TSTP Solution File: SWW653_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW653_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : Fri Sep 1 00:51:01 EDT 2023
% Result : Theorem 10.78s 2.38s
% Output : Proof 12.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW653_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sun Aug 27 19:22:38 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.48/1.27 Prover 1: Preprocessing ...
% 3.48/1.27 Prover 6: Preprocessing ...
% 3.48/1.27 Prover 2: Preprocessing ...
% 3.48/1.27 Prover 3: Preprocessing ...
% 3.48/1.27 Prover 5: Preprocessing ...
% 3.48/1.27 Prover 0: Preprocessing ...
% 3.48/1.28 Prover 4: Preprocessing ...
% 6.65/1.78 Prover 3: Warning: ignoring some quantifiers
% 7.02/1.80 Prover 1: Warning: ignoring some quantifiers
% 7.02/1.81 Prover 3: Constructing countermodel ...
% 7.02/1.83 Prover 6: Proving ...
% 7.02/1.83 Prover 5: Proving ...
% 7.02/1.83 Prover 2: Proving ...
% 7.02/1.83 Prover 4: Warning: ignoring some quantifiers
% 7.02/1.84 Prover 1: Constructing countermodel ...
% 7.02/1.84 Prover 0: Proving ...
% 7.54/1.88 Prover 4: Constructing countermodel ...
% 10.78/2.37 Prover 0: proved (1747ms)
% 10.78/2.38
% 10.78/2.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.78/2.38
% 10.78/2.38 Prover 3: stopped
% 10.78/2.38 Prover 6: stopped
% 10.78/2.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.78/2.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.78/2.38 Prover 2: stopped
% 10.78/2.38 Prover 5: stopped
% 10.78/2.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.78/2.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.78/2.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.50/2.45 Prover 1: Found proof (size 68)
% 11.50/2.45 Prover 1: proved (1819ms)
% 11.50/2.45 Prover 4: stopped
% 11.50/2.47 Prover 7: Preprocessing ...
% 11.50/2.48 Prover 11: Preprocessing ...
% 11.50/2.49 Prover 13: Preprocessing ...
% 12.01/2.49 Prover 7: stopped
% 12.01/2.51 Prover 11: stopped
% 12.01/2.52 Prover 13: stopped
% 12.01/2.52 Prover 8: Preprocessing ...
% 12.01/2.53 Prover 10: Preprocessing ...
% 12.01/2.55 Prover 10: stopped
% 12.46/2.60 Prover 8: Warning: ignoring some quantifiers
% 12.64/2.60 Prover 8: Constructing countermodel ...
% 12.64/2.61 Prover 8: stopped
% 12.64/2.61
% 12.64/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.64/2.61
% 12.64/2.62 % SZS output start Proof for theBenchmark
% 12.64/2.62 Assumptions after simplification:
% 12.64/2.62 ---------------------------------
% 12.64/2.62
% 12.64/2.62 (path_refl)
% 12.64/2.64 ! [v0: graph1] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ (path1(v0, v1,
% 12.64/2.64 v1) = v2) | ~ graph1(v0))
% 12.64/2.64
% 12.64/2.64 (same_def)
% 12.64/2.64 ! [v0: uf_pure1] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v3 = 0 | ~
% 12.64/2.64 (same1(v0, v1, v2) = v3) | ~ uf_pure1(v0) | ? [v4: int] : ? [v5: any] :
% 12.64/2.64 ? [v6: any] : (repr1(v0, v2, v4) = v6 & repr1(v0, v1, v4) = v5 & ( ~ (v6 =
% 12.64/2.64 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0))) & ! [v0: uf_pure1] : ! [v1:
% 12.64/2.64 int] : ! [v2: int] : ( ~ (same1(v0, v1, v2) = 0) | ~ uf_pure1(v0) | ( !
% 12.64/2.64 [v3: int] : ! [v4: int] : (v4 = 0 | ~ (repr1(v0, v1, v3) = v4) | ? [v5:
% 12.64/2.64 int] : ( ~ (v5 = 0) & repr1(v0, v2, v3) = v5)) & ! [v3: int] : ( ~
% 12.64/2.64 (repr1(v0, v1, v3) = 0) | repr1(v0, v2, v3) = 0)))
% 12.64/2.64
% 12.64/2.64 (wP_parameter_build_maze)
% 12.64/2.65 ? [v0: int] : ? [v1: graph1] : ? [v2: int] : ($lesseq(0, v2) & $lesseq(1,
% 12.64/2.65 v0) & $product(v0, v0) = v2 & graph1(v1) & ! [v3: int] : ! [v4: int] :
% 12.64/2.65 (v4 = v3 | ~ (path1(v1, v3, v4) = 0)) & ! [v3: int] : ! [v4: int] : (v4 =
% 12.64/2.65 0 | ~ (path1(v1, v3, v3) = v4)) & ? [v3: uf_pure1] : (num1(v3) = v2 &
% 12.64/2.65 size1(v3) = v2 & uf_pure1(v3) & ! [v4: int] : ! [v5: int] : (v5 = 0 | ~
% 12.64/2.65 ($lesseq(1, $difference(v2, v4))) | ~ ($lesseq(0, v4)) | ~ (repr1(v3,
% 12.64/2.65 v4, v4) = v5)) & ! [v4: int] : ! [v5: int] : ( ~ ($lesseq(1,
% 12.64/2.65 $difference(v2, v5))) | ~ ($lesseq(0, v5)) | ~ ($lesseq(1,
% 12.64/2.65 $difference(v2, v4))) | ~ ($lesseq(0, v4)) | ~ (same1(v3, v4, v5)
% 12.64/2.65 = 0) | (v5 = v4 & repr1(v3, v4, v4) = 0)) & ( ~ ($lesseq(1, v2)) | ?
% 12.64/2.65 [v4: int] : ? [v5: int] : ? [v6: any] : ? [v7: any] : ($lesseq(1,
% 12.64/2.65 $difference(v2, v5)) & $lesseq(0, v5) & $lesseq(1, $difference(v2,
% 12.64/2.65 v4)) & $lesseq(0, v4) & path1(v1, v4, v5) = v7 & same1(v3, v4, v5)
% 12.64/2.65 = v6 & ((v7 = 0 & ~ (v6 = 0)) | (v6 = 0 & ~ (v7 = 0)))))))
% 12.64/2.65
% 12.64/2.65 (function-axioms)
% 12.64/2.65 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: bool1] :
% 12.64/2.65 ! [v5: ty] : (v1 = v0 | ~ (match_bool1(v5, v4, v3, v2) = v1) | ~
% 12.64/2.65 (match_bool1(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.64/2.65 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: graph1] : (v1 =
% 12.64/2.65 v0 | ~ (path1(v4, v3, v2) = v1) | ~ (path1(v4, v3, v2) = v0)) & ! [v0:
% 12.64/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3:
% 12.64/2.65 int] : ! [v4: uf_pure1] : (v1 = v0 | ~ (same1(v4, v3, v2) = v1) | ~
% 12.64/2.65 (same1(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.64/2.65 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: uf_pure1] : (v1 =
% 12.64/2.65 v0 | ~ (repr1(v4, v3, v2) = v1) | ~ (repr1(v4, v3, v2) = v0)) & ! [v0:
% 12.64/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uf_pure1] : !
% 12.64/2.66 [v3: uf_pure1] : (v1 = v0 | ~ (same_reprs1(v3, v2) = v1) | ~
% 12.64/2.66 (same_reprs1(v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] :
% 12.64/2.66 ! [v3: ty] : (v1 = v0 | ~ (contents(v3, v2) = v1) | ~ (contents(v3, v2) =
% 12.64/2.66 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0
% 12.64/2.66 | ~ (mk_ref(v3, v2) = v1) | ~ (mk_ref(v3, v2) = v0)) & ! [v0:
% 12.64/2.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni] : ! [v3: ty]
% 12.64/2.66 : (v1 = v0 | ~ (sort1(v3, v2) = v1) | ~ (sort1(v3, v2) = v0)) & ! [v0: uf1]
% 12.64/2.66 : ! [v1: uf1] : ! [v2: uf_pure1] : (v1 = v0 | ~ (mk_uf1(v2) = v1) | ~
% 12.64/2.66 (mk_uf1(v2) = v0)) & ! [v0: uf_pure1] : ! [v1: uf_pure1] : ! [v2: uf1] :
% 12.64/2.66 (v1 = v0 | ~ (state1(v2) = v1) | ~ (state1(v2) = v0)) & ! [v0: int] : !
% 12.64/2.66 [v1: int] : ! [v2: uf_pure1] : (v1 = v0 | ~ (num1(v2) = v1) | ~ (num1(v2) =
% 12.64/2.66 v0)) & ! [v0: int] : ! [v1: int] : ! [v2: uf_pure1] : (v1 = v0 | ~
% 12.64/2.66 (size1(v2) = v1) | ~ (size1(v2) = v0)) & ! [v0: ty] : ! [v1: ty] : !
% 12.64/2.66 [v2: ty] : (v1 = v0 | ~ (ref(v2) = v1) | ~ (ref(v2) = v0)) & ! [v0: uni] :
% 12.64/2.66 ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (witness1(v2) = v1) | ~
% 12.64/2.66 (witness1(v2) = v0))
% 12.64/2.66
% 12.64/2.66 Further assumptions not needed in the proof:
% 12.64/2.66 --------------------------------------------
% 12.64/2.66 bool_inversion, compatOrderMult, contents_def1, contents_sort1, ineq1,
% 12.64/2.66 match_bool_False, match_bool_True, match_bool_sort1, mk_ref_sort1, oneClass,
% 12.64/2.66 path_inversion, path_sym, path_trans, ref_inversion1, repr_function_1,
% 12.64/2.66 repr_function_2, same_reprs_def, state_def1, true_False, tuple0_inversion,
% 12.64/2.66 uf_inversion1, witness_sort1
% 12.64/2.66
% 12.64/2.66 Those formulas are unsatisfiable:
% 12.64/2.66 ---------------------------------
% 12.64/2.66
% 12.64/2.66 Begin of proof
% 12.64/2.66 |
% 12.64/2.66 | ALPHA: (same_def) implies:
% 12.64/2.66 | (1) ! [v0: uf_pure1] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v3 =
% 12.64/2.66 | 0 | ~ (same1(v0, v1, v2) = v3) | ~ uf_pure1(v0) | ? [v4: int] : ?
% 12.64/2.66 | [v5: any] : ? [v6: any] : (repr1(v0, v2, v4) = v6 & repr1(v0, v1,
% 12.64/2.66 | v4) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0)))
% 12.64/2.66 |
% 12.64/2.66 | ALPHA: (function-axioms) implies:
% 12.64/2.66 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int]
% 12.64/2.66 | : ! [v3: int] : ! [v4: uf_pure1] : (v1 = v0 | ~ (repr1(v4, v3, v2) =
% 12.64/2.66 | v1) | ~ (repr1(v4, v3, v2) = v0))
% 12.64/2.66 |
% 12.64/2.66 | DELTA: instantiating (wP_parameter_build_maze) with fresh symbols all_42_0,
% 12.64/2.66 | all_42_1, all_42_2 gives:
% 12.64/2.66 | (3) $lesseq(0, all_42_0) & $lesseq(1, all_42_2) & $product(all_42_2,
% 12.64/2.66 | all_42_2) = all_42_0 & graph1(all_42_1) & ! [v0: int] : ! [v1: int]
% 12.64/2.66 | : (v1 = v0 | ~ (path1(all_42_1, v0, v1) = 0)) & ! [v0: int] : ! [v1:
% 12.64/2.66 | int] : (v1 = 0 | ~ (path1(all_42_1, v0, v0) = v1)) & ? [v0:
% 12.64/2.66 | uf_pure1] : (num1(v0) = all_42_0 & size1(v0) = all_42_0 &
% 12.64/2.66 | uf_pure1(v0) & ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ ($lesseq(1,
% 12.64/2.66 | $difference(all_42_0, v1))) | ~ ($lesseq(0, v1)) | ~
% 12.64/2.66 | (repr1(v0, v1, v1) = v2)) & ! [v1: int] : ! [v2: int] : ( ~
% 12.64/2.66 | ($lesseq(1, $difference(all_42_0, v2))) | ~ ($lesseq(0, v2)) | ~
% 12.64/2.66 | ($lesseq(1, $difference(all_42_0, v1))) | ~ ($lesseq(0, v1)) | ~
% 12.64/2.66 | (same1(v0, v1, v2) = 0) | (v2 = v1 & repr1(v0, v1, v1) = 0)) & ( ~
% 12.64/2.66 | ($lesseq(1, all_42_0)) | ? [v1: int] : ? [v2: int] : ? [v3: any]
% 12.64/2.66 | : ? [v4: any] : ($lesseq(1, $difference(all_42_0, v2)) &
% 12.64/2.66 | $lesseq(0, v2) & $lesseq(1, $difference(all_42_0, v1)) &
% 12.64/2.66 | $lesseq(0, v1) & path1(all_42_1, v1, v2) = v4 & same1(v0, v1, v2)
% 12.64/2.66 | = v3 & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))))
% 12.64/2.66 |
% 12.64/2.66 | ALPHA: (3) implies:
% 12.64/2.66 | (4) $lesseq(1, all_42_2)
% 12.64/2.66 | (5) graph1(all_42_1)
% 12.64/2.66 | (6) $product(all_42_2, all_42_2) = all_42_0
% 12.64/2.67 | (7) ! [v0: int] : ! [v1: int] : (v1 = v0 | ~ (path1(all_42_1, v0, v1) =
% 12.64/2.67 | 0))
% 12.64/2.67 | (8) ? [v0: uf_pure1] : (num1(v0) = all_42_0 & size1(v0) = all_42_0 &
% 12.64/2.67 | uf_pure1(v0) & ! [v1: int] : ! [v2: int] : (v2 = 0 | ~ ($lesseq(1,
% 12.64/2.67 | $difference(all_42_0, v1))) | ~ ($lesseq(0, v1)) | ~
% 12.64/2.67 | (repr1(v0, v1, v1) = v2)) & ! [v1: int] : ! [v2: int] : ( ~
% 12.64/2.67 | ($lesseq(1, $difference(all_42_0, v2))) | ~ ($lesseq(0, v2)) | ~
% 12.64/2.67 | ($lesseq(1, $difference(all_42_0, v1))) | ~ ($lesseq(0, v1)) | ~
% 12.64/2.67 | (same1(v0, v1, v2) = 0) | (v2 = v1 & repr1(v0, v1, v1) = 0)) & ( ~
% 12.64/2.67 | ($lesseq(1, all_42_0)) | ? [v1: int] : ? [v2: int] : ? [v3: any]
% 12.64/2.67 | : ? [v4: any] : ($lesseq(1, $difference(all_42_0, v2)) &
% 12.64/2.67 | $lesseq(0, v2) & $lesseq(1, $difference(all_42_0, v1)) &
% 12.64/2.67 | $lesseq(0, v1) & path1(all_42_1, v1, v2) = v4 & same1(v0, v1, v2)
% 12.64/2.67 | = v3 & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))))
% 12.64/2.67 |
% 12.64/2.67 | DELTA: instantiating (8) with fresh symbol all_46_0 gives:
% 12.64/2.67 | (9) num1(all_46_0) = all_42_0 & size1(all_46_0) = all_42_0 &
% 12.64/2.67 | uf_pure1(all_46_0) & ! [v0: int] : ! [v1: int] : (v1 = 0 | ~
% 12.64/2.67 | ($lesseq(1, $difference(all_42_0, v0))) | ~ ($lesseq(0, v0)) | ~
% 12.64/2.67 | (repr1(all_46_0, v0, v0) = v1)) & ! [v0: int] : ! [v1: int] : ( ~
% 12.64/2.67 | ($lesseq(1, $difference(all_42_0, v1))) | ~ ($lesseq(0, v1)) | ~
% 12.64/2.67 | ($lesseq(1, $difference(all_42_0, v0))) | ~ ($lesseq(0, v0)) | ~
% 12.64/2.67 | (same1(all_46_0, v0, v1) = 0) | (v1 = v0 & repr1(all_46_0, v0, v0) =
% 12.64/2.67 | 0)) & ( ~ ($lesseq(1, all_42_0)) | ? [v0: int] : ? [v1: int] : ?
% 12.64/2.67 | [v2: any] : ? [v3: any] : ($lesseq(1, $difference(all_42_0, v1)) &
% 12.64/2.67 | $lesseq(0, v1) & $lesseq(1, $difference(all_42_0, v0)) & $lesseq(0,
% 12.64/2.67 | v0) & path1(all_42_1, v0, v1) = v3 & same1(all_46_0, v0, v1) = v2
% 12.64/2.67 | & ((v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0)))))
% 12.64/2.67 |
% 12.64/2.67 | ALPHA: (9) implies:
% 12.64/2.67 | (10) uf_pure1(all_46_0)
% 12.64/2.67 | (11) ~ ($lesseq(1, all_42_0)) | ? [v0: int] : ? [v1: int] : ? [v2: any]
% 12.64/2.67 | : ? [v3: any] : ($lesseq(1, $difference(all_42_0, v1)) & $lesseq(0,
% 12.64/2.67 | v1) & $lesseq(1, $difference(all_42_0, v0)) & $lesseq(0, v0) &
% 12.64/2.67 | path1(all_42_1, v0, v1) = v3 & same1(all_46_0, v0, v1) = v2 & ((v3 =
% 12.64/2.67 | 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0))))
% 12.64/2.67 | (12) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(all_42_0,
% 12.64/2.67 | v1))) | ~ ($lesseq(0, v1)) | ~ ($lesseq(1,
% 12.64/2.67 | $difference(all_42_0, v0))) | ~ ($lesseq(0, v0)) | ~
% 12.64/2.67 | (same1(all_46_0, v0, v1) = 0) | (v1 = v0 & repr1(all_46_0, v0, v0) =
% 12.64/2.67 | 0))
% 12.64/2.67 |
% 12.64/2.67 | THEORY_AXIOM GroebnerMultiplication:
% 12.64/2.67 | (13) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, $difference($product(2,
% 12.64/2.67 | v0), v1))) | ~ ($lesseq(1, v0)) | ~ ($product(v0, v0) =
% 12.64/2.67 | v1))
% 12.64/2.67 |
% 12.64/2.67 | GROUND_INST: instantiating (13) with all_42_2, all_42_0, simplifying with (6)
% 12.64/2.67 | gives:
% 12.64/2.67 | (14) ~ ($lesseq(2, $difference($product(2, all_42_2), all_42_0))) | ~
% 12.64/2.67 | ($lesseq(1, all_42_2))
% 12.64/2.67 |
% 12.64/2.67 | BETA: splitting (14) gives:
% 12.64/2.67 |
% 12.64/2.67 | Case 1:
% 12.64/2.67 | |
% 12.64/2.67 | | (15) $lesseq(all_42_2, 0)
% 12.64/2.67 | |
% 12.64/2.67 | | COMBINE_INEQS: (4), (15) imply:
% 12.64/2.67 | | (16) $false
% 12.64/2.67 | |
% 12.64/2.67 | | CLOSE: (16) is inconsistent.
% 12.64/2.67 | |
% 12.64/2.67 | Case 2:
% 12.64/2.67 | |
% 12.64/2.68 | | (17) $lesseq(-1, $difference(all_42_0, $product(2, all_42_2)))
% 12.64/2.68 | |
% 12.64/2.68 | | COMBINE_INEQS: (4), (17) imply:
% 12.64/2.68 | | (18) $lesseq(1, all_42_0)
% 12.64/2.68 | |
% 12.64/2.68 | | BETA: splitting (11) gives:
% 12.64/2.68 | |
% 12.64/2.68 | | Case 1:
% 12.64/2.68 | | |
% 12.64/2.68 | | | (19) $lesseq(all_42_0, 0)
% 12.64/2.68 | | |
% 12.64/2.68 | | | COMBINE_INEQS: (18), (19) imply:
% 12.64/2.68 | | | (20) $false
% 12.64/2.68 | | |
% 12.64/2.68 | | | CLOSE: (20) is inconsistent.
% 12.64/2.68 | | |
% 12.64/2.68 | | Case 2:
% 12.64/2.68 | | |
% 12.64/2.68 | | | (21) ? [v0: int] : ? [v1: int] : ? [v2: any] : ? [v3: any] :
% 12.64/2.68 | | | ($lesseq(1, $difference(all_42_0, v1)) & $lesseq(0, v1) &
% 12.64/2.68 | | | $lesseq(1, $difference(all_42_0, v0)) & $lesseq(0, v0) &
% 12.64/2.68 | | | path1(all_42_1, v0, v1) = v3 & same1(all_46_0, v0, v1) = v2 &
% 12.64/2.68 | | | ((v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0))))
% 12.64/2.68 | | |
% 12.64/2.68 | | | DELTA: instantiating (21) with fresh symbols all_57_0, all_57_1, all_57_2,
% 12.64/2.68 | | | all_57_3 gives:
% 12.64/2.68 | | | (22) $lesseq(1, $difference(all_42_0, all_57_2)) & $lesseq(0, all_57_2)
% 12.64/2.68 | | | & $lesseq(1, $difference(all_42_0, all_57_3)) & $lesseq(0,
% 12.64/2.68 | | | all_57_3) & path1(all_42_1, all_57_3, all_57_2) = all_57_0 &
% 12.64/2.68 | | | same1(all_46_0, all_57_3, all_57_2) = all_57_1 & ((all_57_0 = 0 &
% 12.64/2.68 | | | ~ (all_57_1 = 0)) | (all_57_1 = 0 & ~ (all_57_0 = 0)))
% 12.64/2.68 | | |
% 12.64/2.68 | | | ALPHA: (22) implies:
% 12.64/2.68 | | | (23) $lesseq(0, all_57_3)
% 12.64/2.68 | | | (24) $lesseq(1, $difference(all_42_0, all_57_3))
% 12.64/2.68 | | | (25) $lesseq(0, all_57_2)
% 12.64/2.68 | | | (26) $lesseq(1, $difference(all_42_0, all_57_2))
% 12.64/2.68 | | | (27) same1(all_46_0, all_57_3, all_57_2) = all_57_1
% 12.64/2.68 | | | (28) path1(all_42_1, all_57_3, all_57_2) = all_57_0
% 12.64/2.68 | | | (29) (all_57_0 = 0 & ~ (all_57_1 = 0)) | (all_57_1 = 0 & ~ (all_57_0
% 12.64/2.68 | | | = 0))
% 12.64/2.68 | | |
% 12.64/2.68 | | | GROUND_INST: instantiating (1) with all_46_0, all_57_3, all_57_2,
% 12.64/2.68 | | | all_57_1, simplifying with (10), (27) gives:
% 12.64/2.68 | | | (30) all_57_1 = 0 | ? [v0: int] : ? [v1: any] : ? [v2: any] :
% 12.64/2.68 | | | (repr1(all_46_0, all_57_2, v0) = v2 & repr1(all_46_0, all_57_3,
% 12.64/2.68 | | | v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 12.64/2.68 | | |
% 12.64/2.68 | | | GROUND_INST: instantiating (path_refl) with all_42_1, all_57_3, all_57_0,
% 12.64/2.68 | | | simplifying with (5) gives:
% 12.64/2.68 | | | (31) all_57_0 = 0 | ~ (path1(all_42_1, all_57_3, all_57_3) = all_57_0)
% 12.64/2.68 | | |
% 12.64/2.68 | | | BETA: splitting (29) gives:
% 12.64/2.68 | | |
% 12.64/2.68 | | | Case 1:
% 12.64/2.68 | | | |
% 12.64/2.68 | | | | (32) all_57_0 = 0 & ~ (all_57_1 = 0)
% 12.64/2.68 | | | |
% 12.64/2.68 | | | | ALPHA: (32) implies:
% 12.64/2.68 | | | | (33) all_57_0 = 0
% 12.64/2.68 | | | | (34) ~ (all_57_1 = 0)
% 12.64/2.68 | | | |
% 12.64/2.68 | | | | REDUCE: (28), (33) imply:
% 12.64/2.68 | | | | (35) path1(all_42_1, all_57_3, all_57_2) = 0
% 12.64/2.68 | | | |
% 12.64/2.68 | | | | BETA: splitting (30) gives:
% 12.64/2.68 | | | |
% 12.64/2.68 | | | | Case 1:
% 12.64/2.68 | | | | |
% 12.64/2.68 | | | | | (36) all_57_1 = 0
% 12.64/2.68 | | | | |
% 12.64/2.68 | | | | | REDUCE: (34), (36) imply:
% 12.64/2.68 | | | | | (37) $false
% 12.64/2.68 | | | | |
% 12.64/2.68 | | | | | CLOSE: (37) is inconsistent.
% 12.64/2.68 | | | | |
% 12.64/2.68 | | | | Case 2:
% 12.64/2.68 | | | | |
% 12.64/2.68 | | | | | (38) ? [v0: int] : ? [v1: any] : ? [v2: any] : (repr1(all_46_0,
% 12.64/2.68 | | | | | all_57_2, v0) = v2 & repr1(all_46_0, all_57_3, v0) = v1 &
% 12.64/2.68 | | | | | ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 12.64/2.68 | | | | |
% 12.64/2.68 | | | | | DELTA: instantiating (38) with fresh symbols all_112_0, all_112_1,
% 12.64/2.68 | | | | | all_112_2 gives:
% 12.64/2.68 | | | | | (39) repr1(all_46_0, all_57_2, all_112_2) = all_112_0 &
% 12.64/2.68 | | | | | repr1(all_46_0, all_57_3, all_112_2) = all_112_1 & ( ~
% 12.64/2.68 | | | | | (all_112_0 = 0) | ~ (all_112_1 = 0)) & (all_112_0 = 0 |
% 12.64/2.68 | | | | | all_112_1 = 0)
% 12.64/2.68 | | | | |
% 12.64/2.68 | | | | | ALPHA: (39) implies:
% 12.64/2.68 | | | | | (40) repr1(all_46_0, all_57_3, all_112_2) = all_112_1
% 12.64/2.68 | | | | | (41) repr1(all_46_0, all_57_2, all_112_2) = all_112_0
% 12.64/2.68 | | | | | (42) all_112_0 = 0 | all_112_1 = 0
% 12.64/2.68 | | | | | (43) ~ (all_112_0 = 0) | ~ (all_112_1 = 0)
% 12.64/2.68 | | | | |
% 12.64/2.68 | | | | | GROUND_INST: instantiating (2) with all_112_1, all_112_0, all_112_2,
% 12.64/2.68 | | | | | all_57_3, all_46_0, simplifying with (40) gives:
% 12.64/2.68 | | | | | (44) all_112_0 = all_112_1 | ~ (repr1(all_46_0, all_57_3,
% 12.64/2.68 | | | | | all_112_2) = all_112_0)
% 12.64/2.68 | | | | |
% 12.64/2.68 | | | | | GROUND_INST: instantiating (7) with all_57_3, all_57_2, simplifying
% 12.64/2.68 | | | | | with (35) gives:
% 12.64/2.69 | | | | | (45) all_57_2 = all_57_3
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | | REDUCE: (41), (45) imply:
% 12.64/2.69 | | | | | (46) repr1(all_46_0, all_57_3, all_112_2) = all_112_0
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | | BETA: splitting (44) gives:
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | | Case 1:
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | (47) ~ (repr1(all_46_0, all_57_3, all_112_2) = all_112_0)
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | PRED_UNIFY: (46), (47) imply:
% 12.64/2.69 | | | | | | (48) $false
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | CLOSE: (48) is inconsistent.
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | Case 2:
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | (49) all_112_0 = all_112_1
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | BETA: splitting (42) gives:
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | Case 1:
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | (50) all_112_0 = 0
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | COMBINE_EQS: (49), (50) imply:
% 12.64/2.69 | | | | | | | (51) all_112_1 = 0
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | BETA: splitting (43) gives:
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | Case 1:
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | (52) ~ (all_112_0 = 0)
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | REDUCE: (50), (52) imply:
% 12.64/2.69 | | | | | | | | (53) $false
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | CLOSE: (53) is inconsistent.
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | Case 2:
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | (54) ~ (all_112_1 = 0)
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | REDUCE: (51), (54) imply:
% 12.64/2.69 | | | | | | | | (55) $false
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | CLOSE: (55) is inconsistent.
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | End of split
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | Case 2:
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | (56) all_112_1 = 0
% 12.64/2.69 | | | | | | | (57) ~ (all_112_0 = 0)
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | COMBINE_EQS: (49), (56) imply:
% 12.64/2.69 | | | | | | | (58) all_112_0 = 0
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | REDUCE: (57), (58) imply:
% 12.64/2.69 | | | | | | | (59) $false
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | CLOSE: (59) is inconsistent.
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | End of split
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | End of split
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | End of split
% 12.64/2.69 | | | |
% 12.64/2.69 | | | Case 2:
% 12.64/2.69 | | | |
% 12.64/2.69 | | | | (60) all_57_1 = 0 & ~ (all_57_0 = 0)
% 12.64/2.69 | | | |
% 12.64/2.69 | | | | ALPHA: (60) implies:
% 12.64/2.69 | | | | (61) all_57_1 = 0
% 12.64/2.69 | | | | (62) ~ (all_57_0 = 0)
% 12.64/2.69 | | | |
% 12.64/2.69 | | | | REDUCE: (27), (61) imply:
% 12.64/2.69 | | | | (63) same1(all_46_0, all_57_3, all_57_2) = 0
% 12.64/2.69 | | | |
% 12.64/2.69 | | | | BETA: splitting (31) gives:
% 12.64/2.69 | | | |
% 12.64/2.69 | | | | Case 1:
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | | (64) ~ (path1(all_42_1, all_57_3, all_57_3) = all_57_0)
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | | PRED_UNIFY: (28), (64) imply:
% 12.64/2.69 | | | | | (65) ~ (all_57_2 = all_57_3)
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | | GROUND_INST: instantiating (12) with all_57_3, all_57_2, simplifying
% 12.64/2.69 | | | | | with (63) gives:
% 12.64/2.69 | | | | | (66) ~ ($lesseq(1, $difference(all_42_0, all_57_2))) | ~
% 12.64/2.69 | | | | | ($lesseq(0, all_57_2)) | ~ ($lesseq(1, $difference(all_42_0,
% 12.64/2.69 | | | | | all_57_3))) | ~ ($lesseq(0, all_57_3)) | (all_57_2 =
% 12.64/2.69 | | | | | all_57_3 & repr1(all_46_0, all_57_3, all_57_3) = 0)
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | | BETA: splitting (66) gives:
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | | Case 1:
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | (67) $lesseq(all_57_2, -1)
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | COMBINE_INEQS: (25), (67) imply:
% 12.64/2.69 | | | | | | (68) $false
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | CLOSE: (68) is inconsistent.
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | Case 2:
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | (69) ~ ($lesseq(1, $difference(all_42_0, all_57_2))) | ~
% 12.64/2.69 | | | | | | ($lesseq(1, $difference(all_42_0, all_57_3))) | ~
% 12.64/2.69 | | | | | | ($lesseq(0, all_57_3)) | (all_57_2 = all_57_3 &
% 12.64/2.69 | | | | | | repr1(all_46_0, all_57_3, all_57_3) = 0)
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | BETA: splitting (69) gives:
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | | Case 1:
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | (70) $lesseq(all_57_3, -1)
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | COMBINE_INEQS: (23), (70) imply:
% 12.64/2.69 | | | | | | | (71) $false
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | CLOSE: (71) is inconsistent.
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | Case 2:
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | (72) ~ ($lesseq(1, $difference(all_42_0, all_57_2))) | ~
% 12.64/2.69 | | | | | | | ($lesseq(1, $difference(all_42_0, all_57_3))) | (all_57_2
% 12.64/2.69 | | | | | | | = all_57_3 & repr1(all_46_0, all_57_3, all_57_3) = 0)
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | BETA: splitting (72) gives:
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | | Case 1:
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | (73) $lesseq(all_42_0, all_57_2)
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | COMBINE_INEQS: (26), (73) imply:
% 12.64/2.69 | | | | | | | | (74) $false
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | CLOSE: (74) is inconsistent.
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | Case 2:
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | (75) ~ ($lesseq(1, $difference(all_42_0, all_57_3))) |
% 12.64/2.69 | | | | | | | | (all_57_2 = all_57_3 & repr1(all_46_0, all_57_3,
% 12.64/2.69 | | | | | | | | all_57_3) = 0)
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | BETA: splitting (75) gives:
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | | Case 1:
% 12.64/2.69 | | | | | | | | |
% 12.64/2.69 | | | | | | | | | (76) $lesseq(all_42_0, all_57_3)
% 12.64/2.69 | | | | | | | | |
% 12.64/2.69 | | | | | | | | | COMBINE_INEQS: (24), (76) imply:
% 12.64/2.69 | | | | | | | | | (77) $false
% 12.64/2.69 | | | | | | | | |
% 12.64/2.69 | | | | | | | | | CLOSE: (77) is inconsistent.
% 12.64/2.69 | | | | | | | | |
% 12.64/2.69 | | | | | | | | Case 2:
% 12.64/2.69 | | | | | | | | |
% 12.64/2.69 | | | | | | | | | (78) all_57_2 = all_57_3 & repr1(all_46_0, all_57_3,
% 12.64/2.69 | | | | | | | | | all_57_3) = 0
% 12.64/2.69 | | | | | | | | |
% 12.64/2.69 | | | | | | | | | ALPHA: (78) implies:
% 12.64/2.69 | | | | | | | | | (79) all_57_2 = all_57_3
% 12.64/2.69 | | | | | | | | |
% 12.64/2.69 | | | | | | | | | REDUCE: (65), (79) imply:
% 12.64/2.69 | | | | | | | | | (80) $false
% 12.64/2.69 | | | | | | | | |
% 12.64/2.69 | | | | | | | | | CLOSE: (80) is inconsistent.
% 12.64/2.69 | | | | | | | | |
% 12.64/2.69 | | | | | | | | End of split
% 12.64/2.69 | | | | | | | |
% 12.64/2.69 | | | | | | | End of split
% 12.64/2.69 | | | | | | |
% 12.64/2.69 | | | | | | End of split
% 12.64/2.69 | | | | | |
% 12.64/2.69 | | | | | End of split
% 12.64/2.69 | | | | |
% 12.64/2.69 | | | | Case 2:
% 12.64/2.69 | | | | |
% 12.64/2.70 | | | | | (81) all_57_0 = 0
% 12.64/2.70 | | | | |
% 12.64/2.70 | | | | | REDUCE: (62), (81) imply:
% 12.64/2.70 | | | | | (82) $false
% 12.64/2.70 | | | | |
% 12.64/2.70 | | | | | CLOSE: (82) is inconsistent.
% 12.64/2.70 | | | | |
% 12.64/2.70 | | | | End of split
% 12.64/2.70 | | | |
% 12.64/2.70 | | | End of split
% 12.64/2.70 | | |
% 12.64/2.70 | | End of split
% 12.64/2.70 | |
% 12.64/2.70 | End of split
% 12.64/2.70 |
% 12.64/2.70 End of proof
% 12.64/2.70 % SZS output end Proof for theBenchmark
% 12.64/2.70
% 12.64/2.70 2086ms
%------------------------------------------------------------------------------