0.23/1.41 # Initial clauses in saturation : 21
% 0.23/1.41 # Processed clauses : 53
% 0.23/1.41 # ...of these trivial : 0
% 0.23/1.41 # ...subsumed : 5
% 0.23/1.41 # ...remaining for further processing : 48
% 0.23/1.41 # Other redundant clauses eliminated : 4
% 0.23/1.41 # Clauses deleted for lack of memory : 0
% 0.23/1.41 # Backward-subsumed : 0
% 0.23/1.41 # Backward-rewritten : 11
% 0.23/1.41 # Generated clauses : 118
% 0.23/1.41 # ...of the previous two non-trivial : 100
% 0.23/1.41 # Contextual simplify-reflections : 1
% 0.23/1.41 # Paramodulations : 95
% 0.23/1.41 # Factorizations : 8
% 0.23/1.41 # Equation resolutions : 15
% 0.23/1.41 # Current number of processed clauses : 36
% 0.23/1.41 # Positive orientable unit clauses : 9
% 0.23/1.41 # Positive unorientable unit clauses: 1
% 0.23/1.41 # Negative unit clauses : 5
% 0.23/1.41 # Non-unit-clauses : 21
% 0.23/1.41 # Current number of unprocessed clauses: 53
% 0.23/1.41 # ...number of literals in the above : 161
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 11
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 79
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 67
% 0.23/1.41 # Non-unit clause-clause subsumptions : 6
% 0.23/1.41 # Unit Clause-clause subsumption calls : 24
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 6
% 0.23/1.41 # BW rewrite match successes : 6
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 1960
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.017 s
% 0.23/1.41 # System time : 0.002 s
% 0.23/1.41 # Total time : 0.019 s
% 0.23/1.41 # Maximum resident set size: 2776 pages
%------------------------------------------------------------------------------