TSTP Solution File: ITP050^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP050^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.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 22:16:04 EDT 2024
% Result : Theorem 1.09s 0.65s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 51 ( 12 unt; 18 typ; 0 def)
% Number of atoms : 71 ( 7 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 248 ( 24 ~; 23 |; 3 &; 190 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 66 ( 4 ^ 62 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
product_prod_nat_nat: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
set_Pr1986765409at_nat: $tType ).
thf(decl_sort4,type,
nat: $tType ).
thf(decl_sort5,type,
list_P559422087at_nat: $tType ).
thf(decl_32,type,
e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(decl_37,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(decl_38,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(decl_45,type,
inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(decl_50,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(decl_54,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(decl_59,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(decl_62,type,
c: product_prod_nat_nat > a ).
thf(decl_63,type,
edges: set_Pr1986765409at_nat ).
thf(decl_64,type,
p: list_P559422087at_nat ).
thf(decl_65,type,
s: nat ).
thf(decl_66,type,
t: nat ).
thf(decl_151,type,
esk85_2: set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat ).
thf(fact_257_inf_Oorder__iff,axiom,
( ord_le841296385at_nat
= ( ^ [X28: set_Pr1986765409at_nat,X29: set_Pr1986765409at_nat] :
( X28
= ( inf_in586391887at_nat @ X28 @ X29 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_inf_Oorder__iff) ).
thf(fact_200_Graph_OshortestPath__is__path,axiom,
! [X17: product_prod_nat_nat > a,X2: nat,X14: list_P559422087at_nat,X15: nat] :
( ( isShortestPath_a @ X17 @ X2 @ X14 @ X15 )
=> ( isPath_a @ X17 @ X2 @ X14 @ X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Graph_OshortestPath__is__path) ).
thf(fact_164_IntD2,axiom,
! [X377: product_prod_nat_nat,X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ X377 @ ( inf_in586391887at_nat @ X3 @ X4 ) )
=> ( member701585322at_nat @ X377 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_IntD2) ).
thf(fact_146_Graph_OisPath__edgeset,axiom,
! [X17: product_prod_nat_nat > a,X2: nat,X14: list_P559422087at_nat,X15: nat,X16: product_prod_nat_nat] :
( ( isPath_a @ X17 @ X2 @ X14 @ X15 )
=> ( ( member701585322at_nat @ X16 @ ( set_Pr2131844118at_nat @ X14 ) )
=> ( member701585322at_nat @ X16 @ ( e_a @ X17 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Graph_OisPath__edgeset) ).
thf(fact_0_SP,axiom,
isShortestPath_a @ c @ s @ p @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_SP) ).
thf(fact_130_subset__eq,axiom,
( ord_le841296385at_nat
= ( ^ [X313: set_Pr1986765409at_nat,X314: set_Pr1986765409at_nat] :
! [X336: product_prod_nat_nat] :
( ( member701585322at_nat @ X336 @ X313 )
=> ( member701585322at_nat @ X336 @ X314 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_subset__eq) ).
thf(fact_1_SP__EDGES,axiom,
ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_SP__EDGES) ).
thf(conj_0,conjecture,
ord_le841296385at_nat @ edges @ ( e_a @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(c_0_8,plain,
! [X1647: set_Pr1986765409at_nat,X1648: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ X1647 @ X1648 )
<=> ( X1647
= ( inf_in586391887at_nat @ X1647 @ X1648 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_257_inf_Oorder__iff])]) ).
thf(c_0_9,plain,
! [X2246: product_prod_nat_nat > a,X2247: nat,X2248: list_P559422087at_nat,X2249: nat] :
( ~ ( isShortestPath_a @ X2246 @ X2247 @ X2248 @ X2249 )
| ( isPath_a @ X2246 @ X2247 @ X2248 @ X2249 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_200_Graph_OshortestPath__is__path])])]) ).
thf(c_0_10,plain,
! [X2167: product_prod_nat_nat,X2168: set_Pr1986765409at_nat,X2169: set_Pr1986765409at_nat] :
( ~ ( member701585322at_nat @ X2167 @ ( inf_in586391887at_nat @ X2168 @ X2169 ) )
| ( member701585322at_nat @ X2167 @ X2169 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_164_IntD2])])]) ).
thf(c_0_11,plain,
! [X2368: set_Pr1986765409at_nat,X2369: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ X2368 @ X2369 )
| ( X2368
= ( inf_in586391887at_nat @ X2368 @ X2369 ) ) )
& ( ( X2368
!= ( inf_in586391887at_nat @ X2368 @ X2369 ) )
| ( ord_le841296385at_nat @ X2368 @ X2369 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
thf(c_0_12,plain,
! [X2114: product_prod_nat_nat > a,X2115: nat,X2116: list_P559422087at_nat,X2117: nat,X2118: product_prod_nat_nat] :
( ~ ( isPath_a @ X2114 @ X2115 @ X2116 @ X2117 )
| ~ ( member701585322at_nat @ X2118 @ ( set_Pr2131844118at_nat @ X2116 ) )
| ( member701585322at_nat @ X2118 @ ( e_a @ X2114 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_146_Graph_OisPath__edgeset])])]) ).
thf(c_0_13,plain,
! [X2: nat,X17: product_prod_nat_nat > a,X14: list_P559422087at_nat,X8: nat] :
( ( isPath_a @ X17 @ X2 @ X14 @ X8 )
| ~ ( isShortestPath_a @ X17 @ X2 @ X14 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
isShortestPath_a @ c @ s @ p @ t,
inference(split_conjunct,[status(thm)],[fact_0_SP]) ).
thf(c_0_15,plain,
! [X3: set_Pr1986765409at_nat,X5: product_prod_nat_nat,X4: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ X5 @ X4 )
| ~ ( member701585322at_nat @ X5 @ ( inf_in586391887at_nat @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
! [X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat] :
( ( X3
= ( inf_in586391887at_nat @ X3 @ X4 ) )
| ~ ( ord_le841296385at_nat @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
! [X1630: set_Pr1986765409at_nat,X1631: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ X1630 @ X1631 )
<=> ! [X336: product_prod_nat_nat] :
( ( member701585322at_nat @ X336 @ X1630 )
=> ( member701585322at_nat @ X336 @ X1631 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_130_subset__eq])]) ).
thf(c_0_18,plain,
! [X2: nat,X5: product_prod_nat_nat,X8: nat,X17: product_prod_nat_nat > a,X14: list_P559422087at_nat] :
( ( member701585322at_nat @ X5 @ ( e_a @ X17 ) )
| ~ ( isPath_a @ X17 @ X2 @ X14 @ X8 )
| ~ ( member701585322at_nat @ X5 @ ( set_Pr2131844118at_nat @ X14 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
isPath_a @ c @ s @ p @ t,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_20,plain,
! [X5: product_prod_nat_nat,X4: set_Pr1986765409at_nat,X3: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ X5 @ X3 )
| ~ ( member701585322at_nat @ X5 @ X4 )
| ~ ( ord_le841296385at_nat @ X4 @ X3 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_21,plain,
ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ),
inference(split_conjunct,[status(thm)],[fact_1_SP__EDGES]) ).
thf(c_0_22,plain,
! [X2073: set_Pr1986765409at_nat,X2074: set_Pr1986765409at_nat,X2075: product_prod_nat_nat,X2076: set_Pr1986765409at_nat,X2077: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ X2073 @ X2074 )
| ~ ( member701585322at_nat @ X2075 @ X2073 )
| ( member701585322at_nat @ X2075 @ X2074 ) )
& ( ( member701585322at_nat @ ( esk85_2 @ X2076 @ X2077 ) @ X2076 )
| ( ord_le841296385at_nat @ X2076 @ X2077 ) )
& ( ~ ( member701585322at_nat @ ( esk85_2 @ X2076 @ X2077 ) @ X2077 )
| ( ord_le841296385at_nat @ X2076 @ X2077 ) ) ),
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)],[c_0_17])])])])])])]) ).
thf(c_0_23,plain,
! [X5: product_prod_nat_nat] :
( ( member701585322at_nat @ X5 @ ( e_a @ c ) )
| ~ ( member701585322at_nat @ X5 @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,plain,
! [X5: product_prod_nat_nat] :
( ( member701585322at_nat @ X5 @ ( set_Pr2131844118at_nat @ p ) )
| ~ ( member701585322at_nat @ X5 @ edges ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_25,negated_conjecture,
~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
thf(c_0_26,plain,
! [X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ X3 @ X4 )
| ~ ( member701585322at_nat @ ( esk85_2 @ X3 @ X4 ) @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_27,plain,
! [X5: product_prod_nat_nat] :
( ( member701585322at_nat @ X5 @ ( e_a @ c ) )
| ~ ( member701585322at_nat @ X5 @ edges ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_28,negated_conjecture,
~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ),
inference(fof_nnf,[status(thm)],[c_0_25]) ).
thf(c_0_29,plain,
! [X3: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ X3 @ ( e_a @ c ) )
| ~ ( member701585322at_nat @ ( esk85_2 @ X3 @ ( e_a @ c ) ) @ edges ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_30,plain,
! [X3: set_Pr1986765409at_nat,X4: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( esk85_2 @ X3 @ X4 ) @ X3 )
| ( ord_le841296385at_nat @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_31,negated_conjecture,
~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_32,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP050^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n006.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 : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 17:38:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.49 Running higher-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.09/0.65 # Version: 3.1.0-ho
% 1.09/0.65 # Preprocessing class: HSLSSMSSSSMNHSA.
% 1.09/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.65 # Starting sh1 with 1500s (5) cores
% 1.09/0.65 # Starting new_ho_8 with 300s (1) cores
% 1.09/0.65 # Starting new_ho_11 with 300s (1) cores
% 1.09/0.65 # Starting sh5l with 300s (1) cores
% 1.09/0.65 # new_ho_11 with pid 5324 completed with status 0
% 1.09/0.65 # Result found by new_ho_11
% 1.09/0.65 # Preprocessing class: HSLSSMSSSSMNHSA.
% 1.09/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.65 # Starting sh1 with 1500s (5) cores
% 1.09/0.65 # Starting new_ho_8 with 300s (1) cores
% 1.09/0.65 # Starting new_ho_11 with 300s (1) cores
% 1.09/0.65 # No SInE strategy applied
% 1.09/0.65 # Search class: HGHSM-FSLM32-MHSFFSBN
% 1.09/0.65 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.09/0.65 # Starting new_ho_10 with 163s (1) cores
% 1.09/0.65 # new_ho_10 with pid 5333 completed with status 0
% 1.09/0.65 # Result found by new_ho_10
% 1.09/0.65 # Preprocessing class: HSLSSMSSSSMNHSA.
% 1.09/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.65 # Starting sh1 with 1500s (5) cores
% 1.09/0.65 # Starting new_ho_8 with 300s (1) cores
% 1.09/0.65 # Starting new_ho_11 with 300s (1) cores
% 1.09/0.65 # No SInE strategy applied
% 1.09/0.65 # Search class: HGHSM-FSLM32-MHSFFSBN
% 1.09/0.65 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.09/0.65 # Starting new_ho_10 with 163s (1) cores
% 1.09/0.65 # Preprocessing time : 0.009 s
% 1.09/0.65 # Presaturation interreduction done
% 1.09/0.65
% 1.09/0.65 # Proof found!
% 1.09/0.65 # SZS status Theorem
% 1.09/0.65 # SZS output start CNFRefutation
% See solution above
% 1.09/0.65 # Parsed axioms : 408
% 1.09/0.65 # Removed by relevancy pruning/SinE : 0
% 1.09/0.65 # Initial clauses : 707
% 1.09/0.65 # Removed in clause preprocessing : 94
% 1.09/0.65 # Initial clauses in saturation : 613
% 1.09/0.65 # Processed clauses : 973
% 1.09/0.65 # ...of these trivial : 24
% 1.09/0.65 # ...subsumed : 256
% 1.09/0.65 # ...remaining for further processing : 693
% 1.09/0.65 # Other redundant clauses eliminated : 82
% 1.09/0.65 # Clauses deleted for lack of memory : 0
% 1.09/0.65 # Backward-subsumed : 5
% 1.09/0.65 # Backward-rewritten : 5
% 1.09/0.65 # Generated clauses : 932
% 1.09/0.65 # ...of the previous two non-redundant : 757
% 1.09/0.65 # ...aggressively subsumed : 0
% 1.09/0.65 # Contextual simplify-reflections : 1
% 1.09/0.65 # Paramodulations : 843
% 1.09/0.65 # Factorizations : 2
% 1.09/0.65 # NegExts : 0
% 1.09/0.65 # Equation resolutions : 84
% 1.09/0.65 # Disequality decompositions : 0
% 1.09/0.65 # Total rewrite steps : 155
% 1.09/0.65 # ...of those cached : 112
% 1.09/0.65 # Propositional unsat checks : 0
% 1.09/0.65 # Propositional check models : 0
% 1.09/0.65 # Propositional check unsatisfiable : 0
% 1.09/0.65 # Propositional clauses : 0
% 1.09/0.65 # Propositional clauses after purity: 0
% 1.09/0.65 # Propositional unsat core size : 0
% 1.09/0.65 # Propositional preprocessing time : 0.000
% 1.09/0.65 # Propositional encoding time : 0.000
% 1.09/0.65 # Propositional solver time : 0.000
% 1.09/0.65 # Success case prop preproc time : 0.000
% 1.09/0.65 # Success case prop encoding time : 0.000
% 1.09/0.65 # Success case prop solver time : 0.000
% 1.09/0.65 # Current number of processed clauses : 260
% 1.09/0.65 # Positive orientable unit clauses : 43
% 1.09/0.65 # Positive unorientable unit clauses: 0
% 1.09/0.65 # Negative unit clauses : 2
% 1.09/0.65 # Non-unit-clauses : 215
% 1.09/0.65 # Current number of unprocessed clauses: 743
% 1.09/0.65 # ...number of literals in the above : 2264
% 1.09/0.65 # Current number of archived formulas : 0
% 1.09/0.65 # Current number of archived clauses : 357
% 1.09/0.65 # Clause-clause subsumption calls (NU) : 30276
% 1.09/0.65 # Rec. Clause-clause subsumption calls : 21972
% 1.09/0.65 # Non-unit clause-clause subsumptions : 276
% 1.09/0.65 # Unit Clause-clause subsumption calls : 242
% 1.09/0.65 # Rewrite failures with RHS unbound : 0
% 1.09/0.65 # BW rewrite match attempts : 21
% 1.09/0.65 # BW rewrite match successes : 5
% 1.09/0.65 # Condensation attempts : 973
% 1.09/0.65 # Condensation successes : 14
% 1.09/0.65 # Termbank termtop insertions : 67249
% 1.09/0.65 # Search garbage collected termcells : 14629
% 1.09/0.65
% 1.09/0.65 # -------------------------------------------------
% 1.09/0.65 # User time : 0.114 s
% 1.09/0.65 # System time : 0.017 s
% 1.09/0.65 # Total time : 0.131 s
% 1.09/0.65 # Maximum resident set size: 5108 pages
% 1.09/0.65
% 1.09/0.65 # -------------------------------------------------
% 1.09/0.65 # User time : 0.131 s
% 1.09/0.65 # System time : 0.021 s
% 1.09/0.65 # Total time : 0.152 s
% 1.09/0.65 # Maximum resident set size: 2644 pages
% 1.09/0.65 % E---3.1 exiting
% 1.09/0.65 % E exiting
%------------------------------------------------------------------------------