TSTP Solution File: SET662+3 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.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 19:23:17 EDT 2023
% Result : Theorem 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 8 unt; 0 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 180 ( 72 ~; 65 |; 13 &)
% ( 6 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 4 sgn; 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pc26YQyaOU/E---3.1_29638.p',p11) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pc26YQyaOU/E---3.1_29638.p',p14) ).
fof(p20,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/tmp/tmp.pc26YQyaOU/E---3.1_29638.p',p20) ).
fof(p4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
file('/export/starexec/sandbox/tmp/tmp.pc26YQyaOU/E---3.1_29638.p',p4) ).
fof(prove_relset_1_25,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(empty_set,relation_type(X1,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.pc26YQyaOU/E---3.1_29638.p',prove_relset_1_25) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pc26YQyaOU/E---3.1_29638.p',p2) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pc26YQyaOU/E---3.1_29638.p',p7) ).
fof(p12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pc26YQyaOU/E---3.1_29638.p',p12) ).
fof(c_0_8,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p11]) ).
fof(c_0_9,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p14]) ).
fof(c_0_10,plain,
! [X27,X28] :
( ( ~ empty(X27)
| ~ ilf_type(X28,set_type)
| ~ member(X28,X27)
| ~ ilf_type(X27,set_type) )
& ( ilf_type(esk5_1(X27),set_type)
| empty(X27)
| ~ ilf_type(X27,set_type) )
& ( member(esk5_1(X27),X27)
| empty(X27)
| ~ ilf_type(X27,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
fof(c_0_11,plain,
! [X7] : ilf_type(X7,set_type),
inference(variable_rename,[status(thm)],[p20]) ).
fof(c_0_12,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
inference(fof_simplification,[status(thm)],[p4]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(empty_set,relation_type(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_25]) ).
fof(c_0_14,plain,
! [X8,X9,X10,X11] :
( ( ~ ilf_type(X10,subset_type(cross_product(X8,X9)))
| ilf_type(X10,relation_type(X8,X9))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type) )
& ( ~ ilf_type(X11,relation_type(X8,X9))
| ilf_type(X11,subset_type(cross_product(X8,X9)))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
fof(c_0_15,plain,
! [X16,X17] :
( ( ~ ilf_type(X17,subset_type(X16))
| ilf_type(X17,member_type(power_set(X16)))
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type) )
& ( ~ ilf_type(X17,member_type(power_set(X16)))
| ilf_type(X17,subset_type(X16))
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
fof(c_0_16,plain,
! [X30,X31] :
( ( ~ ilf_type(X30,member_type(X31))
| member(X30,X31)
| empty(X31)
| ~ ilf_type(X31,set_type)
| ~ ilf_type(X30,set_type) )
& ( ~ member(X30,X31)
| ilf_type(X30,member_type(X31))
| empty(X31)
| ~ ilf_type(X31,set_type)
| ~ ilf_type(X30,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_17,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_19,plain,
! [X15] :
( ~ ilf_type(X15,set_type)
| ~ member(X15,empty_set) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_20,plain,
! [X34,X35,X36] :
( ( ~ member(X34,power_set(X35))
| ~ ilf_type(X36,set_type)
| ~ member(X36,X34)
| member(X36,X35)
| ~ ilf_type(X35,set_type)
| ~ ilf_type(X34,set_type) )
& ( ilf_type(esk7_2(X34,X35),set_type)
| member(X34,power_set(X35))
| ~ ilf_type(X35,set_type)
| ~ ilf_type(X34,set_type) )
& ( member(esk7_2(X34,X35),X34)
| member(X34,power_set(X35))
| ~ ilf_type(X35,set_type)
| ~ ilf_type(X34,set_type) )
& ( ~ member(esk7_2(X34,X35),X35)
| member(X34,power_set(X35))
| ~ ilf_type(X35,set_type)
| ~ ilf_type(X34,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])])])]) ).
fof(c_0_21,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,set_type)
& ~ ilf_type(empty_set,relation_type(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_22,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18])]) ).
cnf(c_0_26,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( member(esk7_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
~ ilf_type(empty_set,relation_type(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_18]),c_0_18])]) ).
cnf(c_0_30,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_18]),c_0_18])]) ).
cnf(c_0_31,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_18]),c_0_18])]),c_0_25]) ).
cnf(c_0_32,plain,
~ member(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_18])]) ).
cnf(c_0_33,plain,
( member(esk7_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_18]),c_0_18])]) ).
cnf(c_0_34,negated_conjecture,
~ ilf_type(empty_set,subset_type(cross_product(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
member(empty_set,power_set(X1)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 2400
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Oct 2 16:43:46 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.18/0.43 Running first-order model finding
% 0.18/0.43 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.pc26YQyaOU/E---3.1_29638.p
% 0.18/0.45 # Version: 3.1pre001
% 0.18/0.45 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.45 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.45 # Starting new_bool_3 with 300s (1) cores
% 0.18/0.45 # Starting new_bool_1 with 300s (1) cores
% 0.18/0.45 # Starting sh5l with 300s (1) cores
% 0.18/0.45 # new_bool_3 with pid 29716 completed with status 0
% 0.18/0.45 # Result found by new_bool_3
% 0.18/0.45 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.45 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.45 # Starting new_bool_3 with 300s (1) cores
% 0.18/0.45 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.45 # Search class: FGHSF-FFMS21-SFFFFFNN
% 0.18/0.45 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.45 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 181s (1) cores
% 0.18/0.45 # G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with pid 29720 completed with status 0
% 0.18/0.45 # Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y
% 0.18/0.45 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.45 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.45 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.45 # Starting new_bool_3 with 300s (1) cores
% 0.18/0.45 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.45 # Search class: FGHSF-FFMS21-SFFFFFNN
% 0.18/0.45 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.45 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 181s (1) cores
% 0.18/0.45 # Preprocessing time : 0.001 s
% 0.18/0.45 # Presaturation interreduction done
% 0.18/0.45
% 0.18/0.45 # Proof found!
% 0.18/0.45 # SZS status Theorem
% 0.18/0.45 # SZS output start CNFRefutation
% See solution above
% 0.18/0.45 # Parsed axioms : 22
% 0.18/0.45 # Removed by relevancy pruning/SinE : 2
% 0.18/0.45 # Initial clauses : 39
% 0.18/0.45 # Removed in clause preprocessing : 0
% 0.18/0.45 # Initial clauses in saturation : 39
% 0.18/0.45 # Processed clauses : 88
% 0.18/0.45 # ...of these trivial : 8
% 0.18/0.45 # ...subsumed : 5
% 0.18/0.45 # ...remaining for further processing : 75
% 0.18/0.45 # Other redundant clauses eliminated : 1
% 0.18/0.45 # Clauses deleted for lack of memory : 0
% 0.18/0.45 # Backward-subsumed : 0
% 0.18/0.45 # Backward-rewritten : 3
% 0.18/0.45 # Generated clauses : 48
% 0.18/0.45 # ...of the previous two non-redundant : 33
% 0.18/0.45 # ...aggressively subsumed : 0
% 0.18/0.45 # Contextual simplify-reflections : 1
% 0.18/0.45 # Paramodulations : 47
% 0.18/0.45 # Factorizations : 0
% 0.18/0.45 # NegExts : 0
% 0.18/0.45 # Equation resolutions : 1
% 0.18/0.45 # Total rewrite steps : 76
% 0.18/0.45 # Propositional unsat checks : 0
% 0.18/0.45 # Propositional check models : 0
% 0.18/0.45 # Propositional check unsatisfiable : 0
% 0.18/0.45 # Propositional clauses : 0
% 0.18/0.45 # Propositional clauses after purity: 0
% 0.18/0.45 # Propositional unsat core size : 0
% 0.18/0.45 # Propositional preprocessing time : 0.000
% 0.18/0.45 # Propositional encoding time : 0.000
% 0.18/0.45 # Propositional solver time : 0.000
% 0.18/0.45 # Success case prop preproc time : 0.000
% 0.18/0.45 # Success case prop encoding time : 0.000
% 0.18/0.45 # Success case prop solver time : 0.000
% 0.18/0.45 # Current number of processed clauses : 43
% 0.18/0.45 # Positive orientable unit clauses : 14
% 0.18/0.45 # Positive unorientable unit clauses: 0
% 0.18/0.45 # Negative unit clauses : 4
% 0.18/0.45 # Non-unit-clauses : 25
% 0.18/0.45 # Current number of unprocessed clauses: 13
% 0.18/0.45 # ...number of literals in the above : 27
% 0.18/0.45 # Current number of archived formulas : 0
% 0.18/0.45 # Current number of archived clauses : 32
% 0.18/0.45 # Clause-clause subsumption calls (NU) : 66
% 0.18/0.45 # Rec. Clause-clause subsumption calls : 49
% 0.18/0.45 # Non-unit clause-clause subsumptions : 2
% 0.18/0.45 # Unit Clause-clause subsumption calls : 26
% 0.18/0.45 # Rewrite failures with RHS unbound : 0
% 0.18/0.45 # BW rewrite match attempts : 6
% 0.18/0.45 # BW rewrite match successes : 3
% 0.18/0.45 # Condensation attempts : 0
% 0.18/0.45 # Condensation successes : 0
% 0.18/0.45 # Termbank termtop insertions : 3604
% 0.18/0.45
% 0.18/0.45 # -------------------------------------------------
% 0.18/0.45 # User time : 0.009 s
% 0.18/0.45 # System time : 0.001 s
% 0.18/0.45 # Total time : 0.010 s
% 0.18/0.45 # Maximum resident set size: 1840 pages
% 0.18/0.45
% 0.18/0.45 # -------------------------------------------------
% 0.18/0.45 # User time : 0.012 s
% 0.18/0.45 # System time : 0.001 s
% 0.18/0.45 # Total time : 0.013 s
% 0.18/0.45 # Maximum resident set size: 1700 pages
% 0.18/0.45 % E---3.1 exiting
%------------------------------------------------------------------------------