TSTP Solution File: GRA008+2 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : GRA008+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 : 300s
% DateTime : Mon May 20 20:41:22 EDT 2024
% Result : Theorem 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 9 unt; 0 def)
% Number of atoms : 178 ( 43 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 227 ( 94 ~; 88 |; 34 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 106 ( 3 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sequential_is_triangle,conjecture,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(sequential_defn,axiom,
! [X7,X8] :
( sequential(X7,X8)
<=> ( edge(X7)
& edge(X8)
& X7 != X8
& head_of(X7) = tail_of(X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(back_edge,lemma,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ? [X9] :
( edge(X9)
& tail_of(X9) = head_of(X8)
& head_of(X9) = tail_of(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
fof(triangle_defn,axiom,
! [X7,X8,X9] :
( triangle(X7,X8,X9)
<=> ( edge(X7)
& edge(X8)
& edge(X9)
& sequential(X7,X8)
& sequential(X8,X9)
& sequential(X9,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
fof(c_0_5,negated_conjecture,
~ ( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
inference(assume_negation,[status(cth)],[sequential_is_triangle]) ).
fof(c_0_6,plain,
! [X7,X8] :
( sequential(X7,X8)
<=> ( edge(X7)
& edge(X8)
& X7 != X8
& head_of(X7) = tail_of(X8) ) ),
inference(fof_simplification,[status(thm)],[sequential_defn]) ).
fof(c_0_7,lemma,
! [X43,X44,X45,X46,X47] :
( ( edge(esk7_4(X43,X44,X45,X46))
| ~ shortest_path(X43,X44,X47)
| ~ precedes(X45,X46,X47)
| ~ complete )
& ( tail_of(esk7_4(X43,X44,X45,X46)) = head_of(X46)
| ~ shortest_path(X43,X44,X47)
| ~ precedes(X45,X46,X47)
| ~ complete )
& ( head_of(esk7_4(X43,X44,X45,X46)) = tail_of(X45)
| ~ shortest_path(X43,X44,X47)
| ~ precedes(X45,X46,X47)
| ~ complete ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[back_edge])])])])])])]) ).
fof(c_0_8,negated_conjecture,
! [X18] :
( complete
& shortest_path(esk1_0,esk2_0,esk5_0)
& precedes(esk3_0,esk4_0,esk5_0)
& sequential(esk3_0,esk4_0)
& ~ triangle(esk3_0,esk4_0,X18) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
fof(c_0_9,plain,
! [X19,X20,X21] :
( ( edge(X19)
| ~ triangle(X19,X20,X21) )
& ( edge(X20)
| ~ triangle(X19,X20,X21) )
& ( edge(X21)
| ~ triangle(X19,X20,X21) )
& ( sequential(X19,X20)
| ~ triangle(X19,X20,X21) )
& ( sequential(X20,X21)
| ~ triangle(X19,X20,X21) )
& ( sequential(X21,X19)
| ~ triangle(X19,X20,X21) )
& ( ~ edge(X19)
| ~ edge(X20)
| ~ edge(X21)
| ~ sequential(X19,X20)
| ~ sequential(X20,X21)
| ~ sequential(X21,X19)
| triangle(X19,X20,X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])])]) ).
fof(c_0_10,plain,
! [X22,X23] :
( ( edge(X22)
| ~ sequential(X22,X23) )
& ( edge(X23)
| ~ sequential(X22,X23) )
& ( X22 != X23
| ~ sequential(X22,X23) )
& ( head_of(X22) = tail_of(X23)
| ~ sequential(X22,X23) )
& ( ~ edge(X22)
| ~ edge(X23)
| X22 = X23
| head_of(X22) != tail_of(X23)
| sequential(X22,X23) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_11,lemma,
( head_of(esk7_4(X1,X2,X3,X4)) = tail_of(X3)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,lemma,
( edge(esk7_4(X1,X2,X3,X4))
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( triangle(X1,X2,X3)
| ~ edge(X1)
| ~ edge(X2)
| ~ edge(X3)
| ~ sequential(X1,X2)
| ~ sequential(X2,X3)
| ~ sequential(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,lemma,
( head_of(esk7_4(X1,X2,X3,X4)) = tail_of(X3)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).
cnf(c_0_17,negated_conjecture,
shortest_path(esk1_0,esk2_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,lemma,
( edge(esk7_4(X1,X2,X3,X4))
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12])]) ).
cnf(c_0_19,lemma,
( tail_of(esk7_4(X1,X2,X3,X4)) = head_of(X4)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
~ triangle(esk3_0,esk4_0,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_14,c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
sequential(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( head_of(esk7_4(esk1_0,esk2_0,X1,X2)) = tail_of(X1)
| ~ precedes(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( edge(esk7_4(esk1_0,esk2_0,X1,X2))
| ~ precedes(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_26,lemma,
( tail_of(esk7_4(X1,X2,X3,X4)) = head_of(X4)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_12])]) ).
fof(c_0_27,plain,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
inference(fof_simplification,[status(thm)],[no_loops]) ).
cnf(c_0_28,negated_conjecture,
( ~ sequential(X1,esk3_0)
| ~ sequential(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_29,negated_conjecture,
( esk7_4(esk1_0,esk2_0,X1,X2) = X3
| sequential(esk7_4(esk1_0,esk2_0,X1,X2),X3)
| tail_of(X3) != tail_of(X1)
| ~ precedes(X1,X2,esk5_0)
| ~ edge(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_30,negated_conjecture,
edge(esk3_0),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( tail_of(esk7_4(esk1_0,esk2_0,X1,X2)) = head_of(X2)
| ~ precedes(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_32,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_33,plain,
! [X52] :
( ~ edge(X52)
| head_of(X52) != tail_of(X52) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_34,negated_conjecture,
( esk7_4(esk1_0,esk2_0,X1,X2) = esk3_0
| tail_of(esk3_0) != tail_of(X1)
| ~ precedes(X1,X2,esk5_0)
| ~ sequential(esk4_0,esk7_4(esk1_0,esk2_0,X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_35,negated_conjecture,
( X1 = esk7_4(esk1_0,esk2_0,X2,X3)
| sequential(X1,esk7_4(esk1_0,esk2_0,X2,X3))
| head_of(X3) != head_of(X1)
| ~ precedes(X2,X3,esk5_0)
| ~ edge(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_31]),c_0_25]) ).
cnf(c_0_36,negated_conjecture,
edge(esk4_0),
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_37,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( esk7_4(esk1_0,esk2_0,X1,X2) = esk4_0
| esk7_4(esk1_0,esk2_0,X1,X2) = esk3_0
| tail_of(esk3_0) != tail_of(X1)
| head_of(X2) != head_of(esk4_0)
| ~ precedes(X1,X2,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,negated_conjecture,
( tail_of(esk7_4(esk1_0,esk2_0,X1,X2)) != tail_of(X1)
| ~ precedes(X1,X2,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_24]),c_0_25]) ).
cnf(c_0_40,negated_conjecture,
( esk7_4(esk1_0,esk2_0,X1,X2) = esk3_0
| head_of(X2) = tail_of(esk4_0)
| tail_of(esk3_0) != tail_of(X1)
| head_of(X2) != head_of(esk4_0)
| ~ precedes(X1,X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( head_of(X1) = tail_of(esk4_0)
| tail_of(esk3_0) != tail_of(X2)
| head_of(X1) != head_of(esk4_0)
| ~ precedes(X2,X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
precedes(esk3_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_43,negated_conjecture,
head_of(esk4_0) = tail_of(esk4_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_43]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRA008+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 12:42:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order model finding
% 0.20/0.47 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/benchmark/theBenchmark.p
% 0.20/0.53 # Version: 3.1.0
% 0.20/0.53 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # new_bool_3 with pid 12171 completed with status 0
% 0.20/0.53 # Result found by new_bool_3
% 0.20/0.53 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53 # Search class: FGHSF-FFMS32-SFFFFFNN
% 0.20/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting G-E--_301_C18_F1_URBAN_S0Y with 181s (1) cores
% 0.20/0.53 # G-E--_301_C18_F1_URBAN_S0Y with pid 12174 completed with status 0
% 0.20/0.53 # Result found by G-E--_301_C18_F1_URBAN_S0Y
% 0.20/0.53 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53 # Search class: FGHSF-FFMS32-SFFFFFNN
% 0.20/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting G-E--_301_C18_F1_URBAN_S0Y with 181s (1) cores
% 0.20/0.53 # Preprocessing time : 0.002 s
% 0.20/0.53
% 0.20/0.53 # Proof found!
% 0.20/0.53 # SZS status Theorem
% 0.20/0.53 # SZS output start CNFRefutation
% See solution above
% 0.20/0.53 # Parsed axioms : 19
% 0.20/0.53 # Removed by relevancy pruning/SinE : 9
% 0.20/0.53 # Initial clauses : 38
% 0.20/0.53 # Removed in clause preprocessing : 1
% 0.20/0.53 # Initial clauses in saturation : 37
% 0.20/0.53 # Processed clauses : 231
% 0.20/0.53 # ...of these trivial : 2
% 0.20/0.53 # ...subsumed : 55
% 0.20/0.53 # ...remaining for further processing : 174
% 0.20/0.53 # Other redundant clauses eliminated : 1
% 0.20/0.53 # Clauses deleted for lack of memory : 0
% 0.20/0.53 # Backward-subsumed : 8
% 0.20/0.53 # Backward-rewritten : 35
% 0.20/0.53 # Generated clauses : 826
% 0.20/0.53 # ...of the previous two non-redundant : 744
% 0.20/0.53 # ...aggressively subsumed : 0
% 0.20/0.53 # Contextual simplify-reflections : 29
% 0.20/0.53 # Paramodulations : 806
% 0.20/0.53 # Factorizations : 12
% 0.20/0.53 # NegExts : 0
% 0.20/0.53 # Equation resolutions : 8
% 0.20/0.53 # Disequality decompositions : 0
% 0.20/0.53 # Total rewrite steps : 196
% 0.20/0.53 # ...of those cached : 187
% 0.20/0.53 # Propositional unsat checks : 0
% 0.20/0.53 # Propositional check models : 0
% 0.20/0.53 # Propositional check unsatisfiable : 0
% 0.20/0.53 # Propositional clauses : 0
% 0.20/0.53 # Propositional clauses after purity: 0
% 0.20/0.53 # Propositional unsat core size : 0
% 0.20/0.53 # Propositional preprocessing time : 0.000
% 0.20/0.53 # Propositional encoding time : 0.000
% 0.20/0.53 # Propositional solver time : 0.000
% 0.20/0.53 # Success case prop preproc time : 0.000
% 0.20/0.53 # Success case prop encoding time : 0.000
% 0.20/0.53 # Success case prop solver time : 0.000
% 0.20/0.53 # Current number of processed clauses : 130
% 0.20/0.53 # Positive orientable unit clauses : 10
% 0.20/0.53 # Positive unorientable unit clauses: 0
% 0.20/0.53 # Negative unit clauses : 5
% 0.20/0.53 # Non-unit-clauses : 115
% 0.20/0.53 # Current number of unprocessed clauses: 516
% 0.20/0.53 # ...number of literals in the above : 3422
% 0.20/0.53 # Current number of archived formulas : 0
% 0.20/0.53 # Current number of archived clauses : 43
% 0.20/0.53 # Clause-clause subsumption calls (NU) : 3566
% 0.20/0.53 # Rec. Clause-clause subsumption calls : 761
% 0.20/0.53 # Non-unit clause-clause subsumptions : 64
% 0.20/0.53 # Unit Clause-clause subsumption calls : 133
% 0.20/0.53 # Rewrite failures with RHS unbound : 0
% 0.20/0.53 # BW rewrite match attempts : 1
% 0.20/0.53 # BW rewrite match successes : 1
% 0.20/0.53 # Condensation attempts : 0
% 0.20/0.53 # Condensation successes : 0
% 0.20/0.53 # Termbank termtop insertions : 28327
% 0.20/0.53 # Search garbage collected termcells : 838
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.045 s
% 0.20/0.53 # System time : 0.004 s
% 0.20/0.53 # Total time : 0.049 s
% 0.20/0.53 # Maximum resident set size: 1868 pages
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.047 s
% 0.20/0.53 # System time : 0.006 s
% 0.20/0.53 # Total time : 0.053 s
% 0.20/0.53 # Maximum resident set size: 1732 pages
% 0.20/0.53 % E---3.1 exiting
%------------------------------------------------------------------------------