TSTP Solution File: GRA002+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.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 : Thu Aug 31 00:04:27 EDT 2023
% Result : Theorem 9.12s 2.10s
% Output : Proof 11.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n025.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 : Sun Aug 27 03:56:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.63 ________ _____
% 0.19/0.63 ___ __ \_________(_)________________________________
% 0.19/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.63
% 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.63 (2023-06-19)
% 0.19/0.63
% 0.19/0.63 (c) Philipp Rümmer, 2009-2023
% 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.63 Amanda Stjerna.
% 0.19/0.63 Free software under BSD-3-Clause.
% 0.19/0.63
% 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.63
% 0.19/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.64 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.22/1.24 Prover 4: Preprocessing ...
% 3.22/1.24 Prover 1: Preprocessing ...
% 3.22/1.28 Prover 3: Preprocessing ...
% 3.22/1.28 Prover 2: Preprocessing ...
% 3.22/1.28 Prover 5: Preprocessing ...
% 3.22/1.28 Prover 6: Preprocessing ...
% 3.89/1.29 Prover 0: Preprocessing ...
% 7.79/1.82 Prover 3: Constructing countermodel ...
% 7.79/1.84 Prover 6: Proving ...
% 7.79/1.86 Prover 1: Constructing countermodel ...
% 7.79/1.86 Prover 5: Proving ...
% 7.79/1.89 Prover 2: Proving ...
% 9.12/2.01 Prover 0: Proving ...
% 9.12/2.02 Prover 4: Constructing countermodel ...
% 9.12/2.10 Prover 6: proved (1449ms)
% 9.12/2.10
% 9.12/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.12/2.10
% 9.39/2.10 Prover 3: stopped
% 9.39/2.11 Prover 2: stopped
% 9.39/2.11 Prover 5: stopped
% 9.39/2.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.39/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.39/2.11 Prover 0: stopped
% 9.39/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.39/2.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.39/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.94/2.17 Prover 1: Found proof (size 41)
% 9.94/2.17 Prover 1: proved (1525ms)
% 9.94/2.17 Prover 4: stopped
% 9.94/2.18 Prover 11: Preprocessing ...
% 9.94/2.18 Prover 7: Preprocessing ...
% 9.94/2.19 Prover 10: Preprocessing ...
% 9.94/2.19 Prover 8: Preprocessing ...
% 9.94/2.21 Prover 13: Preprocessing ...
% 10.71/2.22 Prover 7: stopped
% 10.71/2.22 Prover 10: stopped
% 10.71/2.24 Prover 11: stopped
% 10.71/2.25 Prover 13: stopped
% 11.18/2.31 Prover 8: Warning: ignoring some quantifiers
% 11.18/2.32 Prover 8: Constructing countermodel ...
% 11.18/2.32 Prover 8: stopped
% 11.18/2.32
% 11.18/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.18/2.32
% 11.18/2.33 % SZS output start Proof for theBenchmark
% 11.18/2.33 Assumptions after simplification:
% 11.18/2.33 ---------------------------------
% 11.18/2.33
% 11.18/2.33 (graph_has_them_all)
% 11.18/2.36 $i(graph) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 11.18/2.36 int] : (v4 = 0 | ~ (number_of_in(v0, v1) = v2) | ~ (number_of_in(v0,
% 11.18/2.36 graph) = v3) | ~ (less_or_equal(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0))
% 11.18/2.36
% 11.18/2.36 (length_defn)
% 11.18/2.36 $i(edges) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) =
% 11.18/2.36 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 11.18/2.36 (number_of_in(edges, v2) = v3 & length_of(v2) = v3 & $i(v3)))
% 11.18/2.36
% 11.18/2.36 (maximal_path_length)
% 11.18/2.36 $i(graph) & $i(triangles) & $i(n1) & ? [v0: $i] : (number_of_in(triangles,
% 11.18/2.36 graph) = v0 & $i(v0) & complete & ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 11.18/2.36 : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & minus(v4, n1) =
% 11.18/2.36 v5 & shortest_path(v2, v3, v1) = 0 & length_of(v1) = v4 &
% 11.18/2.36 less_or_equal(v5, v0) = v6 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)))
% 11.18/2.36
% 11.18/2.36 (path_length_sequential_pairs)
% 11.18/2.37 $i(n1) & $i(sequential_pairs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 11.18/2.37 (path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 11.18/2.37 ? [v4: $i] : (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 &
% 11.18/2.37 length_of(v2) = v4 & $i(v4) & $i(v3)))
% 11.18/2.37
% 11.18/2.37 (shortest_path_defn)
% 11.18/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = v0 |
% 11.18/2.37 ~ (shortest_path(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 11.18/2.37 [v4: any] : ? [v5: $i] : (length_of(v2) = v5 & path(v0, v1, v2) = v4 &
% 11.18/2.37 $i(v5) & ( ~ (v4 = 0) | ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8
% 11.18/2.37 = 0) & length_of(v6) = v7 & less_or_equal(v5, v7) = v8 & path(v0,
% 11.18/2.37 v1, v6) = 0 & $i(v7) & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : !
% 11.18/2.37 [v2: $i] : ( ~ (shortest_path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 11.18/2.37 $i(v0) | ( ~ (v1 = v0) & ? [v3: $i] : (length_of(v2) = v3 & path(v0, v1,
% 11.18/2.37 v2) = 0 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0
% 11.18/2.37 | ~ (length_of(v4) = v5) | ~ (less_or_equal(v3, v5) = v6) | ~
% 11.18/2.37 $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & path(v0, v1, v4) = v7)))))
% 11.18/2.37
% 11.18/2.37 (triangles_and_sequential_pairs)
% 11.18/2.37 $i(triangles) & $i(sequential_pairs) & ( ~ complete | ! [v0: $i] : ! [v1:
% 11.18/2.37 $i] : ! [v2: $i] : ( ~ (shortest_path(v1, v2, v0) = 0) | ~ $i(v2) | ~
% 11.18/2.37 $i(v1) | ~ $i(v0) | ? [v3: $i] : (number_of_in(triangles, v0) = v3 &
% 11.18/2.37 number_of_in(sequential_pairs, v0) = v3 & $i(v3))))
% 11.18/2.37
% 11.18/2.37 (function-axioms)
% 11.61/2.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.61/2.38 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~
% 11.61/2.38 (triangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.61/2.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 11.61/2.38 (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & !
% 11.61/2.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.61/2.38 $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~
% 11.61/2.38 (precedes(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.61/2.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 11.61/2.38 (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 11.61/2.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~
% 11.61/2.38 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.61/2.38 $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) =
% 11.61/2.38 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.61/2.38 $i] : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~
% 11.61/2.38 (less_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.61/2.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.61/2.38 (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0:
% 11.61/2.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.61/2.38 : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0:
% 11.61/2.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.61/2.38 : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0:
% 11.61/2.38 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (path_cons(v3,
% 11.61/2.38 v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 11.61/2.38 ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) &
% 11.61/2.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 11.61/2.38 v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0: $i] : ! [v1:
% 11.61/2.38 $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) =
% 11.61/2.38 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.61/2.38 $i] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0: $i] : !
% 11.61/2.38 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) =
% 11.61/2.38 v0))
% 11.61/2.38
% 11.61/2.38 Further assumptions not needed in the proof:
% 11.61/2.38 --------------------------------------------
% 11.61/2.38 complete_properties, edge_ends_are_vertices, in_path_properties, no_loops,
% 11.61/2.38 on_path_properties, path_defn, path_properties, precedes_defn,
% 11.61/2.38 precedes_properties, sequential_defn, sequential_pairs_and_triangles,
% 11.61/2.38 shortest_path_properties, triangle_defn
% 11.61/2.38
% 11.61/2.38 Those formulas are unsatisfiable:
% 11.61/2.38 ---------------------------------
% 11.61/2.38
% 11.61/2.38 Begin of proof
% 11.61/2.38 |
% 11.61/2.38 | ALPHA: (shortest_path_defn) implies:
% 11.61/2.39 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v0, v1,
% 11.61/2.39 | v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ?
% 11.61/2.39 | [v3: $i] : (length_of(v2) = v3 & path(v0, v1, v2) = 0 & $i(v3) & !
% 11.61/2.39 | [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~
% 11.61/2.39 | (length_of(v4) = v5) | ~ (less_or_equal(v3, v5) = v6) | ~
% 11.61/2.39 | $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & path(v0, v1, v4) =
% 11.61/2.39 | v7)))))
% 11.61/2.39 |
% 11.61/2.39 | ALPHA: (length_defn) implies:
% 11.61/2.39 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) |
% 11.61/2.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (number_of_in(edges,
% 11.61/2.39 | v2) = v3 & length_of(v2) = v3 & $i(v3)))
% 11.61/2.39 |
% 11.61/2.39 | ALPHA: (path_length_sequential_pairs) implies:
% 11.61/2.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) |
% 11.61/2.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 11.61/2.39 | (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 &
% 11.61/2.39 | length_of(v2) = v4 & $i(v4) & $i(v3)))
% 11.61/2.39 |
% 11.61/2.39 | ALPHA: (graph_has_them_all) implies:
% 11.61/2.39 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 11.61/2.39 | (v4 = 0 | ~ (number_of_in(v0, v1) = v2) | ~ (number_of_in(v0, graph)
% 11.61/2.39 | = v3) | ~ (less_or_equal(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0))
% 11.61/2.39 |
% 11.61/2.39 | ALPHA: (triangles_and_sequential_pairs) implies:
% 11.61/2.39 | (5) ~ complete | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 11.61/2.39 | (shortest_path(v1, v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 11.61/2.39 | ? [v3: $i] : (number_of_in(triangles, v0) = v3 &
% 11.61/2.39 | number_of_in(sequential_pairs, v0) = v3 & $i(v3)))
% 11.61/2.39 |
% 11.61/2.39 | ALPHA: (maximal_path_length) implies:
% 11.61/2.39 | (6) $i(triangles)
% 11.61/2.39 | (7) ? [v0: $i] : (number_of_in(triangles, graph) = v0 & $i(v0) & complete
% 11.61/2.39 | & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i]
% 11.61/2.39 | : ? [v6: int] : ( ~ (v6 = 0) & minus(v4, n1) = v5 &
% 11.61/2.39 | shortest_path(v2, v3, v1) = 0 & length_of(v1) = v4 &
% 11.61/2.39 | less_or_equal(v5, v0) = v6 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 11.61/2.39 | $i(v1)))
% 11.61/2.39 |
% 11.61/2.39 | ALPHA: (function-axioms) implies:
% 11.61/2.39 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (length_of(v2)
% 11.61/2.39 | = v1) | ~ (length_of(v2) = v0))
% 11.61/2.39 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.61/2.39 | (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = v0))
% 11.61/2.39 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.61/2.39 | (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0))
% 11.61/2.39 |
% 11.61/2.40 | DELTA: instantiating (7) with fresh symbol all_20_0 gives:
% 11.61/2.40 | (11) number_of_in(triangles, graph) = all_20_0 & $i(all_20_0) & complete &
% 11.61/2.40 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 11.61/2.40 | ? [v5: int] : ( ~ (v5 = 0) & minus(v3, n1) = v4 & shortest_path(v1,
% 11.61/2.40 | v2, v0) = 0 & length_of(v0) = v3 & less_or_equal(v4, all_20_0) =
% 11.61/2.40 | v5 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.61/2.40 |
% 11.61/2.40 | ALPHA: (11) implies:
% 11.61/2.40 | (12) complete
% 11.61/2.40 | (13) number_of_in(triangles, graph) = all_20_0
% 11.61/2.40 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 11.61/2.40 | ? [v5: int] : ( ~ (v5 = 0) & minus(v3, n1) = v4 & shortest_path(v1,
% 11.61/2.40 | v2, v0) = 0 & length_of(v0) = v3 & less_or_equal(v4, all_20_0) =
% 11.61/2.40 | v5 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.61/2.40 |
% 11.61/2.40 | DELTA: instantiating (14) with fresh symbols all_22_0, all_22_1, all_22_2,
% 11.61/2.40 | all_22_3, all_22_4, all_22_5 gives:
% 11.71/2.40 | (15) ~ (all_22_0 = 0) & minus(all_22_2, n1) = all_22_1 &
% 11.71/2.40 | shortest_path(all_22_4, all_22_3, all_22_5) = 0 & length_of(all_22_5)
% 11.71/2.40 | = all_22_2 & less_or_equal(all_22_1, all_20_0) = all_22_0 &
% 11.71/2.40 | $i(all_22_1) & $i(all_22_2) & $i(all_22_3) & $i(all_22_4) &
% 11.71/2.40 | $i(all_22_5)
% 11.71/2.40 |
% 11.71/2.40 | ALPHA: (15) implies:
% 11.71/2.40 | (16) ~ (all_22_0 = 0)
% 11.71/2.40 | (17) $i(all_22_5)
% 11.71/2.40 | (18) $i(all_22_4)
% 11.71/2.40 | (19) $i(all_22_3)
% 11.71/2.40 | (20) less_or_equal(all_22_1, all_20_0) = all_22_0
% 11.71/2.40 | (21) length_of(all_22_5) = all_22_2
% 11.71/2.40 | (22) shortest_path(all_22_4, all_22_3, all_22_5) = 0
% 11.71/2.40 | (23) minus(all_22_2, n1) = all_22_1
% 11.71/2.40 |
% 11.71/2.40 | BETA: splitting (5) gives:
% 11.71/2.40 |
% 11.71/2.40 | Case 1:
% 11.71/2.40 | |
% 11.71/2.40 | | (24) ~ complete
% 11.71/2.40 | |
% 11.71/2.40 | | PRED_UNIFY: (12), (24) imply:
% 11.71/2.40 | | (25) $false
% 11.71/2.40 | |
% 11.71/2.40 | | CLOSE: (25) is inconsistent.
% 11.71/2.40 | |
% 11.71/2.40 | Case 2:
% 11.71/2.40 | |
% 11.71/2.40 | | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (shortest_path(v1, v2,
% 11.71/2.40 | | v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 11.71/2.40 | | (number_of_in(triangles, v0) = v3 & number_of_in(sequential_pairs,
% 11.71/2.40 | | v0) = v3 & $i(v3)))
% 11.71/2.40 | |
% 11.71/2.41 | | GROUND_INST: instantiating (26) with all_22_5, all_22_4, all_22_3,
% 11.71/2.41 | | simplifying with (17), (18), (19), (22) gives:
% 11.71/2.41 | | (27) ? [v0: $i] : (number_of_in(triangles, all_22_5) = v0 &
% 11.71/2.41 | | number_of_in(sequential_pairs, all_22_5) = v0 & $i(v0))
% 11.71/2.41 | |
% 11.71/2.41 | | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_5,
% 11.71/2.41 | | simplifying with (17), (18), (19), (22) gives:
% 11.71/2.41 | | (28) ~ (all_22_3 = all_22_4) & ? [v0: $i] : (length_of(all_22_5) = v0 &
% 11.71/2.41 | | path(all_22_4, all_22_3, all_22_5) = 0 & $i(v0) & ! [v1: $i] : !
% 11.71/2.41 | | [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (length_of(v1) = v2) | ~
% 11.71/2.41 | | (less_or_equal(v0, v2) = v3) | ~ $i(v1) | ? [v4: int] : ( ~
% 11.71/2.41 | | (v4 = 0) & path(all_22_4, all_22_3, v1) = v4)))
% 11.71/2.41 | |
% 11.71/2.41 | | ALPHA: (28) implies:
% 11.71/2.41 | | (29) ? [v0: $i] : (length_of(all_22_5) = v0 & path(all_22_4, all_22_3,
% 11.71/2.41 | | all_22_5) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.71/2.41 | | int] : (v3 = 0 | ~ (length_of(v1) = v2) | ~ (less_or_equal(v0,
% 11.71/2.41 | | v2) = v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) &
% 11.71/2.41 | | path(all_22_4, all_22_3, v1) = v4)))
% 11.71/2.41 | |
% 11.71/2.41 | | DELTA: instantiating (27) with fresh symbol all_39_0 gives:
% 11.71/2.41 | | (30) number_of_in(triangles, all_22_5) = all_39_0 &
% 11.71/2.41 | | number_of_in(sequential_pairs, all_22_5) = all_39_0 & $i(all_39_0)
% 11.71/2.41 | |
% 11.71/2.41 | | ALPHA: (30) implies:
% 11.71/2.41 | | (31) number_of_in(sequential_pairs, all_22_5) = all_39_0
% 11.71/2.41 | | (32) number_of_in(triangles, all_22_5) = all_39_0
% 11.71/2.41 | |
% 11.71/2.41 | | DELTA: instantiating (29) with fresh symbol all_41_0 gives:
% 11.71/2.41 | | (33) length_of(all_22_5) = all_41_0 & path(all_22_4, all_22_3, all_22_5)
% 11.71/2.41 | | = 0 & $i(all_41_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2
% 11.71/2.41 | | = 0 | ~ (length_of(v0) = v1) | ~ (less_or_equal(all_41_0, v1) =
% 11.71/2.41 | | v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & path(all_22_4,
% 11.71/2.41 | | all_22_3, v0) = v3))
% 11.71/2.41 | |
% 11.71/2.41 | | ALPHA: (33) implies:
% 11.71/2.41 | | (34) path(all_22_4, all_22_3, all_22_5) = 0
% 11.71/2.41 | | (35) length_of(all_22_5) = all_41_0
% 11.71/2.41 | |
% 11.71/2.41 | | GROUND_INST: instantiating (8) with all_22_2, all_41_0, all_22_5,
% 11.71/2.41 | | simplifying with (21), (35) gives:
% 11.71/2.41 | | (36) all_41_0 = all_22_2
% 11.71/2.41 | |
% 11.71/2.41 | | GROUND_INST: instantiating (3) with all_22_4, all_22_3, all_22_5,
% 11.71/2.41 | | simplifying with (17), (18), (19), (34) gives:
% 11.71/2.41 | | (37) ? [v0: $i] : ? [v1: $i] : (minus(v1, n1) = v0 &
% 11.71/2.41 | | number_of_in(sequential_pairs, all_22_5) = v0 &
% 11.71/2.41 | | length_of(all_22_5) = v1 & $i(v1) & $i(v0))
% 11.71/2.41 | |
% 11.71/2.41 | | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_5,
% 11.71/2.41 | | simplifying with (17), (18), (19), (34) gives:
% 11.71/2.41 | | (38) ? [v0: $i] : (number_of_in(edges, all_22_5) = v0 &
% 11.71/2.41 | | length_of(all_22_5) = v0 & $i(v0))
% 11.71/2.41 | |
% 11.71/2.41 | | DELTA: instantiating (38) with fresh symbol all_56_0 gives:
% 11.71/2.41 | | (39) number_of_in(edges, all_22_5) = all_56_0 & length_of(all_22_5) =
% 11.71/2.41 | | all_56_0 & $i(all_56_0)
% 11.79/2.41 | |
% 11.79/2.41 | | ALPHA: (39) implies:
% 11.79/2.41 | | (40) length_of(all_22_5) = all_56_0
% 11.79/2.41 | |
% 11.79/2.41 | | DELTA: instantiating (37) with fresh symbols all_58_0, all_58_1 gives:
% 11.79/2.42 | | (41) minus(all_58_0, n1) = all_58_1 & number_of_in(sequential_pairs,
% 11.79/2.42 | | all_22_5) = all_58_1 & length_of(all_22_5) = all_58_0 &
% 11.79/2.42 | | $i(all_58_0) & $i(all_58_1)
% 11.79/2.42 | |
% 11.79/2.42 | | ALPHA: (41) implies:
% 11.79/2.42 | | (42) length_of(all_22_5) = all_58_0
% 11.79/2.42 | | (43) number_of_in(sequential_pairs, all_22_5) = all_58_1
% 11.79/2.42 | | (44) minus(all_58_0, n1) = all_58_1
% 11.79/2.42 | |
% 11.79/2.42 | | GROUND_INST: instantiating (8) with all_22_2, all_58_0, all_22_5,
% 11.79/2.42 | | simplifying with (21), (42) gives:
% 11.79/2.42 | | (45) all_58_0 = all_22_2
% 11.79/2.42 | |
% 11.79/2.42 | | GROUND_INST: instantiating (8) with all_56_0, all_58_0, all_22_5,
% 11.79/2.42 | | simplifying with (40), (42) gives:
% 11.79/2.42 | | (46) all_58_0 = all_56_0
% 11.79/2.42 | |
% 11.79/2.42 | | GROUND_INST: instantiating (9) with all_39_0, all_58_1, all_22_5,
% 11.79/2.42 | | sequential_pairs, simplifying with (31), (43) gives:
% 11.79/2.42 | | (47) all_58_1 = all_39_0
% 11.79/2.42 | |
% 11.79/2.42 | | COMBINE_EQS: (45), (46) imply:
% 11.79/2.42 | | (48) all_56_0 = all_22_2
% 11.79/2.42 | |
% 11.79/2.42 | | REDUCE: (44), (45), (47) imply:
% 11.79/2.42 | | (49) minus(all_22_2, n1) = all_39_0
% 11.79/2.42 | |
% 11.79/2.42 | | GROUND_INST: instantiating (10) with all_22_1, all_39_0, n1, all_22_2,
% 11.79/2.42 | | simplifying with (23), (49) gives:
% 11.79/2.42 | | (50) all_39_0 = all_22_1
% 11.79/2.42 | |
% 11.79/2.42 | | REDUCE: (32), (50) imply:
% 11.79/2.42 | | (51) number_of_in(triangles, all_22_5) = all_22_1
% 11.79/2.42 | |
% 11.79/2.42 | | GROUND_INST: instantiating (4) with triangles, all_22_5, all_22_1, all_20_0,
% 11.79/2.42 | | all_22_0, simplifying with (6), (13), (17), (20), (51) gives:
% 11.79/2.42 | | (52) all_22_0 = 0
% 11.79/2.42 | |
% 11.79/2.42 | | REDUCE: (16), (52) imply:
% 11.79/2.42 | | (53) $false
% 11.79/2.42 | |
% 11.79/2.42 | | CLOSE: (53) is inconsistent.
% 11.79/2.42 | |
% 11.79/2.42 | End of split
% 11.79/2.42 |
% 11.79/2.42 End of proof
% 11.79/2.42 % SZS output end Proof for theBenchmark
% 11.79/2.42
% 11.79/2.42 1792ms
%------------------------------------------------------------------------------