TSTP Solution File: GRA010+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GRA010+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 00:04:29 EDT 2023
% Result : Theorem 12.54s 2.50s
% Output : Proof 16.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRA010+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.29 % Computer : n031.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun Aug 27 03:38:23 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.13/0.56 ________ _____
% 0.13/0.56 ___ __ \_________(_)________________________________
% 0.13/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.13/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.13/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.13/0.56
% 0.13/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.13/0.56 (2023-06-19)
% 0.13/0.56
% 0.13/0.56 (c) Philipp Rümmer, 2009-2023
% 0.13/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.13/0.56 Amanda Stjerna.
% 0.13/0.56 Free software under BSD-3-Clause.
% 0.13/0.56
% 0.13/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.13/0.56
% 0.13/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.13/0.57 Running up to 7 provers in parallel.
% 0.13/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.13/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.13/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.13/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.13/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.13/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.13/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.13/1.13 Prover 1: Preprocessing ...
% 3.13/1.13 Prover 4: Preprocessing ...
% 3.13/1.18 Prover 6: Preprocessing ...
% 3.13/1.18 Prover 3: Preprocessing ...
% 3.13/1.18 Prover 2: Preprocessing ...
% 3.13/1.18 Prover 0: Preprocessing ...
% 3.53/1.18 Prover 5: Preprocessing ...
% 8.48/2.03 Prover 6: Proving ...
% 8.48/2.05 Prover 3: Constructing countermodel ...
% 9.28/2.06 Prover 1: Constructing countermodel ...
% 9.28/2.06 Prover 2: Proving ...
% 9.28/2.08 Prover 5: Proving ...
% 11.18/2.29 Prover 0: Proving ...
% 11.73/2.36 Prover 4: Constructing countermodel ...
% 12.54/2.50 Prover 3: proved (1915ms)
% 12.54/2.50
% 12.54/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.54/2.50
% 12.54/2.50 Prover 0: stopped
% 12.54/2.50 Prover 6: stopped
% 12.95/2.51 Prover 2: stopped
% 12.95/2.51 Prover 5: stopped
% 12.95/2.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.95/2.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.95/2.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.95/2.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.95/2.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.95/2.64 Prover 11: Preprocessing ...
% 12.95/2.64 Prover 7: Preprocessing ...
% 12.95/2.65 Prover 13: Preprocessing ...
% 12.95/2.66 Prover 10: Preprocessing ...
% 12.95/2.67 Prover 8: Preprocessing ...
% 14.70/2.78 Prover 1: Found proof (size 35)
% 14.70/2.78 Prover 1: proved (2199ms)
% 14.70/2.78 Prover 4: stopped
% 14.70/2.78 Prover 11: stopped
% 14.70/2.80 Prover 10: Warning: ignoring some quantifiers
% 15.03/2.82 Prover 10: Constructing countermodel ...
% 15.03/2.83 Prover 10: stopped
% 15.23/2.84 Prover 7: Warning: ignoring some quantifiers
% 15.23/2.85 Prover 13: Warning: ignoring some quantifiers
% 15.23/2.85 Prover 7: Constructing countermodel ...
% 15.23/2.87 Prover 7: stopped
% 15.23/2.87 Prover 13: Constructing countermodel ...
% 15.23/2.88 Prover 8: Warning: ignoring some quantifiers
% 15.23/2.88 Prover 8: Constructing countermodel ...
% 15.23/2.88 Prover 13: stopped
% 15.23/2.89 Prover 8: stopped
% 15.23/2.89
% 15.23/2.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.23/2.89
% 15.23/2.90 % SZS output start Proof for theBenchmark
% 15.23/2.90 Assumptions after simplification:
% 15.23/2.90 ---------------------------------
% 15.23/2.90
% 15.23/2.90 (complete_means_sequential_pairs_and_triangles)
% 15.73/2.95 $i(triangles) & $i(sequential_pairs) & complete & ? [v0: $i] : ? [v1: $i] :
% 15.73/2.95 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) &
% 15.73/2.95 number_of_in(triangles, v0) = v4 & number_of_in(sequential_pairs, v0) = v3 &
% 15.73/2.95 path(v1, v2, v0) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5:
% 15.73/2.95 $i] : ! [v6: $i] : ( ~ (on_path(v6, v0) = 0) | ~ (on_path(v5, v0) = 0) |
% 15.73/2.95 ~ $i(v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & sequential(v5, v6) =
% 15.73/2.95 v7) | ? [v7: $i] : (triangle(v5, v6, v7) = 0 & $i(v7))))
% 15.73/2.95
% 15.73/2.95 (path_length_sequential_pairs)
% 15.73/2.95 $i(n1) & $i(sequential_pairs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 15.73/2.95 (path(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 15.73/2.95 ? [v4: $i] : (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 &
% 15.73/2.95 length_of(v2) = v4 & $i(v4) & $i(v3)))
% 15.73/2.95
% 15.73/2.95 (sequential_pairs_and_triangles)
% 15.73/2.95 $i(triangles) & $i(sequential_pairs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 15.73/2.95 : ( ~ (path(v1, v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 15.73/2.95 : ? [v4: $i] : (sequential(v3, v4) = 0 & on_path(v4, v0) = 0 & on_path(v3,
% 15.73/2.95 v0) = 0 & $i(v4) & $i(v3) & ! [v5: $i] : ( ~ (triangle(v3, v4, v5) = 0)
% 15.73/2.95 | ~ $i(v5))) | ? [v3: $i] : (number_of_in(triangles, v0) = v3 &
% 15.73/2.95 number_of_in(sequential_pairs, v0) = v3 & $i(v3)))
% 15.73/2.95
% 15.73/2.95 (function-axioms)
% 15.73/2.96 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 15.73/2.96 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (triangle(v4, v3, v2) = v1) | ~
% 15.73/2.96 (triangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.73/2.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 15.73/2.96 (shortest_path(v4, v3, v2) = v1) | ~ (shortest_path(v4, v3, v2) = v0)) & !
% 15.73/2.96 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 15.73/2.96 $i] : ! [v4: $i] : (v1 = v0 | ~ (precedes(v4, v3, v2) = v1) | ~
% 15.73/2.96 (precedes(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.73/2.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 15.73/2.96 (path(v4, v3, v2) = v1) | ~ (path(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 15.73/2.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~
% 15.73/2.96 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 15.73/2.96 $i] : (v1 = v0 | ~ (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) =
% 15.73/2.96 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.73/2.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~
% 15.73/2.96 (less_or_equal(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.73/2.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.73/2.97 (sequential(v3, v2) = v1) | ~ (sequential(v3, v2) = v0)) & ! [v0:
% 15.73/2.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.73/2.97 : (v1 = v0 | ~ (on_path(v3, v2) = v1) | ~ (on_path(v3, v2) = v0)) & ! [v0:
% 15.73/2.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.73/2.97 : (v1 = v0 | ~ (in_path(v3, v2) = v1) | ~ (in_path(v3, v2) = v0)) & ! [v0:
% 15.73/2.97 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (path_cons(v3,
% 15.73/2.97 v2) = v1) | ~ (path_cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 15.73/2.97 ! [v2: $i] : (v1 = v0 | ~ (length_of(v2) = v1) | ~ (length_of(v2) = v0)) &
% 15.73/2.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 15.73/2.97 v0 | ~ (vertex(v2) = v1) | ~ (vertex(v2) = v0)) & ! [v0: $i] : ! [v1:
% 15.73/2.97 $i] : ! [v2: $i] : (v1 = v0 | ~ (tail_of(v2) = v1) | ~ (tail_of(v2) =
% 15.73/2.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.73/2.97 $i] : (v1 = v0 | ~ (edge(v2) = v1) | ~ (edge(v2) = v0)) & ! [v0: $i] : !
% 15.73/2.97 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (head_of(v2) = v1) | ~ (head_of(v2) =
% 15.73/2.97 v0))
% 15.73/2.97
% 15.73/2.97 Further assumptions not needed in the proof:
% 15.73/2.97 --------------------------------------------
% 15.73/2.97 complete_properties, edge_ends_are_vertices, graph_has_them_all,
% 15.73/2.97 in_path_properties, length_defn, no_loops, on_path_properties, path_defn,
% 15.73/2.97 path_properties, precedes_defn, precedes_properties, sequential_defn,
% 15.73/2.97 sequential_is_triangle, shortest_path_defn, shortest_path_properties,
% 15.73/2.97 triangle_defn
% 15.73/2.97
% 15.73/2.97 Those formulas are unsatisfiable:
% 15.73/2.97 ---------------------------------
% 15.73/2.97
% 15.73/2.97 Begin of proof
% 15.73/2.97 |
% 15.73/2.97 | ALPHA: (path_length_sequential_pairs) implies:
% 15.73/2.97 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v0, v1, v2) = 0) |
% 15.73/2.97 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 15.73/2.97 | (minus(v4, n1) = v3 & number_of_in(sequential_pairs, v2) = v3 &
% 15.73/2.97 | length_of(v2) = v4 & $i(v4) & $i(v3)))
% 15.73/2.97 |
% 15.73/2.97 | ALPHA: (sequential_pairs_and_triangles) implies:
% 15.73/2.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (path(v1, v2, v0) = 0) |
% 15.73/2.97 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 15.73/2.97 | (sequential(v3, v4) = 0 & on_path(v4, v0) = 0 & on_path(v3, v0) = 0 &
% 15.73/2.97 | $i(v4) & $i(v3) & ! [v5: $i] : ( ~ (triangle(v3, v4, v5) = 0) | ~
% 15.73/2.97 | $i(v5))) | ? [v3: $i] : (number_of_in(triangles, v0) = v3 &
% 15.73/2.97 | number_of_in(sequential_pairs, v0) = v3 & $i(v3)))
% 15.73/2.97 |
% 15.73/2.97 | ALPHA: (complete_means_sequential_pairs_and_triangles) implies:
% 15.73/2.97 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 15.73/2.97 | ~ (v4 = v3) & number_of_in(triangles, v0) = v4 &
% 15.73/2.98 | number_of_in(sequential_pairs, v0) = v3 & path(v1, v2, v0) = 0 &
% 15.73/2.98 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6:
% 15.73/2.98 | $i] : ( ~ (on_path(v6, v0) = 0) | ~ (on_path(v5, v0) = 0) | ~
% 15.73/2.98 | $i(v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & sequential(v5,
% 15.73/2.98 | v6) = v7) | ? [v7: $i] : (triangle(v5, v6, v7) = 0 & $i(v7))))
% 15.73/2.98 |
% 15.73/2.98 | ALPHA: (function-axioms) implies:
% 15.73/2.98 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 15.73/2.98 | ! [v3: $i] : (v1 = v0 | ~ (sequential(v3, v2) = v1) | ~
% 15.73/2.98 | (sequential(v3, v2) = v0))
% 15.73/2.98 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.73/2.98 | (number_of_in(v3, v2) = v1) | ~ (number_of_in(v3, v2) = v0))
% 15.73/2.98 |
% 15.73/2.98 | DELTA: instantiating (3) with fresh symbols all_20_0, all_20_1, all_20_2,
% 15.73/2.98 | all_20_3, all_20_4 gives:
% 15.73/2.98 | (6) ~ (all_20_0 = all_20_1) & number_of_in(triangles, all_20_4) = all_20_0
% 15.73/2.98 | & number_of_in(sequential_pairs, all_20_4) = all_20_1 & path(all_20_3,
% 15.73/2.98 | all_20_2, all_20_4) = 0 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2)
% 15.73/2.98 | & $i(all_20_3) & $i(all_20_4) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.73/2.98 | (on_path(v1, all_20_4) = 0) | ~ (on_path(v0, all_20_4) = 0) | ~
% 15.73/2.98 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & sequential(v0, v1)
% 15.73/2.98 | = v2) | ? [v2: $i] : (triangle(v0, v1, v2) = 0 & $i(v2)))
% 15.73/2.98 |
% 15.73/2.98 | ALPHA: (6) implies:
% 15.73/2.98 | (7) ~ (all_20_0 = all_20_1)
% 15.73/2.98 | (8) $i(all_20_4)
% 15.73/2.98 | (9) $i(all_20_3)
% 16.02/2.98 | (10) $i(all_20_2)
% 16.02/2.98 | (11) path(all_20_3, all_20_2, all_20_4) = 0
% 16.02/2.98 | (12) number_of_in(sequential_pairs, all_20_4) = all_20_1
% 16.02/2.98 | (13) number_of_in(triangles, all_20_4) = all_20_0
% 16.02/2.98 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (on_path(v1, all_20_4) = 0) | ~
% 16.02/2.98 | (on_path(v0, all_20_4) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] :
% 16.02/2.98 | ( ~ (v2 = 0) & sequential(v0, v1) = v2) | ? [v2: $i] :
% 16.02/2.98 | (triangle(v0, v1, v2) = 0 & $i(v2)))
% 16.02/2.98 |
% 16.02/2.98 | GROUND_INST: instantiating (2) with all_20_4, all_20_3, all_20_2, simplifying
% 16.02/2.98 | with (8), (9), (10), (11) gives:
% 16.02/2.99 | (15) ? [v0: $i] : ? [v1: $i] : (sequential(v0, v1) = 0 & on_path(v1,
% 16.02/2.99 | all_20_4) = 0 & on_path(v0, all_20_4) = 0 & $i(v1) & $i(v0) & !
% 16.02/2.99 | [v2: $i] : ( ~ (triangle(v0, v1, v2) = 0) | ~ $i(v2))) | ? [v0:
% 16.02/2.99 | $i] : (number_of_in(triangles, all_20_4) = v0 &
% 16.02/2.99 | number_of_in(sequential_pairs, all_20_4) = v0 & $i(v0))
% 16.02/2.99 |
% 16.02/2.99 | GROUND_INST: instantiating (1) with all_20_3, all_20_2, all_20_4, simplifying
% 16.02/2.99 | with (8), (9), (10), (11) gives:
% 16.02/2.99 | (16) ? [v0: $i] : ? [v1: $i] : (minus(v1, n1) = v0 &
% 16.02/2.99 | number_of_in(sequential_pairs, all_20_4) = v0 & length_of(all_20_4)
% 16.02/2.99 | = v1 & $i(v1) & $i(v0))
% 16.02/2.99 |
% 16.02/2.99 | DELTA: instantiating (16) with fresh symbols all_42_0, all_42_1 gives:
% 16.02/2.99 | (17) minus(all_42_0, n1) = all_42_1 & number_of_in(sequential_pairs,
% 16.02/2.99 | all_20_4) = all_42_1 & length_of(all_20_4) = all_42_0 & $i(all_42_0)
% 16.02/2.99 | & $i(all_42_1)
% 16.02/2.99 |
% 16.02/2.99 | ALPHA: (17) implies:
% 16.02/2.99 | (18) number_of_in(sequential_pairs, all_20_4) = all_42_1
% 16.02/2.99 |
% 16.02/2.99 | GROUND_INST: instantiating (5) with all_20_1, all_42_1, all_20_4,
% 16.02/2.99 | sequential_pairs, simplifying with (12), (18) gives:
% 16.02/2.99 | (19) all_42_1 = all_20_1
% 16.02/2.99 |
% 16.02/2.99 | BETA: splitting (15) gives:
% 16.02/2.99 |
% 16.02/2.99 | Case 1:
% 16.02/2.99 | |
% 16.02/2.99 | | (20) ? [v0: $i] : ? [v1: $i] : (sequential(v0, v1) = 0 & on_path(v1,
% 16.02/2.99 | | all_20_4) = 0 & on_path(v0, all_20_4) = 0 & $i(v1) & $i(v0) & !
% 16.02/2.99 | | [v2: $i] : ( ~ (triangle(v0, v1, v2) = 0) | ~ $i(v2)))
% 16.02/2.99 | |
% 16.02/2.99 | | DELTA: instantiating (20) with fresh symbols all_53_0, all_53_1 gives:
% 16.02/2.99 | | (21) sequential(all_53_1, all_53_0) = 0 & on_path(all_53_0, all_20_4) = 0
% 16.02/2.99 | | & on_path(all_53_1, all_20_4) = 0 & $i(all_53_0) & $i(all_53_1) & !
% 16.02/2.99 | | [v0: $i] : ( ~ (triangle(all_53_1, all_53_0, v0) = 0) | ~ $i(v0))
% 16.02/2.99 | |
% 16.02/2.99 | | ALPHA: (21) implies:
% 16.02/2.99 | | (22) $i(all_53_1)
% 16.02/2.99 | | (23) $i(all_53_0)
% 16.02/2.99 | | (24) on_path(all_53_1, all_20_4) = 0
% 16.02/2.99 | | (25) on_path(all_53_0, all_20_4) = 0
% 16.02/2.99 | | (26) sequential(all_53_1, all_53_0) = 0
% 16.02/2.99 | | (27) ! [v0: $i] : ( ~ (triangle(all_53_1, all_53_0, v0) = 0) | ~
% 16.02/2.99 | | $i(v0))
% 16.02/2.99 | |
% 16.02/2.99 | | GROUND_INST: instantiating (14) with all_53_1, all_53_0, simplifying with
% 16.02/2.99 | | (22), (23), (24), (25) gives:
% 16.02/2.99 | | (28) ? [v0: int] : ( ~ (v0 = 0) & sequential(all_53_1, all_53_0) = v0) |
% 16.02/2.99 | | ? [v0: $i] : (triangle(all_53_1, all_53_0, v0) = 0 & $i(v0))
% 16.02/3.00 | |
% 16.02/3.00 | | BETA: splitting (28) gives:
% 16.02/3.00 | |
% 16.02/3.00 | | Case 1:
% 16.02/3.00 | | |
% 16.02/3.00 | | | (29) ? [v0: int] : ( ~ (v0 = 0) & sequential(all_53_1, all_53_0) = v0)
% 16.02/3.00 | | |
% 16.02/3.00 | | | DELTA: instantiating (29) with fresh symbol all_70_0 gives:
% 16.02/3.00 | | | (30) ~ (all_70_0 = 0) & sequential(all_53_1, all_53_0) = all_70_0
% 16.02/3.00 | | |
% 16.02/3.00 | | | ALPHA: (30) implies:
% 16.02/3.00 | | | (31) ~ (all_70_0 = 0)
% 16.02/3.00 | | | (32) sequential(all_53_1, all_53_0) = all_70_0
% 16.02/3.00 | | |
% 16.02/3.00 | | | GROUND_INST: instantiating (4) with 0, all_70_0, all_53_0, all_53_1,
% 16.02/3.00 | | | simplifying with (26), (32) gives:
% 16.02/3.00 | | | (33) all_70_0 = 0
% 16.02/3.00 | | |
% 16.02/3.00 | | | REDUCE: (31), (33) imply:
% 16.02/3.00 | | | (34) $false
% 16.02/3.00 | | |
% 16.02/3.00 | | | CLOSE: (34) is inconsistent.
% 16.02/3.00 | | |
% 16.02/3.00 | | Case 2:
% 16.02/3.00 | | |
% 16.02/3.00 | | | (35) ? [v0: $i] : (triangle(all_53_1, all_53_0, v0) = 0 & $i(v0))
% 16.02/3.00 | | |
% 16.02/3.00 | | | DELTA: instantiating (35) with fresh symbol all_70_0 gives:
% 16.02/3.00 | | | (36) triangle(all_53_1, all_53_0, all_70_0) = 0 & $i(all_70_0)
% 16.02/3.00 | | |
% 16.02/3.00 | | | ALPHA: (36) implies:
% 16.02/3.00 | | | (37) $i(all_70_0)
% 16.02/3.00 | | | (38) triangle(all_53_1, all_53_0, all_70_0) = 0
% 16.02/3.00 | | |
% 16.02/3.00 | | | GROUND_INST: instantiating (27) with all_70_0, simplifying with (37), (38)
% 16.02/3.00 | | | gives:
% 16.02/3.00 | | | (39) $false
% 16.02/3.00 | | |
% 16.02/3.00 | | | CLOSE: (39) is inconsistent.
% 16.02/3.00 | | |
% 16.02/3.00 | | End of split
% 16.02/3.00 | |
% 16.02/3.00 | Case 2:
% 16.02/3.00 | |
% 16.02/3.00 | | (40) ? [v0: $i] : (number_of_in(triangles, all_20_4) = v0 &
% 16.02/3.00 | | number_of_in(sequential_pairs, all_20_4) = v0 & $i(v0))
% 16.02/3.00 | |
% 16.02/3.00 | | DELTA: instantiating (40) with fresh symbol all_53_0 gives:
% 16.02/3.00 | | (41) number_of_in(triangles, all_20_4) = all_53_0 &
% 16.02/3.00 | | number_of_in(sequential_pairs, all_20_4) = all_53_0 & $i(all_53_0)
% 16.02/3.00 | |
% 16.02/3.00 | | ALPHA: (41) implies:
% 16.02/3.00 | | (42) number_of_in(sequential_pairs, all_20_4) = all_53_0
% 16.02/3.00 | | (43) number_of_in(triangles, all_20_4) = all_53_0
% 16.02/3.00 | |
% 16.02/3.00 | | GROUND_INST: instantiating (5) with all_20_1, all_53_0, all_20_4,
% 16.02/3.00 | | sequential_pairs, simplifying with (12), (42) gives:
% 16.02/3.00 | | (44) all_53_0 = all_20_1
% 16.02/3.00 | |
% 16.02/3.00 | | GROUND_INST: instantiating (5) with all_20_0, all_53_0, all_20_4, triangles,
% 16.02/3.00 | | simplifying with (13), (43) gives:
% 16.02/3.00 | | (45) all_53_0 = all_20_0
% 16.02/3.00 | |
% 16.02/3.00 | | COMBINE_EQS: (44), (45) imply:
% 16.02/3.00 | | (46) all_20_0 = all_20_1
% 16.02/3.00 | |
% 16.02/3.01 | | REDUCE: (7), (46) imply:
% 16.02/3.01 | | (47) $false
% 16.02/3.01 | |
% 16.02/3.01 | | CLOSE: (47) is inconsistent.
% 16.02/3.01 | |
% 16.02/3.01 | End of split
% 16.02/3.01 |
% 16.02/3.01 End of proof
% 16.02/3.01 % SZS output end Proof for theBenchmark
% 16.02/3.01
% 16.02/3.01 2448ms
%------------------------------------------------------------------------------