TSTP Solution File: SEU055+1 by E-SAT---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SEU055+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 19:30:18 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 18 unt; 0 def)
% Number of atoms : 110 ( 41 equ)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 116 ( 45 ~; 45 |; 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 : 50 ( 2 sgn; 29 !; 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/sandbox/tmp/tmp.eiqSsYnGyj/E---3.1_21229.p',t124_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/sandbox/tmp/tmp.eiqSsYnGyj/E---3.1_21229.p',d8_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/sandbox/tmp/tmp.eiqSsYnGyj/E---3.1_21229.p',t117_funct_1) ).
fof(t20_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
<=> X1 != X2 ),
file('/export/starexec/sandbox/tmp/tmp.eiqSsYnGyj/E---3.1_21229.p',t20_zfmisc_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.eiqSsYnGyj/E---3.1_21229.p',t37_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/tmp/tmp.eiqSsYnGyj/E---3.1_21229.p',reflexivity_r1_tarski) ).
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,plain,
! [X8,X9,X10] :
( ( ~ one_to_one(X8)
| ~ in(X9,relation_dom(X8))
| ~ in(X10,relation_dom(X8))
| apply(X8,X9) != apply(X8,X10)
| X9 = X10
| ~ relation(X8)
| ~ function(X8) )
& ( in(esk2_1(X8),relation_dom(X8))
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) )
& ( in(esk3_1(X8),relation_dom(X8))
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) )
& ( apply(X8,esk2_1(X8)) = apply(X8,esk3_1(X8))
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) )
& ( esk2_1(X8) != esk3_1(X8)
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
fof(c_0_8,negated_conjecture,
! [X5,X6] :
( relation(esk1_0)
& function(esk1_0)
& relation_image(esk1_0,set_difference(X5,X6)) = set_difference(relation_image(esk1_0,X5),relation_image(esk1_0,X6))
& ~ one_to_one(esk1_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,plain,
! [X22,X23] :
( ~ relation(X23)
| ~ function(X23)
| ~ in(X22,relation_dom(X23))
| relation_image(X23,singleton(X22)) = singleton(apply(X23,X22)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_funct_1])]) ).
cnf(c_0_10,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
function(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
~ one_to_one(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X16,X17] :
( ( set_difference(singleton(X16),singleton(X17)) != singleton(X16)
| X16 != X17 )
& ( X16 = X17
| set_difference(singleton(X16),singleton(X17)) = singleton(X16) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_zfmisc_1])]) ).
fof(c_0_15,plain,
! [X18,X19] :
( ( set_difference(X18,X19) != empty_set
| subset(X18,X19) )
& ( ~ subset(X18,X19)
| set_difference(X18,X19) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(c_0_16,plain,
! [X64] : subset(X64,X64),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_17,plain,
( in(esk3_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
( apply(X1,esk2_1(X1)) = apply(X1,esk3_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( relation_image(X1,singleton(X2)) = singleton(apply(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
in(esk2_1(esk1_0),relation_dom(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_21,plain,
( set_difference(singleton(X1),singleton(X2)) != singleton(X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
relation_image(esk1_0,set_difference(X1,X2)) = set_difference(relation_image(esk1_0,X1),relation_image(esk1_0,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( X1 = X2
| set_difference(singleton(X1),singleton(X2)) = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,negated_conjecture,
in(esk3_1(esk1_0),relation_dom(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_27,negated_conjecture,
apply(esk1_0,esk3_1(esk1_0)) = apply(esk1_0,esk2_1(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_28,negated_conjecture,
singleton(apply(esk1_0,esk2_1(esk1_0))) = relation_image(esk1_0,singleton(esk2_1(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_11]),c_0_12])]) ).
cnf(c_0_29,plain,
set_difference(singleton(X1),singleton(X1)) != singleton(X1),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
set_difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( set_difference(relation_image(esk1_0,singleton(X1)),relation_image(esk1_0,singleton(X2))) = relation_image(esk1_0,singleton(X1))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
relation_image(esk1_0,singleton(esk3_1(esk1_0))) = relation_image(esk1_0,singleton(esk2_1(esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_26]),c_0_11]),c_0_12])]),c_0_27]),c_0_28]) ).
cnf(c_0_33,plain,
singleton(X1) != empty_set,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( one_to_one(X1)
| esk2_1(X1) != esk3_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_35,negated_conjecture,
( set_difference(relation_image(esk1_0,singleton(X1)),relation_image(esk1_0,singleton(esk2_1(esk1_0)))) = relation_image(esk1_0,singleton(X1))
| X1 = esk3_1(esk1_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
relation_image(esk1_0,singleton(esk2_1(esk1_0))) != empty_set,
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
esk3_1(esk1_0) != esk2_1(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_35]),c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU055+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n004.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 : 2400
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Oct 2 09:10:00 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Running first-order model finding
% 0.21/0.49 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.eiqSsYnGyj/E---3.1_21229.p
% 0.21/0.53 # Version: 3.1pre001
% 0.21/0.53 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53 # Starting sh5l with 300s (1) cores
% 0.21/0.53 # sh5l with pid 21362 completed with status 0
% 0.21/0.53 # Result found by sh5l
% 0.21/0.53 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53 # Starting sh5l with 300s (1) cores
% 0.21/0.53 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.53 # Search class: FGHSM-FFMM21-SFFFFFNN
% 0.21/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S0S with 163s (1) cores
% 0.21/0.53 # G-E--_200_B02_F1_SE_CS_SP_PI_S0S with pid 21374 completed with status 0
% 0.21/0.53 # Result found by G-E--_200_B02_F1_SE_CS_SP_PI_S0S
% 0.21/0.53 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53 # Starting sh5l with 300s (1) cores
% 0.21/0.53 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.53 # Search class: FGHSM-FFMM21-SFFFFFNN
% 0.21/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S0S with 163s (1) cores
% 0.21/0.53 # Preprocessing time : 0.002 s
% 0.21/0.53
% 0.21/0.53 # Proof found!
% 0.21/0.53 # SZS status Theorem
% 0.21/0.53 # SZS output start CNFRefutation
% See solution above
% 0.21/0.53 # Parsed axioms : 40
% 0.21/0.53 # Removed by relevancy pruning/SinE : 0
% 0.21/0.53 # Initial clauses : 69
% 0.21/0.53 # Removed in clause preprocessing : 2
% 0.21/0.53 # Initial clauses in saturation : 67
% 0.21/0.53 # Processed clauses : 325
% 0.21/0.53 # ...of these trivial : 34
% 0.21/0.53 # ...subsumed : 40
% 0.21/0.53 # ...remaining for further processing : 251
% 0.21/0.53 # Other redundant clauses eliminated : 8
% 0.21/0.53 # Clauses deleted for lack of memory : 0
% 0.21/0.53 # Backward-subsumed : 5
% 0.21/0.53 # Backward-rewritten : 49
% 0.21/0.53 # Generated clauses : 1036
% 0.21/0.53 # ...of the previous two non-redundant : 1009
% 0.21/0.53 # ...aggressively subsumed : 0
% 0.21/0.53 # Contextual simplify-reflections : 2
% 0.21/0.53 # Paramodulations : 1028
% 0.21/0.53 # Factorizations : 0
% 0.21/0.53 # NegExts : 0
% 0.21/0.53 # Equation resolutions : 8
% 0.21/0.53 # Total rewrite steps : 347
% 0.21/0.53 # Propositional unsat checks : 0
% 0.21/0.53 # Propositional check models : 0
% 0.21/0.53 # Propositional check unsatisfiable : 0
% 0.21/0.53 # Propositional clauses : 0
% 0.21/0.53 # Propositional clauses after purity: 0
% 0.21/0.53 # Propositional unsat core size : 0
% 0.21/0.53 # Propositional preprocessing time : 0.000
% 0.21/0.53 # Propositional encoding time : 0.000
% 0.21/0.53 # Propositional solver time : 0.000
% 0.21/0.53 # Success case prop preproc time : 0.000
% 0.21/0.53 # Success case prop encoding time : 0.000
% 0.21/0.53 # Success case prop solver time : 0.000
% 0.21/0.53 # Current number of processed clauses : 193
% 0.21/0.53 # Positive orientable unit clauses : 105
% 0.21/0.53 # Positive unorientable unit clauses: 0
% 0.21/0.53 # Negative unit clauses : 16
% 0.21/0.53 # Non-unit-clauses : 72
% 0.21/0.53 # Current number of unprocessed clauses: 705
% 0.21/0.53 # ...number of literals in the above : 1507
% 0.21/0.53 # Current number of archived formulas : 0
% 0.21/0.53 # Current number of archived clauses : 55
% 0.21/0.53 # Clause-clause subsumption calls (NU) : 826
% 0.21/0.53 # Rec. Clause-clause subsumption calls : 595
% 0.21/0.53 # Non-unit clause-clause subsumptions : 19
% 0.21/0.53 # Unit Clause-clause subsumption calls : 269
% 0.21/0.53 # Rewrite failures with RHS unbound : 0
% 0.21/0.53 # BW rewrite match attempts : 713
% 0.21/0.53 # BW rewrite match successes : 9
% 0.21/0.53 # Condensation attempts : 0
% 0.21/0.53 # Condensation successes : 0
% 0.21/0.53 # Termbank termtop insertions : 23087
% 0.21/0.53
% 0.21/0.53 # -------------------------------------------------
% 0.21/0.53 # User time : 0.026 s
% 0.21/0.53 # System time : 0.007 s
% 0.21/0.53 # Total time : 0.033 s
% 0.21/0.53 # Maximum resident set size: 1888 pages
% 0.21/0.53
% 0.21/0.53 # -------------------------------------------------
% 0.21/0.53 # User time : 0.030 s
% 0.21/0.53 # System time : 0.007 s
% 0.21/0.53 # Total time : 0.037 s
% 0.21/0.53 # Maximum resident set size: 1708 pages
% 0.21/0.53 % E---3.1 exiting
%------------------------------------------------------------------------------