%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : TOP022+1 : TPTP v8.1.2. Released v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n021.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 05:58:48 EDT 2023 % Result : Theorem 5.55s 1.59s % Output : Proof 8.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : TOP022+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n021.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 23:26:27 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.64 ________ _____ % 0.21/0.64 ___ __ \_________(_)________________________________ % 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.64 % 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.64 (2023-06-19) % 0.21/0.64 % 0.21/0.64 (c) Philipp Rümmer, 2009-2023 % 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.64 Amanda Stjerna. % 0.21/0.64 Free software under BSD-3-Clause. % 0.21/0.64 % 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.64 % 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.04/1.03 Prover 4: Preprocessing ... % 2.04/1.03 Prover 1: Preprocessing ... % 2.04/1.07 Prover 2: Preprocessing ... % 2.04/1.08 Prover 5: Preprocessing ... % 2.04/1.08 Prover 6: Preprocessing ... % 2.04/1.08 Prover 0: Preprocessing ... % 2.04/1.08 Prover 3: Preprocessing ... % 3.41/1.25 Prover 2: Proving ... % 3.41/1.26 Prover 5: Proving ... % 3.41/1.27 Prover 6: Proving ... % 3.41/1.27 Prover 3: Constructing countermodel ... % 3.41/1.30 Prover 0: Proving ... % 3.41/1.30 Prover 1: Constructing countermodel ... % 3.41/1.32 Prover 4: Constructing countermodel ... % 4.42/1.54 Prover 3: gave up % 4.42/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.55/1.57 Prover 1: gave up % 5.55/1.57 Prover 7: Preprocessing ... % 5.55/1.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.55/1.58 Prover 0: proved (923ms) % 5.55/1.59 % 5.55/1.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.55/1.59 % 5.55/1.59 Prover 5: stopped % 5.55/1.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.55/1.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.55/1.59 Prover 6: stopped % 5.55/1.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.55/1.59 Prover 2: stopped % 5.55/1.60 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 5.55/1.61 Prover 10: Preprocessing ... % 5.55/1.62 Prover 8: Preprocessing ... % 5.55/1.62 Prover 13: Preprocessing ... % 5.55/1.63 Prover 11: Preprocessing ... % 5.55/1.64 Prover 16: Preprocessing ... % 5.55/1.64 Prover 7: Warning: ignoring some quantifiers % 6.26/1.65 Prover 7: Constructing countermodel ... % 6.26/1.67 Prover 10: Warning: ignoring some quantifiers % 6.26/1.69 Prover 10: Constructing countermodel ... % 6.63/1.69 Prover 13: Warning: ignoring some quantifiers % 6.63/1.70 Prover 13: Constructing countermodel ... % 6.63/1.70 Prover 8: Warning: ignoring some quantifiers % 6.63/1.71 Prover 16: Warning: ignoring some quantifiers % 6.63/1.71 Prover 16: Constructing countermodel ... % 6.63/1.71 Prover 8: Constructing countermodel ... % 7.04/1.77 Prover 11: Constructing countermodel ... % 7.04/1.77 Prover 7: gave up % 7.04/1.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.04/1.79 Prover 10: gave up % 7.04/1.80 Prover 19: Preprocessing ... % 7.74/1.90 Prover 4: Found proof (size 83) % 7.74/1.90 Prover 4: proved (1239ms) % 7.74/1.90 Prover 13: stopped % 7.74/1.90 Prover 16: stopped % 7.74/1.90 Prover 11: stopped % 7.74/1.90 Prover 8: stopped % 7.74/1.90 Prover 19: Warning: ignoring some quantifiers % 7.74/1.91 Prover 19: Constructing countermodel ... % 7.74/1.92 Prover 19: stopped % 7.74/1.92 % 7.74/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.74/1.92 % 7.74/1.94 % SZS output start Proof for theBenchmark % 8.34/1.94 Assumptions after simplification: % 8.34/1.94 --------------------------------- % 8.34/1.94 % 8.34/1.94 (isomorphic_groups_defn) % 8.34/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ % 8.34/1.98 (isomorphic_groups(v0, v1) = v2) | ~ (a_group_isomorphism_from_to(v3, v0, % 8.34/1.98 v1) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: % 8.34/1.98 $i] : ( ~ (isomorphic_groups(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 8.34/1.98 $i] : (a_group_isomorphism_from_to(v2, v0, v1) = 0 & $i(v2))) % 8.34/1.98 % 8.34/1.98 (m_8_2_1) % 8.34/1.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.34/1.98 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (alpha_hat(v0) = v4) | ~ % 8.34/1.98 (first_homotop_grp(v3, v2) = v6) | ~ (first_homotop_grp(v3, v1) = v5) | ~ % 8.34/1.98 (a_group_isomorphism_from_to(v4, v5, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ % 8.34/1.98 $i(v1) | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & a_path_from_to_in(v0, v1, % 8.34/1.98 v2, v3) = v8)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 8.34/1.98 ( ~ (a_path_from_to_in(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 8.34/1.98 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 8.34/1.98 (alpha_hat(v0) = v4 & first_homotop_grp(v3, v2) = v6 & first_homotop_grp(v3, % 8.34/1.98 v1) = v5 & a_group_isomorphism_from_to(v4, v5, v6) = 0 & $i(v6) & $i(v5) % 8.34/1.98 & $i(v4))) % 8.34/1.98 % 8.34/1.98 (m_8_2_2) % 8.34/1.99 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.34/1.99 int] : ( ~ (v5 = 0) & first_homotop_grp(v0, v2) = v4 & first_homotop_grp(v0, % 8.34/1.99 v1) = v3 & a_member_of(v2, v0) = 0 & a_member_of(v1, v0) = 0 & % 8.34/1.99 path_connected(v0) = 0 & isomorphic_groups(v3, v4) = v5 & $i(v4) & $i(v3) & % 8.34/1.99 $i(v2) & $i(v1) & $i(v0)) % 8.34/1.99 % 8.34/1.99 (path_connected_defn) % 8.58/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: MultipleValueBool] : ! [v4: % 8.58/1.99 MultipleValueBool] : ! [v5: $i] : ( ~ (a_member_of(v2, v0) = v4) | ~ % 8.58/1.99 (a_member_of(v1, v0) = v3) | ~ (a_path_from_to_in(v5, v1, v2, v0) = 0) | ~ % 8.58/1.99 $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | path_connected(v0) = 0) & ! % 8.58/1.99 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: MultipleValueBool] : ! [v4: % 8.58/2.00 int] : (v4 = 0 | ~ (a_member_of(v2, v0) = v4) | ~ (a_member_of(v1, v0) = % 8.58/2.00 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | path_connected(v0) = 0) & ! % 8.58/2.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: % 8.58/2.00 MultipleValueBool] : (v3 = 0 | ~ (a_member_of(v2, v0) = v4) | ~ % 8.58/2.00 (a_member_of(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 8.58/2.00 path_connected(v0) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 8.58/2.00 (a_member_of(v2, v0) = 0) | ~ (a_member_of(v1, v0) = 0) | ~ $i(v2) | ~ % 8.58/2.00 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ($i(v4) & % 8.58/2.00 ((v5 = 0 & a_path_from_to_in(v4, v1, v2, v0) = 0) | ( ~ (v3 = 0) & % 8.58/2.00 path_connected(v0) = v3)))) % 8.58/2.00 % 8.58/2.00 (function-axioms) % 8.58/2.00 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.58/2.00 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (a_path_from_to_in(v5, % 8.58/2.00 v4, v3, v2) = v1) | ~ (a_path_from_to_in(v5, v4, v3, v2) = v0)) & ! % 8.58/2.00 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.58/2.00 $i] : ! [v4: $i] : (v1 = v0 | ~ (a_group_isomorphism_from_to(v4, v3, v2) = % 8.58/2.00 v1) | ~ (a_group_isomorphism_from_to(v4, v3, v2) = v0)) & ! [v0: $i] : % 8.58/2.00 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (first_homotop_grp(v3, % 8.58/2.00 v2) = v1) | ~ (first_homotop_grp(v3, v2) = v0)) & ! [v0: % 8.58/2.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.58/2.00 : (v1 = v0 | ~ (a_member_of(v3, v2) = v1) | ~ (a_member_of(v3, v2) = v0)) & % 8.58/2.00 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.58/2.00 $i] : (v1 = v0 | ~ (isomorphic_groups(v3, v2) = v1) | ~ % 8.58/2.00 (isomorphic_groups(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 8.58/2.00 : (v1 = v0 | ~ (alpha_hat(v2) = v1) | ~ (alpha_hat(v2) = v0)) & ! [v0: % 8.58/2.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.58/2.00 ~ (path_connected(v2) = v1) | ~ (path_connected(v2) = v0)) % 8.58/2.00 % 8.58/2.00 Those formulas are unsatisfiable: % 8.58/2.00 --------------------------------- % 8.58/2.00 % 8.58/2.00 Begin of proof % 8.58/2.01 | % 8.58/2.01 | ALPHA: (isomorphic_groups_defn) implies: % 8.58/2.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ % 8.58/2.01 | (isomorphic_groups(v0, v1) = v2) | ~ % 8.58/2.01 | (a_group_isomorphism_from_to(v3, v0, v1) = 0) | ~ $i(v3) | ~ $i(v1) % 8.58/2.01 | | ~ $i(v0)) % 8.58/2.01 | % 8.58/2.01 | ALPHA: (path_connected_defn) implies: % 8.58/2.01 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_member_of(v2, v0) = 0) % 8.58/2.01 | | ~ (a_member_of(v1, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 8.58/2.01 | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ($i(v4) & ((v5 = 0 & % 8.58/2.01 | a_path_from_to_in(v4, v1, v2, v0) = 0) | ( ~ (v3 = 0) & % 8.58/2.01 | path_connected(v0) = v3)))) % 8.58/2.01 | % 8.58/2.01 | ALPHA: (m_8_2_1) implies: % 8.58/2.01 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.58/2.01 | (a_path_from_to_in(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 8.58/2.01 | $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 8.58/2.01 | (alpha_hat(v0) = v4 & first_homotop_grp(v3, v2) = v6 & % 8.58/2.02 | first_homotop_grp(v3, v1) = v5 & a_group_isomorphism_from_to(v4, % 8.58/2.02 | v5, v6) = 0 & $i(v6) & $i(v5) & $i(v4))) % 8.58/2.02 | % 8.58/2.02 | ALPHA: (function-axioms) implies: % 8.58/2.02 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.58/2.02 | (v1 = v0 | ~ (path_connected(v2) = v1) | ~ (path_connected(v2) = v0)) % 8.58/2.02 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.58/2.02 | (first_homotop_grp(v3, v2) = v1) | ~ (first_homotop_grp(v3, v2) = % 8.58/2.02 | v0)) % 8.58/2.02 | % 8.58/2.02 | DELTA: instantiating (m_8_2_2) with fresh symbols all_6_0, all_6_1, all_6_2, % 8.58/2.02 | all_6_3, all_6_4, all_6_5 gives: % 8.58/2.02 | (6) ~ (all_6_0 = 0) & first_homotop_grp(all_6_5, all_6_3) = all_6_1 & % 8.58/2.02 | first_homotop_grp(all_6_5, all_6_4) = all_6_2 & a_member_of(all_6_3, % 8.58/2.02 | all_6_5) = 0 & a_member_of(all_6_4, all_6_5) = 0 & % 8.58/2.02 | path_connected(all_6_5) = 0 & isomorphic_groups(all_6_2, all_6_1) = % 8.58/2.02 | all_6_0 & $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & $i(all_6_4) & % 8.58/2.02 | $i(all_6_5) % 8.58/2.02 | % 8.58/2.02 | ALPHA: (6) implies: % 8.58/2.02 | (7) ~ (all_6_0 = 0) % 8.58/2.02 | (8) $i(all_6_5) % 8.58/2.02 | (9) $i(all_6_4) % 8.58/2.02 | (10) $i(all_6_3) % 8.58/2.02 | (11) isomorphic_groups(all_6_2, all_6_1) = all_6_0 % 8.58/2.02 | (12) path_connected(all_6_5) = 0 % 8.58/2.02 | (13) a_member_of(all_6_4, all_6_5) = 0 % 8.58/2.02 | (14) a_member_of(all_6_3, all_6_5) = 0 % 8.58/2.03 | (15) first_homotop_grp(all_6_5, all_6_4) = all_6_2 % 8.58/2.03 | (16) first_homotop_grp(all_6_5, all_6_3) = all_6_1 % 8.58/2.03 | % 8.58/2.03 | GROUND_INST: instantiating (2) with all_6_5, all_6_4, all_6_4, simplifying % 8.58/2.03 | with (8), (9), (13) gives: % 8.58/2.03 | (17) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ($i(v1) & ((v2 = 0 & % 8.58/2.03 | a_path_from_to_in(v1, all_6_4, all_6_4, all_6_5) = 0) | ( ~ (v0 % 8.58/2.03 | = 0) & path_connected(all_6_5) = v0))) % 8.58/2.03 | % 8.58/2.03 | GROUND_INST: instantiating (2) with all_6_5, all_6_3, all_6_3, simplifying % 8.58/2.03 | with (8), (10), (14) gives: % 8.58/2.03 | (18) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ($i(v1) & ((v2 = 0 & % 8.58/2.03 | a_path_from_to_in(v1, all_6_3, all_6_3, all_6_5) = 0) | ( ~ (v0 % 8.58/2.03 | = 0) & path_connected(all_6_5) = v0))) % 8.58/2.03 | % 8.58/2.03 | GROUND_INST: instantiating (2) with all_6_5, all_6_4, all_6_3, simplifying % 8.58/2.03 | with (8), (9), (10), (13), (14) gives: % 8.58/2.03 | (19) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ($i(v1) & ((v2 = 0 & % 8.58/2.03 | a_path_from_to_in(v1, all_6_4, all_6_3, all_6_5) = 0) | ( ~ (v0 % 8.58/2.03 | = 0) & path_connected(all_6_5) = v0))) % 8.58/2.03 | % 8.58/2.03 | GROUND_INST: instantiating (2) with all_6_5, all_6_3, all_6_4, simplifying % 8.58/2.03 | with (8), (9), (10), (13), (14) gives: % 8.58/2.04 | (20) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ($i(v1) & ((v2 = 0 & % 8.58/2.04 | a_path_from_to_in(v1, all_6_3, all_6_4, all_6_5) = 0) | ( ~ (v0 % 8.58/2.04 | = 0) & path_connected(all_6_5) = v0))) % 8.58/2.04 | % 8.58/2.04 | DELTA: instantiating (20) with fresh symbols all_13_0, all_13_1, all_13_2 % 8.58/2.04 | gives: % 8.58/2.04 | (21) $i(all_13_1) & ((all_13_0 = 0 & a_path_from_to_in(all_13_1, all_6_3, % 8.58/2.04 | all_6_4, all_6_5) = 0) | ( ~ (all_13_2 = 0) & % 8.58/2.04 | path_connected(all_6_5) = all_13_2)) % 8.58/2.04 | % 8.58/2.04 | ALPHA: (21) implies: % 8.58/2.04 | (22) $i(all_13_1) % 8.58/2.04 | (23) (all_13_0 = 0 & a_path_from_to_in(all_13_1, all_6_3, all_6_4, all_6_5) % 8.58/2.04 | = 0) | ( ~ (all_13_2 = 0) & path_connected(all_6_5) = all_13_2) % 8.58/2.04 | % 8.58/2.04 | DELTA: instantiating (18) with fresh symbols all_15_0, all_15_1, all_15_2 % 8.58/2.04 | gives: % 8.58/2.04 | (24) $i(all_15_1) & ((all_15_0 = 0 & a_path_from_to_in(all_15_1, all_6_3, % 8.58/2.04 | all_6_3, all_6_5) = 0) | ( ~ (all_15_2 = 0) & % 8.58/2.04 | path_connected(all_6_5) = all_15_2)) % 8.58/2.04 | % 8.58/2.04 | ALPHA: (24) implies: % 8.58/2.04 | (25) $i(all_15_1) % 8.58/2.04 | (26) (all_15_0 = 0 & a_path_from_to_in(all_15_1, all_6_3, all_6_3, all_6_5) % 8.58/2.04 | = 0) | ( ~ (all_15_2 = 0) & path_connected(all_6_5) = all_15_2) % 8.58/2.04 | % 8.58/2.04 | DELTA: instantiating (19) with fresh symbols all_17_0, all_17_1, all_17_2 % 8.58/2.04 | gives: % 8.58/2.04 | (27) $i(all_17_1) & ((all_17_0 = 0 & a_path_from_to_in(all_17_1, all_6_4, % 8.58/2.04 | all_6_3, all_6_5) = 0) | ( ~ (all_17_2 = 0) & % 8.58/2.04 | path_connected(all_6_5) = all_17_2)) % 8.58/2.04 | % 8.58/2.04 | ALPHA: (27) implies: % 8.58/2.04 | (28) $i(all_17_1) % 8.58/2.04 | (29) (all_17_0 = 0 & a_path_from_to_in(all_17_1, all_6_4, all_6_3, all_6_5) % 8.58/2.04 | = 0) | ( ~ (all_17_2 = 0) & path_connected(all_6_5) = all_17_2) % 8.58/2.04 | % 8.58/2.04 | DELTA: instantiating (17) with fresh symbols all_19_0, all_19_1, all_19_2 % 8.58/2.04 | gives: % 8.58/2.04 | (30) $i(all_19_1) & ((all_19_0 = 0 & a_path_from_to_in(all_19_1, all_6_4, % 8.58/2.04 | all_6_4, all_6_5) = 0) | ( ~ (all_19_2 = 0) & % 8.58/2.04 | path_connected(all_6_5) = all_19_2)) % 8.58/2.04 | % 8.58/2.04 | ALPHA: (30) implies: % 8.58/2.05 | (31) $i(all_19_1) % 8.58/2.05 | (32) (all_19_0 = 0 & a_path_from_to_in(all_19_1, all_6_4, all_6_4, all_6_5) % 8.58/2.05 | = 0) | ( ~ (all_19_2 = 0) & path_connected(all_6_5) = all_19_2) % 8.58/2.05 | % 8.85/2.05 | BETA: splitting (26) gives: % 8.85/2.05 | % 8.85/2.05 | Case 1: % 8.85/2.05 | | % 8.85/2.05 | | (33) all_15_0 = 0 & a_path_from_to_in(all_15_1, all_6_3, all_6_3, % 8.85/2.05 | | all_6_5) = 0 % 8.85/2.05 | | % 8.85/2.05 | | ALPHA: (33) implies: % 8.85/2.05 | | (34) a_path_from_to_in(all_15_1, all_6_3, all_6_3, all_6_5) = 0 % 8.85/2.05 | | % 8.85/2.05 | | BETA: splitting (23) gives: % 8.85/2.05 | | % 8.85/2.05 | | Case 1: % 8.85/2.05 | | | % 8.85/2.05 | | | (35) all_13_0 = 0 & a_path_from_to_in(all_13_1, all_6_3, all_6_4, % 8.85/2.05 | | | all_6_5) = 0 % 8.85/2.05 | | | % 8.85/2.05 | | | ALPHA: (35) implies: % 8.85/2.05 | | | (36) a_path_from_to_in(all_13_1, all_6_3, all_6_4, all_6_5) = 0 % 8.85/2.05 | | | % 8.85/2.05 | | | BETA: splitting (32) gives: % 8.85/2.05 | | | % 8.85/2.05 | | | Case 1: % 8.85/2.05 | | | | % 8.85/2.05 | | | | (37) all_19_0 = 0 & a_path_from_to_in(all_19_1, all_6_4, all_6_4, % 8.85/2.05 | | | | all_6_5) = 0 % 8.85/2.05 | | | | % 8.85/2.05 | | | | ALPHA: (37) implies: % 8.85/2.05 | | | | (38) a_path_from_to_in(all_19_1, all_6_4, all_6_4, all_6_5) = 0 % 8.85/2.05 | | | | % 8.85/2.05 | | | | BETA: splitting (29) gives: % 8.85/2.05 | | | | % 8.85/2.05 | | | | Case 1: % 8.85/2.05 | | | | | % 8.85/2.05 | | | | | (39) all_17_0 = 0 & a_path_from_to_in(all_17_1, all_6_4, all_6_3, % 8.85/2.05 | | | | | all_6_5) = 0 % 8.85/2.05 | | | | | % 8.85/2.05 | | | | | ALPHA: (39) implies: % 8.85/2.05 | | | | | (40) a_path_from_to_in(all_17_1, all_6_4, all_6_3, all_6_5) = 0 % 8.85/2.05 | | | | | % 8.85/2.05 | | | | | GROUND_INST: instantiating (3) with all_13_1, all_6_3, all_6_4, % 8.85/2.05 | | | | | all_6_5, simplifying with (8), (9), (10), (22), (36) % 8.85/2.05 | | | | | gives: % 8.85/2.06 | | | | | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (alpha_hat(all_13_1) % 8.85/2.06 | | | | | = v0 & first_homotop_grp(all_6_5, all_6_3) = v1 & % 8.85/2.06 | | | | | first_homotop_grp(all_6_5, all_6_4) = v2 & % 8.85/2.06 | | | | | a_group_isomorphism_from_to(v0, v1, v2) = 0 & $i(v2) & % 8.85/2.06 | | | | | $i(v1) & $i(v0)) % 8.85/2.06 | | | | | % 8.85/2.06 | | | | | GROUND_INST: instantiating (3) with all_15_1, all_6_3, all_6_3, % 8.85/2.06 | | | | | all_6_5, simplifying with (8), (10), (25), (34) gives: % 8.85/2.06 | | | | | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (alpha_hat(all_15_1) % 8.85/2.06 | | | | | = v0 & first_homotop_grp(all_6_5, all_6_3) = v2 & % 8.85/2.06 | | | | | first_homotop_grp(all_6_5, all_6_3) = v1 & % 8.85/2.06 | | | | | a_group_isomorphism_from_to(v0, v1, v2) = 0 & $i(v2) & % 8.85/2.06 | | | | | $i(v1) & $i(v0)) % 8.85/2.06 | | | | | % 8.85/2.06 | | | | | GROUND_INST: instantiating (3) with all_17_1, all_6_4, all_6_3, % 8.85/2.06 | | | | | all_6_5, simplifying with (8), (9), (10), (28), (40) % 8.85/2.06 | | | | | gives: % 8.85/2.06 | | | | | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (alpha_hat(all_17_1) % 8.85/2.06 | | | | | = v0 & first_homotop_grp(all_6_5, all_6_3) = v2 & % 8.85/2.06 | | | | | first_homotop_grp(all_6_5, all_6_4) = v1 & % 8.85/2.06 | | | | | a_group_isomorphism_from_to(v0, v1, v2) = 0 & $i(v2) & % 8.85/2.06 | | | | | $i(v1) & $i(v0)) % 8.85/2.06 | | | | | % 8.85/2.06 | | | | | GROUND_INST: instantiating (3) with all_19_1, all_6_4, all_6_4, % 8.85/2.06 | | | | | all_6_5, simplifying with (8), (9), (31), (38) gives: % 8.85/2.06 | | | | | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (alpha_hat(all_19_1) % 8.85/2.06 | | | | | = v0 & first_homotop_grp(all_6_5, all_6_4) = v2 & % 8.85/2.06 | | | | | first_homotop_grp(all_6_5, all_6_4) = v1 & % 8.85/2.06 | | | | | a_group_isomorphism_from_to(v0, v1, v2) = 0 & $i(v2) & % 8.85/2.06 | | | | | $i(v1) & $i(v0)) % 8.85/2.06 | | | | | % 8.85/2.06 | | | | | DELTA: instantiating (44) with fresh symbols all_42_0, all_42_1, % 8.85/2.06 | | | | | all_42_2 gives: % 8.85/2.07 | | | | | (45) alpha_hat(all_19_1) = all_42_2 & first_homotop_grp(all_6_5, % 8.85/2.07 | | | | | all_6_4) = all_42_0 & first_homotop_grp(all_6_5, all_6_4) = % 8.85/2.07 | | | | | all_42_1 & a_group_isomorphism_from_to(all_42_2, all_42_1, % 8.85/2.07 | | | | | all_42_0) = 0 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) % 8.85/2.07 | | | | | % 8.85/2.07 | | | | | ALPHA: (45) implies: % 8.85/2.07 | | | | | (46) $i(all_42_1) % 8.85/2.07 | | | | | (47) first_homotop_grp(all_6_5, all_6_4) = all_42_1 % 8.85/2.07 | | | | | (48) first_homotop_grp(all_6_5, all_6_4) = all_42_0 % 8.85/2.07 | | | | | % 8.85/2.07 | | | | | DELTA: instantiating (42) with fresh symbols all_44_0, all_44_1, % 8.85/2.07 | | | | | all_44_2 gives: % 8.85/2.07 | | | | | (49) alpha_hat(all_15_1) = all_44_2 & first_homotop_grp(all_6_5, % 8.85/2.07 | | | | | all_6_3) = all_44_0 & first_homotop_grp(all_6_5, all_6_3) = % 8.85/2.07 | | | | | all_44_1 & a_group_isomorphism_from_to(all_44_2, all_44_1, % 8.85/2.07 | | | | | all_44_0) = 0 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) % 8.85/2.07 | | | | | % 8.85/2.07 | | | | | ALPHA: (49) implies: % 8.85/2.07 | | | | | (50) $i(all_44_1) % 8.85/2.07 | | | | | (51) first_homotop_grp(all_6_5, all_6_3) = all_44_1 % 8.85/2.07 | | | | | (52) first_homotop_grp(all_6_5, all_6_3) = all_44_0 % 8.85/2.07 | | | | | % 8.85/2.07 | | | | | DELTA: instantiating (41) with fresh symbols all_46_0, all_46_1, % 8.85/2.07 | | | | | all_46_2 gives: % 8.85/2.07 | | | | | (53) alpha_hat(all_13_1) = all_46_2 & first_homotop_grp(all_6_5, % 8.85/2.07 | | | | | all_6_3) = all_46_1 & first_homotop_grp(all_6_5, all_6_4) = % 8.85/2.07 | | | | | all_46_0 & a_group_isomorphism_from_to(all_46_2, all_46_1, % 8.85/2.07 | | | | | all_46_0) = 0 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2) % 8.85/2.07 | | | | | % 8.85/2.07 | | | | | ALPHA: (53) implies: % 8.85/2.07 | | | | | (54) first_homotop_grp(all_6_5, all_6_4) = all_46_0 % 8.85/2.07 | | | | | (55) first_homotop_grp(all_6_5, all_6_3) = all_46_1 % 8.85/2.07 | | | | | % 8.85/2.07 | | | | | DELTA: instantiating (43) with fresh symbols all_48_0, all_48_1, % 8.85/2.07 | | | | | all_48_2 gives: % 8.85/2.07 | | | | | (56) alpha_hat(all_17_1) = all_48_2 & first_homotop_grp(all_6_5, % 8.85/2.07 | | | | | all_6_3) = all_48_0 & first_homotop_grp(all_6_5, all_6_4) = % 8.85/2.07 | | | | | all_48_1 & a_group_isomorphism_from_to(all_48_2, all_48_1, % 8.85/2.07 | | | | | all_48_0) = 0 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) % 8.85/2.07 | | | | | % 8.85/2.07 | | | | | ALPHA: (56) implies: % 8.85/2.07 | | | | | (57) $i(all_48_2) % 8.85/2.08 | | | | | (58) a_group_isomorphism_from_to(all_48_2, all_48_1, all_48_0) = 0 % 8.85/2.08 | | | | | (59) first_homotop_grp(all_6_5, all_6_4) = all_48_1 % 8.85/2.08 | | | | | (60) first_homotop_grp(all_6_5, all_6_3) = all_48_0 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | GROUND_INST: instantiating (5) with all_42_1, all_46_0, all_6_4, % 8.85/2.08 | | | | | all_6_5, simplifying with (47), (54) gives: % 8.85/2.08 | | | | | (61) all_46_0 = all_42_1 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | GROUND_INST: instantiating (5) with all_6_2, all_48_1, all_6_4, % 8.85/2.08 | | | | | all_6_5, simplifying with (15), (59) gives: % 8.85/2.08 | | | | | (62) all_48_1 = all_6_2 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | GROUND_INST: instantiating (5) with all_46_0, all_48_1, all_6_4, % 8.85/2.08 | | | | | all_6_5, simplifying with (54), (59) gives: % 8.85/2.08 | | | | | (63) all_48_1 = all_46_0 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | GROUND_INST: instantiating (5) with all_42_0, all_48_1, all_6_4, % 8.85/2.08 | | | | | all_6_5, simplifying with (48), (59) gives: % 8.85/2.08 | | | | | (64) all_48_1 = all_42_0 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | GROUND_INST: instantiating (5) with all_6_1, all_44_0, all_6_3, % 8.85/2.08 | | | | | all_6_5, simplifying with (16), (52) gives: % 8.85/2.08 | | | | | (65) all_44_0 = all_6_1 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | GROUND_INST: instantiating (5) with all_44_0, all_46_1, all_6_3, % 8.85/2.08 | | | | | all_6_5, simplifying with (52), (55) gives: % 8.85/2.08 | | | | | (66) all_46_1 = all_44_0 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | GROUND_INST: instantiating (5) with all_46_1, all_48_0, all_6_3, % 8.85/2.08 | | | | | all_6_5, simplifying with (55), (60) gives: % 8.85/2.08 | | | | | (67) all_48_0 = all_46_1 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | GROUND_INST: instantiating (5) with all_44_1, all_48_0, all_6_3, % 8.85/2.08 | | | | | all_6_5, simplifying with (51), (60) gives: % 8.85/2.08 | | | | | (68) all_48_0 = all_44_1 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | COMBINE_EQS: (67), (68) imply: % 8.85/2.08 | | | | | (69) all_46_1 = all_44_1 % 8.85/2.08 | | | | | % 8.85/2.08 | | | | | SIMP: (69) implies: % 8.85/2.09 | | | | | (70) all_46_1 = all_44_1 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | COMBINE_EQS: (63), (64) imply: % 8.85/2.09 | | | | | (71) all_46_0 = all_42_0 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | SIMP: (71) implies: % 8.85/2.09 | | | | | (72) all_46_0 = all_42_0 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | COMBINE_EQS: (62), (64) imply: % 8.85/2.09 | | | | | (73) all_42_0 = all_6_2 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | COMBINE_EQS: (61), (72) imply: % 8.85/2.09 | | | | | (74) all_42_0 = all_42_1 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | SIMP: (74) implies: % 8.85/2.09 | | | | | (75) all_42_0 = all_42_1 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | COMBINE_EQS: (66), (70) imply: % 8.85/2.09 | | | | | (76) all_44_0 = all_44_1 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | SIMP: (76) implies: % 8.85/2.09 | | | | | (77) all_44_0 = all_44_1 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | COMBINE_EQS: (65), (77) imply: % 8.85/2.09 | | | | | (78) all_44_1 = all_6_1 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | SIMP: (78) implies: % 8.85/2.09 | | | | | (79) all_44_1 = all_6_1 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | COMBINE_EQS: (73), (75) imply: % 8.85/2.09 | | | | | (80) all_42_1 = all_6_2 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | SIMP: (80) implies: % 8.85/2.09 | | | | | (81) all_42_1 = all_6_2 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | COMBINE_EQS: (68), (79) imply: % 8.85/2.09 | | | | | (82) all_48_0 = all_6_1 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | REDUCE: (58), (62), (82) imply: % 8.85/2.09 | | | | | (83) a_group_isomorphism_from_to(all_48_2, all_6_2, all_6_1) = 0 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | REDUCE: (50), (79) imply: % 8.85/2.09 | | | | | (84) $i(all_6_1) % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | REDUCE: (46), (81) imply: % 8.85/2.09 | | | | | (85) $i(all_6_2) % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | GROUND_INST: instantiating (1) with all_6_2, all_6_1, all_6_0, % 8.85/2.09 | | | | | all_48_2, simplifying with (11), (57), (83), (84), (85) % 8.85/2.09 | | | | | gives: % 8.85/2.09 | | | | | (86) all_6_0 = 0 % 8.85/2.09 | | | | | % 8.85/2.09 | | | | | REDUCE: (7), (86) imply: % 8.85/2.09 | | | | | (87) $false % 8.85/2.10 | | | | | % 8.85/2.10 | | | | | CLOSE: (87) is inconsistent. % 8.85/2.10 | | | | | % 8.85/2.10 | | | | Case 2: % 8.85/2.10 | | | | | % 8.85/2.10 | | | | | (88) ~ (all_17_2 = 0) & path_connected(all_6_5) = all_17_2 % 8.85/2.10 | | | | | % 8.85/2.10 | | | | | ALPHA: (88) implies: % 8.85/2.10 | | | | | (89) ~ (all_17_2 = 0) % 8.85/2.10 | | | | | (90) path_connected(all_6_5) = all_17_2 % 8.85/2.10 | | | | | % 8.85/2.10 | | | | | GROUND_INST: instantiating (4) with 0, all_17_2, all_6_5, simplifying % 8.85/2.10 | | | | | with (12), (90) gives: % 8.85/2.10 | | | | | (91) all_17_2 = 0 % 8.85/2.10 | | | | | % 8.85/2.10 | | | | | REDUCE: (89), (91) imply: % 8.85/2.10 | | | | | (92) $false % 8.85/2.10 | | | | | % 8.85/2.10 | | | | | CLOSE: (92) is inconsistent. % 8.85/2.10 | | | | | % 8.85/2.10 | | | | End of split % 8.85/2.10 | | | | % 8.85/2.10 | | | Case 2: % 8.85/2.10 | | | | % 8.85/2.10 | | | | (93) ~ (all_19_2 = 0) & path_connected(all_6_5) = all_19_2 % 8.85/2.10 | | | | % 8.85/2.10 | | | | ALPHA: (93) implies: % 8.85/2.10 | | | | (94) ~ (all_19_2 = 0) % 8.85/2.10 | | | | (95) path_connected(all_6_5) = all_19_2 % 8.85/2.10 | | | | % 8.85/2.10 | | | | GROUND_INST: instantiating (4) with 0, all_19_2, all_6_5, simplifying % 8.85/2.10 | | | | with (12), (95) gives: % 8.85/2.10 | | | | (96) all_19_2 = 0 % 8.85/2.10 | | | | % 8.85/2.10 | | | | REDUCE: (94), (96) imply: % 8.85/2.10 | | | | (97) $false % 8.85/2.10 | | | | % 8.85/2.10 | | | | CLOSE: (97) is inconsistent. % 8.85/2.10 | | | | % 8.85/2.10 | | | End of split % 8.85/2.10 | | | % 8.85/2.10 | | Case 2: % 8.85/2.10 | | | % 8.85/2.10 | | | (98) ~ (all_13_2 = 0) & path_connected(all_6_5) = all_13_2 % 8.85/2.10 | | | % 8.85/2.10 | | | ALPHA: (98) implies: % 8.85/2.11 | | | (99) ~ (all_13_2 = 0) % 8.85/2.11 | | | (100) path_connected(all_6_5) = all_13_2 % 8.85/2.11 | | | % 8.85/2.11 | | | GROUND_INST: instantiating (4) with 0, all_13_2, all_6_5, simplifying with % 8.85/2.11 | | | (12), (100) gives: % 8.85/2.11 | | | (101) all_13_2 = 0 % 8.85/2.11 | | | % 8.85/2.11 | | | REDUCE: (99), (101) imply: % 8.85/2.11 | | | (102) $false % 8.85/2.11 | | | % 8.85/2.11 | | | CLOSE: (102) is inconsistent. % 8.85/2.11 | | | % 8.85/2.11 | | End of split % 8.85/2.11 | | % 8.85/2.11 | Case 2: % 8.85/2.11 | | % 8.85/2.11 | | (103) ~ (all_15_2 = 0) & path_connected(all_6_5) = all_15_2 % 8.85/2.11 | | % 8.85/2.11 | | ALPHA: (103) implies: % 8.85/2.11 | | (104) ~ (all_15_2 = 0) % 8.85/2.11 | | (105) path_connected(all_6_5) = all_15_2 % 8.85/2.11 | | % 8.85/2.11 | | GROUND_INST: instantiating (4) with 0, all_15_2, all_6_5, simplifying with % 8.85/2.11 | | (12), (105) gives: % 8.85/2.11 | | (106) all_15_2 = 0 % 8.85/2.11 | | % 8.85/2.11 | | REDUCE: (104), (106) imply: % 8.85/2.11 | | (107) $false % 8.85/2.11 | | % 8.85/2.11 | | CLOSE: (107) is inconsistent. % 8.85/2.11 | | % 8.85/2.11 | End of split % 8.85/2.11 | % 8.85/2.11 End of proof % 8.85/2.11 % SZS output end Proof for theBenchmark % 8.85/2.11 % 8.85/2.11 1472ms %------------------------------------------------------------------------------