%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------