TSTP Solution File: SEU055+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU055+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n027.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 09:16:37 EDT 2022
% Result : Theorem 0.22s 2.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 120 ( 42 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 135 ( 54 ~; 55 |; 15 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 6 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t124_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2,X3] : relation_image(X1,set_difference(X2,X3)) = set_difference(relation_image(X1,X2),relation_image(X1,X3))
=> one_to_one(X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t124_funct_1) ).
fof(t117_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(X2))
=> relation_image(X2,singleton(X1)) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t117_funct_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d8_funct_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t37_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t20_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
<=> X1 != X2 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t20_zfmisc_1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2,X3] : relation_image(X1,set_difference(X2,X3)) = set_difference(relation_image(X1,X2),relation_image(X1,X3))
=> one_to_one(X1) ) ),
inference(assume_negation,[status(cth)],[t124_funct_1]) ).
fof(c_0_7,negated_conjecture,
! [X5,X6] :
( relation(esk15_0)
& function(esk15_0)
& relation_image(esk15_0,set_difference(X5,X6)) = set_difference(relation_image(esk15_0,X5),relation_image(esk15_0,X6))
& ~ one_to_one(esk15_0) ),
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)],[c_0_6])])])])])]) ).
fof(c_0_8,plain,
! [X3,X4] :
( ~ relation(X4)
| ~ function(X4)
| ~ in(X3,relation_dom(X4))
| relation_image(X4,singleton(X3)) = singleton(apply(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_funct_1])]) ).
cnf(c_0_9,negated_conjecture,
relation_image(esk15_0,set_difference(X1,X2)) = set_difference(relation_image(esk15_0,X1),relation_image(esk15_0,X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( relation_image(X1,singleton(X2)) = singleton(apply(X1,X2))
| ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,plain,
! [X4,X5,X6] :
( ( ~ one_to_one(X4)
| ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk2_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk3_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( apply(X4,esk2_1(X4)) = apply(X4,esk3_1(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( esk2_1(X4) != esk3_1(X4)
| one_to_one(X4)
| ~ relation(X4)
| ~ function(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)],[d8_funct_1])])])])])])]) ).
fof(c_0_14,plain,
! [X3,X4,X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])])])]) ).
fof(c_0_15,plain,
! [X3] : subset(X3,X3),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_16,negated_conjecture,
( set_difference(relation_image(esk15_0,X1),singleton(apply(esk15_0,X2))) = relation_image(esk15_0,set_difference(X1,singleton(X2)))
| ~ in(X2,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]) ).
cnf(c_0_17,plain,
( one_to_one(X1)
| apply(X1,esk2_1(X1)) = apply(X1,esk3_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
~ one_to_one(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( set_difference(relation_image(esk15_0,X1),singleton(apply(esk15_0,esk2_1(esk15_0)))) = relation_image(esk15_0,set_difference(X1,singleton(esk3_1(esk15_0))))
| ~ in(esk3_1(esk15_0),relation_dom(esk15_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_11]),c_0_12])]),c_0_18]) ).
cnf(c_0_22,plain,
set_difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_23,plain,
! [X3,X4,X3,X4] :
( ( set_difference(singleton(X3),singleton(X4)) != singleton(X3)
| X3 != X4 )
& ( X3 = X4
| set_difference(singleton(X3),singleton(X4)) = singleton(X3) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_zfmisc_1])])])]) ).
cnf(c_0_24,negated_conjecture,
( relation_image(esk15_0,set_difference(X1,singleton(esk3_1(esk15_0)))) = relation_image(esk15_0,set_difference(X1,singleton(esk2_1(esk15_0))))
| ~ in(esk2_1(esk15_0),relation_dom(esk15_0))
| ~ in(esk3_1(esk15_0),relation_dom(esk15_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
relation_image(esk15_0,empty_set) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_22]),c_0_22]) ).
cnf(c_0_26,plain,
( X1 != X2
| set_difference(singleton(X1),singleton(X2)) != singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( relation_image(esk15_0,set_difference(singleton(esk3_1(esk15_0)),singleton(esk2_1(esk15_0)))) = empty_set
| ~ in(esk2_1(esk15_0),relation_dom(esk15_0))
| ~ in(esk3_1(esk15_0),relation_dom(esk15_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_25]) ).
cnf(c_0_28,plain,
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
set_difference(singleton(X1),singleton(X1)) != singleton(X1),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( relation_image(esk15_0,singleton(esk3_1(esk15_0))) = empty_set
| esk3_1(esk15_0) = esk2_1(esk15_0)
| ~ in(esk2_1(esk15_0),relation_dom(esk15_0))
| ~ in(esk3_1(esk15_0),relation_dom(esk15_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
singleton(X1) != empty_set,
inference(rw,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_32,negated_conjecture,
( esk3_1(esk15_0) = esk2_1(esk15_0)
| ~ in(esk3_1(esk15_0),relation_dom(esk15_0))
| ~ in(esk2_1(esk15_0),relation_dom(esk15_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_30]),c_0_11]),c_0_12])]),c_0_31]) ).
cnf(c_0_33,plain,
( one_to_one(X1)
| in(esk3_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,negated_conjecture,
( esk3_1(esk15_0) = esk2_1(esk15_0)
| ~ in(esk2_1(esk15_0),relation_dom(esk15_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_11]),c_0_12])]),c_0_18]) ).
cnf(c_0_35,plain,
( one_to_one(X1)
| in(esk2_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_36,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk2_1(X1) != esk3_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,negated_conjecture,
esk3_1(esk15_0) = esk2_1(esk15_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_11]),c_0_12])]),c_0_18]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_11]),c_0_12])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU055+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 05:43:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.22/2.41 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.22/2.41 # Preprocessing time : 0.017 s
% 0.22/2.41
% 0.22/2.41 # Proof found!
% 0.22/2.41 # SZS status Theorem
% 0.22/2.41 # SZS output start CNFRefutation
% See solution above
% 0.22/2.41 # Proof object total steps : 39
% 0.22/2.41 # Proof object clause steps : 26
% 0.22/2.41 # Proof object formula steps : 13
% 0.22/2.41 # Proof object conjectures : 17
% 0.22/2.41 # Proof object clause conjectures : 14
% 0.22/2.41 # Proof object formula conjectures : 3
% 0.22/2.41 # Proof object initial clauses used : 13
% 0.22/2.41 # Proof object initial formulas used : 6
% 0.22/2.41 # Proof object generating inferences : 11
% 0.22/2.41 # Proof object simplifying inferences : 27
% 0.22/2.41 # Training examples: 0 positive, 0 negative
% 0.22/2.41 # Parsed axioms : 40
% 0.22/2.41 # Removed by relevancy pruning/SinE : 0
% 0.22/2.41 # Initial clauses : 69
% 0.22/2.41 # Removed in clause preprocessing : 2
% 0.22/2.41 # Initial clauses in saturation : 67
% 0.22/2.41 # Processed clauses : 1951
% 0.22/2.41 # ...of these trivial : 5
% 0.22/2.41 # ...subsumed : 1066
% 0.22/2.41 # ...remaining for further processing : 880
% 0.22/2.41 # Other redundant clauses eliminated : 5
% 0.22/2.41 # Clauses deleted for lack of memory : 0
% 0.22/2.41 # Backward-subsumed : 43
% 0.22/2.41 # Backward-rewritten : 197
% 0.22/2.41 # Generated clauses : 24990
% 0.22/2.41 # ...of the previous two non-trivial : 12268
% 0.22/2.41 # Contextual simplify-reflections : 906
% 0.22/2.41 # Paramodulations : 24953
% 0.22/2.41 # Factorizations : 2
% 0.22/2.41 # Equation resolutions : 35
% 0.22/2.41 # Current number of processed clauses : 638
% 0.22/2.41 # Positive orientable unit clauses : 42
% 0.22/2.41 # Positive unorientable unit clauses: 0
% 0.22/2.41 # Negative unit clauses : 19
% 0.22/2.41 # Non-unit-clauses : 577
% 0.22/2.41 # Current number of unprocessed clauses: 3064
% 0.22/2.41 # ...number of literals in the above : 12181
% 0.22/2.41 # Current number of archived formulas : 0
% 0.22/2.41 # Current number of archived clauses : 240
% 0.22/2.41 # Clause-clause subsumption calls (NU) : 417583
% 0.22/2.41 # Rec. Clause-clause subsumption calls : 101916
% 0.22/2.41 # Non-unit clause-clause subsumptions : 1741
% 0.22/2.41 # Unit Clause-clause subsumption calls : 523
% 0.22/2.41 # Rewrite failures with RHS unbound : 0
% 0.22/2.41 # BW rewrite match attempts : 14
% 0.22/2.41 # BW rewrite match successes : 7
% 0.22/2.41 # Condensation attempts : 0
% 0.22/2.41 # Condensation successes : 0
% 0.22/2.41 # Termbank termtop insertions : 7839957
% 0.22/2.41
% 0.22/2.41 # -------------------------------------------------
% 0.22/2.41 # User time : 1.045 s
% 0.22/2.41 # System time : 0.010 s
% 0.22/2.41 # Total time : 1.055 s
% 0.22/2.41 # Maximum resident set size: 19064 pages
% 0.22/23.40 eprover: CPU time limit exceeded, terminating
% 0.22/23.40 eprover: CPU time limit exceeded, terminating
% 0.22/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.42 eprover: No such file or directory
% 0.22/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.42 eprover: No such file or directory
% 0.22/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.42 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------