TSTP Solution File: SET961+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:24:28 EDT 2023
% Result : Theorem 0.16s 0.43s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 83 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 86 ( 35 ~; 36 |; 8 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 11 sgn; 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t114_zfmisc_1,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = empty_set
| X2 = empty_set
| X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.y2bpvwkRBh/E---3.1_22661.p',t114_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/tmp/tmp.y2bpvwkRBh/E---3.1_22661.p',l55_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.y2bpvwkRBh/E---3.1_22661.p',d1_xboole_0) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.y2bpvwkRBh/E---3.1_22661.p',t2_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X2) = cartesian_product2(X2,X1)
=> ( X1 = empty_set
| X2 = empty_set
| X1 = X2 ) ),
inference(assume_negation,[status(cth)],[t114_zfmisc_1]) ).
fof(c_0_5,plain,
! [X11,X12,X13,X14] :
( ( in(X11,X13)
| ~ in(ordered_pair(X11,X12),cartesian_product2(X13,X14)) )
& ( in(X12,X14)
| ~ in(ordered_pair(X11,X12),cartesian_product2(X13,X14)) )
& ( ~ in(X11,X13)
| ~ in(X12,X14)
| in(ordered_pair(X11,X12),cartesian_product2(X13,X14)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(c_0_6,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk2_0,esk1_0)
& esk1_0 != empty_set
& esk2_0 != empty_set
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_8,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X7,X8,X9] :
( ( X7 != empty_set
| ~ in(X8,X7) )
& ( in(esk3_1(X9),X9)
| X9 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
cnf(c_0_11,negated_conjecture,
( in(X1,esk2_0)
| ~ in(ordered_pair(X2,X1),cartesian_product2(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_13,plain,
! [X17,X18] :
( ( ~ in(esk4_2(X17,X18),X17)
| ~ in(esk4_2(X17,X18),X18)
| X17 = X18 )
& ( in(esk4_2(X17,X18),X17)
| in(esk4_2(X17,X18),X18)
| X17 = X18 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_14,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk1_0)
| ~ in(X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( in(esk4_2(X1,X2),X1)
| in(esk4_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( esk1_0 = X1
| in(esk4_2(esk1_0,X1),esk2_0)
| in(esk4_2(esk1_0,X1),X1)
| ~ in(X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( empty_set = X1
| in(esk4_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
( esk1_0 = X1
| in(esk4_2(esk1_0,X1),esk2_0)
| in(esk4_2(esk1_0,X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( in(X1,esk1_0)
| ~ in(ordered_pair(X1,X2),cartesian_product2(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_9]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ in(esk4_2(X1,X2),X1)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
in(esk4_2(esk1_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_22]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X2,esk1_0)
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_12]) ).
cnf(c_0_28,negated_conjecture,
esk1_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk4_2(esk1_0,esk2_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.09/0.31 % Computer : n016.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 2400
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Mon Oct 2 18:01:21 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.16/0.41 Running first-order model finding
% 0.16/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.y2bpvwkRBh/E---3.1_22661.p
% 0.16/0.43 # Version: 3.1pre001
% 0.16/0.43 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.43 # Starting new_bool_3 with 300s (1) cores
% 0.16/0.43 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.43 # Starting sh5l with 300s (1) cores
% 0.16/0.43 # new_bool_1 with pid 22740 completed with status 0
% 0.16/0.43 # Result found by new_bool_1
% 0.16/0.43 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.43 # Starting new_bool_3 with 300s (1) cores
% 0.16/0.43 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.43 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.43 # Search class: FGHSF-FFSS21-SFFFFFNN
% 0.16/0.43 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.43 # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.16/0.43 # SAT001_MinMin_p005000_rr_RG with pid 22745 completed with status 0
% 0.16/0.43 # Result found by SAT001_MinMin_p005000_rr_RG
% 0.16/0.43 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.43 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.43 # Starting new_bool_3 with 300s (1) cores
% 0.16/0.43 # Starting new_bool_1 with 300s (1) cores
% 0.16/0.43 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.43 # Search class: FGHSF-FFSS21-SFFFFFNN
% 0.16/0.43 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.43 # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.16/0.43 # Preprocessing time : 0.001 s
% 0.16/0.43 # Presaturation interreduction done
% 0.16/0.43
% 0.16/0.43 # Proof found!
% 0.16/0.43 # SZS status Theorem
% 0.16/0.43 # SZS output start CNFRefutation
% See solution above
% 0.16/0.43 # Parsed axioms : 11
% 0.16/0.43 # Removed by relevancy pruning/SinE : 2
% 0.16/0.43 # Initial clauses : 16
% 0.16/0.43 # Removed in clause preprocessing : 0
% 0.16/0.43 # Initial clauses in saturation : 16
% 0.16/0.43 # Processed clauses : 70
% 0.16/0.43 # ...of these trivial : 0
% 0.16/0.43 # ...subsumed : 5
% 0.16/0.43 # ...remaining for further processing : 65
% 0.16/0.43 # Other redundant clauses eliminated : 1
% 0.16/0.43 # Clauses deleted for lack of memory : 0
% 0.16/0.43 # Backward-subsumed : 2
% 0.16/0.43 # Backward-rewritten : 3
% 0.16/0.43 # Generated clauses : 73
% 0.16/0.43 # ...of the previous two non-redundant : 63
% 0.16/0.43 # ...aggressively subsumed : 0
% 0.16/0.43 # Contextual simplify-reflections : 0
% 0.16/0.43 # Paramodulations : 68
% 0.16/0.43 # Factorizations : 4
% 0.16/0.43 # NegExts : 0
% 0.16/0.43 # Equation resolutions : 1
% 0.16/0.43 # Total rewrite steps : 4
% 0.16/0.43 # Propositional unsat checks : 0
% 0.16/0.43 # Propositional check models : 0
% 0.16/0.43 # Propositional check unsatisfiable : 0
% 0.16/0.43 # Propositional clauses : 0
% 0.16/0.43 # Propositional clauses after purity: 0
% 0.16/0.43 # Propositional unsat core size : 0
% 0.16/0.43 # Propositional preprocessing time : 0.000
% 0.16/0.43 # Propositional encoding time : 0.000
% 0.16/0.43 # Propositional solver time : 0.000
% 0.16/0.43 # Success case prop preproc time : 0.000
% 0.16/0.43 # Success case prop encoding time : 0.000
% 0.16/0.43 # Success case prop solver time : 0.000
% 0.16/0.43 # Current number of processed clauses : 43
% 0.16/0.43 # Positive orientable unit clauses : 7
% 0.16/0.43 # Positive unorientable unit clauses: 0
% 0.16/0.43 # Negative unit clauses : 12
% 0.16/0.43 # Non-unit-clauses : 24
% 0.16/0.43 # Current number of unprocessed clauses: 12
% 0.16/0.43 # ...number of literals in the above : 39
% 0.16/0.43 # Current number of archived formulas : 0
% 0.16/0.43 # Current number of archived clauses : 21
% 0.16/0.43 # Clause-clause subsumption calls (NU) : 147
% 0.16/0.43 # Rec. Clause-clause subsumption calls : 134
% 0.16/0.43 # Non-unit clause-clause subsumptions : 5
% 0.16/0.43 # Unit Clause-clause subsumption calls : 54
% 0.16/0.43 # Rewrite failures with RHS unbound : 0
% 0.16/0.43 # BW rewrite match attempts : 3
% 0.16/0.43 # BW rewrite match successes : 3
% 0.16/0.43 # Condensation attempts : 0
% 0.16/0.43 # Condensation successes : 0
% 0.16/0.43 # Termbank termtop insertions : 1638
% 0.16/0.43
% 0.16/0.43 # -------------------------------------------------
% 0.16/0.43 # User time : 0.006 s
% 0.16/0.43 # System time : 0.002 s
% 0.16/0.43 # Total time : 0.008 s
% 0.16/0.43 # Maximum resident set size: 1736 pages
% 0.16/0.43
% 0.16/0.43 # -------------------------------------------------
% 0.16/0.43 # User time : 0.007 s
% 0.16/0.43 # System time : 0.003 s
% 0.16/0.43 # Total time : 0.010 s
% 0.16/0.43 # Maximum resident set size: 1680 pages
% 0.16/0.43 % E---3.1 exiting
%------------------------------------------------------------------------------