%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV608+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:35:19 PM UTC 2026
% Result : Theorem 1.30s 6.47s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 48 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 17 ~; 14 |; 4 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('_HAMMER_GOAL',conjecture,
! [X76] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X76)
=> ! [X82] :
( cColor_2egraph___24t(X82)
=> ! [X95] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X95)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X76),X82)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X95)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X95,X82)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X82)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('Color.select_terminates',axiom,
! [X76] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X76)
=> ! [X82] :
( cColor_2egraph___24t(X82)
=> ! [X95] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X95)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X76),X82)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X95)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X95,X82)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X82)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Color.select_terminates') ).
fof('$adef_Color.low_deg_$a1',axiom,
! [X2683] : happ(cColor_2elow__deg,X2683) = cColor_2elow__deg___24a1(X2683),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Color.low_deg_$a1') ).
fof(c_0_3,negated_conjecture,
~ ! [X76] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X76)
=> ! [X82] :
( cColor_2egraph___24t(X82)
=> ! [X95] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X95)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X76),X82)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X95)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X95,X82)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X82)) ) ) ) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_4,plain,
! [X2774,X2775,X2776] :
( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2776,X2775)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X2775))
| cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X2774),X2775)) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2776)
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2776)
| ~ cColor_2egraph___24t(X2775)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2774) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Color.select_terminates'])])])]) ).
fof(c_0_5,plain,
! [X2785] : happ(cColor_2elow__deg,X2785) = cColor_2elow__deg___24a1(X2785),
inference(variable_rename,[status(thm)],['$adef_Color.low_deg_$a1']) ).
fof(c_0_6,negated_conjecture,
( ~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(esk3_0,esk2_0)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,esk2_0))
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(esk1_0),esk2_0)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,esk3_0)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(esk3_0)
& cColor_2egraph___24t(esk2_0)
& cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
cnf(c_0_7,plain,
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X1),X2)) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X3)
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X3)
| ~ cColor_2egraph___24t(X2)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1)
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X3,X2)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
happ(cColor_2elow__deg,X1) = cColor_2elow__deg___24a1(X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(esk1_0),esk2_0)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ cColor_2egraph___24t(X2)
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X1)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X3)
| cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(happ(cColor_2elow__deg,X3),X2)) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X1)
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X1,X2)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X2)) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(happ(cColor_2elow__deg,esk1_0),esk2_0)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,esk3_0),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
cColor_2egraph___24t(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(esk3_0,esk2_0)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
( ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X1)
| cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,esk3_0) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X1)
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X1,esk2_0)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[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_16,negated_conjecture,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV608+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.40 % Computer : n008.cluster.edu
% 0.15/5.40 % Model : x86_64 x86_64
% 0.15/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.40 % Memory : 8046.5625MB
% 0.15/5.40 % OS : Linux 6.8.0-71-generic
% 0.15/5.40 % CPULimit : 300
% 0.15/5.40 % WCLimit : 300
% 0.15/5.40 % DateTime : Mon Sep 21 07:30:15 UTC 2026
% 0.15/5.41 % CPUTime :
% 0.15/5.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.48 Running first-order theorem proving
% 0.15/5.48 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.30/6.47 % Version: 3.5.1
% 1.30/6.47 % Preprocessing class: FMLLSMLLSSSNFFN.
% 1.30/6.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/6.47 % Starting new_bool_3 with 900s (3) cores
% 1.30/6.47 % Starting new_bool_1 with 900s (3) cores
% 1.30/6.47 % Starting sh5l with 300s (1) cores
% 1.30/6.47 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 1.30/6.47 % new_bool_1 with pid 492449 completed with status 0
% 1.30/6.47 % Result found by new_bool_1
% 1.30/6.47 % Preprocessing class: FMLLSMLLSSSNFFN.
% 1.30/6.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/6.47 % Starting new_bool_3 with 900s (3) cores
% 1.30/6.47 % Starting new_bool_1 with 900s (3) cores
% 1.30/6.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.30/6.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.30/6.47 % Search class: FGHSS-FMLM32-MFFFFFNN
% 1.30/6.47 % partial match(1): FGHSS-FSLM32-MFFFFFNN
% 1.30/6.47 % Scheduled 5 strats onto 3 cores with 900 seconds (900 total)
% 1.30/6.47 % Starting SubtermCWHack with 91s (1) cores
% 1.30/6.47 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 541s (1) cores
% 1.30/6.47 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 91s (1) cores
% 1.30/6.47 % G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 492454 completed with status 0
% 1.30/6.47 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 1.30/6.47 % Preprocessing class: FMLLSMLLSSSNFFN.
% 1.30/6.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.30/6.47 % Starting new_bool_3 with 900s (3) cores
% 1.30/6.47 % Starting new_bool_1 with 900s (3) cores
% 1.30/6.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.30/6.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.30/6.47 % Search class: FGHSS-FMLM32-MFFFFFNN
% 1.30/6.47 % partial match(1): FGHSS-FSLM32-MFFFFFNN
% 1.30/6.47 % Scheduled 5 strats onto 3 cores with 900 seconds (900 total)
% 1.30/6.47 % Starting SubtermCWHack with 91s (1) cores
% 1.30/6.47 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 541s (1) cores
% 1.30/6.47 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 91s (1) cores
% 1.30/6.47 % Preprocessing time : 0.036 s
% 1.30/6.47 % Presaturation interreduction done
% 1.30/6.47
% 1.30/6.47 % Proof found!
% 1.30/6.47 % SZS status Theorem
% 1.30/6.47 % SZS output start CNFRefutation
% See solution above
% 1.30/6.47 % Parsed axioms : 2868
% 1.30/6.47 % Removed by relevancy pruning/SinE : 2711
% 1.30/6.47 % Initial clauses : 708
% 1.30/6.47 % Removed in clause preprocessing : 19
% 1.30/6.47 % Initial clauses in saturation : 689
% 1.30/6.47 % Processed clauses : 1146
% 1.30/6.47 % ...of these trivial : 0
% 1.30/6.47 % ...subsumed : 406
% 1.30/6.47 % ...remaining for further processing : 740
% 1.30/6.47 % Other redundant clauses eliminated : 9
% 1.30/6.47 % Clauses deleted for lack of memory : 0
% 1.30/6.47 % Backward-subsumed : 1
% 1.30/6.47 % Backward-rewritten : 1
% 1.30/6.47 % Generated clauses : 717
% 1.30/6.47 % ...of the previous two non-redundant : 666
% 1.30/6.47 % ...aggressively subsumed : 0
% 1.30/6.47 % Contextual simplify-reflections : 25
% 1.30/6.47 % Paramodulations : 697
% 1.30/6.47 % Factorizations : 0
% 1.30/6.47 % NegExts : 0
% 1.30/6.47 % Equation resolutions : 20
% 1.30/6.47 % Disequality decompositions : 0
% 1.30/6.47 % Total rewrite steps : 259
% 1.30/6.47 % ...of those cached : 244
% 1.30/6.47 % Propositional unsat checks : 0
% 1.30/6.47 % Propositional check models : 0
% 1.30/6.47 % Propositional check unsatisfiable : 0
% 1.30/6.47 % Propositional clauses : 0
% 1.30/6.47 % Propositional clauses after purity: 0
% 1.30/6.47 % Propositional unsat core size : 0
% 1.30/6.47 % Propositional preprocessing time : 0.000
% 1.30/6.47 % Propositional encoding time : 0.000
% 1.30/6.47 % Propositional solver time : 0.000
% 1.30/6.47 % Success case prop preproc time : 0.000
% 1.30/6.47 % Success case prop encoding time : 0.000
% 1.30/6.47 % Success case prop solver time : 0.000
% 1.30/6.47 % Current number of processed clauses : 251
% 1.30/6.47 % Positive orientable unit clauses : 27
% 1.30/6.47 % Positive unorientable unit clauses: 1
% 1.30/6.47 % Negative unit clauses : 8
% 1.30/6.47 % Non-unit-clauses : 215
% 1.30/6.47 % Current number of unprocessed clauses: 682
% 1.30/6.47 % ...number of literals in the above : 4072
% 1.30/6.47 % Current number of archived formulas : 0
% 1.30/6.47 % Current number of archived clauses : 480
% 1.30/6.47 % Clause-clause subsumption calls (NU) : 150155
% 1.30/6.47 % Rec. Clause-clause subsumption calls : 12734
% 1.30/6.47 % Non-unit clause-clause subsumptions : 428
% 1.30/6.47 % Unit Clause-clause subsumption calls : 99
% 1.30/6.47 % Rewrite failures with RHS unbound : 0
% 1.30/6.47 % BW rewrite match attempts : 4
% 1.30/6.47 % BW rewrite match successes : 4
% 1.30/6.47 % Condensation attempts : 0
% 1.30/6.47 % Condensation successes : 0
% 1.30/6.47 % Termbank termtop insertions : 164150
% 1.30/6.47 % Search garbage collected termcells : 49024
% 1.30/6.47
% 1.30/6.47 % -------------------------------------------------
% 1.30/6.47 % User time : 0.378 s
% 1.30/6.47 % System time : 0.040 s
% 1.30/6.47 % Total time : 0.418 s
% 1.30/6.47 % Maximum resident set size: 15984 pages
% 1.30/6.47
% 1.30/6.47 % -------------------------------------------------
% 1.30/6.47 % User time : 1.286 s
% 1.30/6.47 % System time : 0.122 s
% 1.30/6.47 % Total time : 1.408 s
% 1.30/6.47 % Maximum resident set size: 12544 pages
% 1.30/6.47 % E exiting
%------------------------------------------------------------------------------