%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : REL008+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n028.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 13:42:46 EDT 2023 % Result : Theorem 8.08s 1.83s % Output : Proof 10.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : REL008+3 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n028.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 21:54:21 EDT 2023 % 0.14/0.34 % 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/sandbox2/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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 1.98/1.06 Prover 4: Preprocessing ... % 1.98/1.06 Prover 1: Preprocessing ... % 2.65/1.09 Prover 3: Preprocessing ... % 2.65/1.09 Prover 5: Preprocessing ... % 2.65/1.09 Prover 2: Preprocessing ... % 2.92/1.09 Prover 6: Preprocessing ... % 2.92/1.09 Prover 0: Preprocessing ... % 4.16/1.37 Prover 6: Constructing countermodel ... % 4.16/1.41 Prover 1: Constructing countermodel ... % 4.16/1.42 Prover 3: Constructing countermodel ... % 4.16/1.45 Prover 4: Constructing countermodel ... % 5.46/1.47 Prover 5: Proving ... % 5.46/1.47 Prover 0: Proving ... % 6.14/1.56 Prover 3: gave up % 6.14/1.56 Prover 1: gave up % 6.14/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.14/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.14/1.58 Prover 2: Proving ... % 6.14/1.60 Prover 7: Preprocessing ... % 6.14/1.62 Prover 8: Preprocessing ... % 6.14/1.63 Prover 6: gave up % 6.14/1.63 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.84/1.66 Prover 9: Preprocessing ... % 7.22/1.70 Prover 8: Warning: ignoring some quantifiers % 7.22/1.72 Prover 8: Constructing countermodel ... % 7.22/1.74 Prover 7: Constructing countermodel ... % 8.08/1.80 Prover 9: Constructing countermodel ... % 8.08/1.81 Prover 0: proved (1178ms) % 8.08/1.83 % 8.08/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.08/1.83 % 8.08/1.83 Prover 9: stopped % 8.08/1.83 Prover 5: stopped % 8.08/1.84 Prover 2: stopped % 8.08/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.08/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.08/1.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.34/1.84 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.34/1.88 Prover 8: gave up % 8.34/1.89 Prover 13: Preprocessing ... % 8.34/1.89 Prover 10: Preprocessing ... % 8.34/1.90 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.34/1.90 Prover 11: Preprocessing ... % 8.34/1.91 Prover 16: Preprocessing ... % 8.99/1.94 Prover 19: Preprocessing ... % 8.99/1.98 Prover 10: Constructing countermodel ... % 8.99/1.99 Prover 11: Constructing countermodel ... % 9.42/1.99 Prover 13: Warning: ignoring some quantifiers % 9.42/2.00 Prover 13: Constructing countermodel ... % 9.42/2.00 Prover 19: Warning: ignoring some quantifiers % 9.42/2.01 Prover 16: Warning: ignoring some quantifiers % 9.42/2.01 Prover 16: Constructing countermodel ... % 9.42/2.01 Prover 10: gave up % 9.42/2.03 Prover 19: Constructing countermodel ... % 9.42/2.10 Prover 19: gave up % 9.42/2.13 Prover 4: Found proof (size 87) % 9.42/2.13 Prover 4: proved (1500ms) % 9.42/2.13 Prover 16: stopped % 9.42/2.13 Prover 13: stopped % 9.42/2.13 Prover 11: stopped % 9.42/2.13 Prover 7: stopped % 9.42/2.14 % 9.42/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.42/2.14 % 10.47/2.15 % SZS output start Proof for theBenchmark % 10.47/2.16 Assumptions after simplification: % 10.47/2.16 --------------------------------- % 10.47/2.16 % 10.47/2.16 (composition_distributivity) % 10.58/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 10.58/2.19 $i] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) = v3) | ~ % 10.58/2.19 (join(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 10.58/2.19 (composition(v6, v2) = v5 & join(v0, v1) = v6 & $i(v6) & $i(v5))) & ! [v0: % 10.58/2.19 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 10.58/2.19 (composition(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 10.58/2.19 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (composition(v1, v2) = v6 & % 10.58/2.19 composition(v0, v2) = v5 & join(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 10.58/2.19 % 10.58/2.19 (converse_additivity) % 10.58/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 10.58/2.19 (converse(v1) = v3) | ~ (converse(v0) = v2) | ~ (join(v2, v3) = v4) | ~ % 10.58/2.19 $i(v1) | ~ $i(v0) | ? [v5: $i] : (converse(v5) = v4 & join(v0, v1) = v5 & % 10.58/2.19 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.58/2.19 (join(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 10.58/2.19 [v5: $i] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & % 10.58/2.19 join(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 10.58/2.19 % 10.58/2.19 (converse_cancellativity) % 10.58/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (composition(v0, v1) = v2) | ~ % 10.58/2.19 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 10.58/2.19 (converse(v0) = v3 & composition(v3, v4) = v5 & complement(v2) = v4 & % 10.58/2.19 complement(v1) = v6 & join(v5, v6) = v6 & $i(v6) & $i(v5) & $i(v4) & % 10.58/2.19 $i(v3))) % 10.58/2.19 % 10.58/2.19 (converse_idempotence) % 10.58/2.19 ! [v0: $i] : ! [v1: $i] : ( ~ (converse(v0) = v1) | ~ $i(v0) | converse(v1) % 10.58/2.19 = v0) % 10.58/2.19 % 10.58/2.19 (converse_multiplicativity) % 10.58/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 10.58/2.19 (converse(v1) = v2) | ~ (converse(v0) = v3) | ~ (composition(v2, v3) = v4) % 10.58/2.19 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (converse(v5) = v4 & composition(v0, % 10.58/2.20 v1) = v5 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 10.58/2.20 ( ~ (composition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 10.58/2.20 $i] : ? [v5: $i] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) % 10.58/2.20 = v5 & composition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 10.58/2.20 % 10.58/2.20 (goals) % 10.58/2.20 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 10.58/2.20 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v4) & composition(v0, v3) = v4 & % 10.58/2.20 composition(v0, v2) = v6 & composition(v0, v1) = v5 & join(v5, v6) = v7 & % 10.58/2.20 join(v1, v2) = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 10.58/2.20 $i(v1) & $i(v0)) % 10.58/2.20 % 10.58/2.20 (maddux1_join_commutativity) % 10.58/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v1, v0) = v2) | ~ $i(v1) % 10.58/2.20 | ~ $i(v0) | (join(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! % 10.58/2.20 [v2: $i] : ( ~ (join(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (join(v1, v0) = % 10.58/2.20 v2 & $i(v2))) % 10.58/2.20 % 10.58/2.20 (function-axioms) % 10.58/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.58/2.20 (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) & ! [v0: $i] : % 10.58/2.20 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (meet(v3, v2) = v1) | % 10.58/2.20 ~ (meet(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 10.58/2.20 $i] : (v1 = v0 | ~ (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) & ! [v0: % 10.58/2.20 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) = v1) | ~ % 10.58/2.20 (converse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 10.58/2.20 ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) % 10.58/2.20 % 10.58/2.20 Further assumptions not needed in the proof: % 10.58/2.20 -------------------------------------------- % 10.58/2.20 composition_associativity, composition_identity, dedekind_law, def_top, % 10.58/2.20 def_zero, maddux2_join_associativity, maddux3_a_kind_of_de_Morgan, % 10.58/2.20 maddux4_definiton_of_meet, modular_law_1, modular_law_2 % 10.58/2.20 % 10.58/2.20 Those formulas are unsatisfiable: % 10.58/2.20 --------------------------------- % 10.58/2.20 % 10.58/2.20 Begin of proof % 10.58/2.20 | % 10.58/2.20 | ALPHA: (maddux1_join_commutativity) implies: % 10.58/2.20 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v1, v0) = v2) | ~ % 10.58/2.20 | $i(v1) | ~ $i(v0) | (join(v0, v1) = v2 & $i(v2))) % 10.58/2.20 | % 10.58/2.20 | ALPHA: (composition_distributivity) implies: % 10.58/2.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 10.58/2.20 | ! [v5: $i] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) = % 10.58/2.20 | v3) | ~ (join(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.58/2.20 | ? [v6: $i] : (composition(v6, v2) = v5 & join(v0, v1) = v6 & $i(v6) & % 10.58/2.20 | $i(v5))) % 10.58/2.20 | % 10.58/2.20 | ALPHA: (converse_additivity) implies: % 10.58/2.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v0, v1) = v2) | ~ % 10.58/2.20 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 10.58/2.20 | (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, % 10.58/2.21 | v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 10.58/2.21 | % 10.58/2.21 | ALPHA: (converse_multiplicativity) implies: % 10.58/2.21 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (composition(v0, v1) = % 10.58/2.21 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 10.58/2.21 | $i] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & % 10.58/2.21 | composition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 10.58/2.21 | % 10.58/2.21 | ALPHA: (function-axioms) implies: % 10.58/2.21 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) = % 10.58/2.21 | v1) | ~ (converse(v2) = v0)) % 10.58/2.21 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.58/2.21 | (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) % 10.58/2.21 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.58/2.21 | (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) % 10.81/2.21 | % 10.81/2.21 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2, % 10.81/2.21 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7 gives: % 10.81/2.21 | (8) ~ (all_20_0 = all_20_3) & composition(all_20_7, all_20_4) = all_20_3 & % 10.81/2.21 | composition(all_20_7, all_20_5) = all_20_1 & composition(all_20_7, % 10.81/2.21 | all_20_6) = all_20_2 & join(all_20_2, all_20_1) = all_20_0 & % 10.81/2.21 | join(all_20_6, all_20_5) = all_20_4 & $i(all_20_0) & $i(all_20_1) & % 10.81/2.21 | $i(all_20_2) & $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & % 10.81/2.21 | $i(all_20_6) & $i(all_20_7) % 10.81/2.21 | % 10.81/2.21 | ALPHA: (8) implies: % 10.81/2.21 | (9) ~ (all_20_0 = all_20_3) % 10.81/2.21 | (10) $i(all_20_7) % 10.81/2.21 | (11) $i(all_20_6) % 10.81/2.21 | (12) $i(all_20_5) % 10.81/2.21 | (13) $i(all_20_3) % 10.81/2.21 | (14) $i(all_20_2) % 10.81/2.21 | (15) $i(all_20_1) % 10.81/2.21 | (16) join(all_20_6, all_20_5) = all_20_4 % 10.81/2.21 | (17) join(all_20_2, all_20_1) = all_20_0 % 10.81/2.21 | (18) composition(all_20_7, all_20_6) = all_20_2 % 10.81/2.21 | (19) composition(all_20_7, all_20_5) = all_20_1 % 10.81/2.21 | (20) composition(all_20_7, all_20_4) = all_20_3 % 10.81/2.21 | % 10.81/2.21 | GROUND_INST: instantiating (1) with all_20_5, all_20_6, all_20_4, simplifying % 10.81/2.21 | with (11), (12), (16) gives: % 10.81/2.21 | (21) join(all_20_5, all_20_6) = all_20_4 & $i(all_20_4) % 10.81/2.21 | % 10.81/2.21 | ALPHA: (21) implies: % 10.81/2.21 | (22) $i(all_20_4) % 10.81/2.21 | % 10.81/2.21 | GROUND_INST: instantiating (3) with all_20_6, all_20_5, all_20_4, simplifying % 10.81/2.21 | with (11), (12), (16) gives: % 10.81/2.22 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_4) = v0 & % 10.81/2.22 | converse(all_20_5) = v2 & converse(all_20_6) = v1 & join(v1, v2) = % 10.81/2.22 | v0 & $i(v2) & $i(v1) & $i(v0)) % 10.81/2.22 | % 10.81/2.22 | GROUND_INST: instantiating (1) with all_20_1, all_20_2, all_20_0, simplifying % 10.81/2.22 | with (14), (15), (17) gives: % 10.81/2.22 | (24) join(all_20_1, all_20_2) = all_20_0 & $i(all_20_0) % 10.81/2.22 | % 10.81/2.22 | ALPHA: (24) implies: % 10.81/2.22 | (25) $i(all_20_0) % 10.81/2.22 | % 10.81/2.22 | GROUND_INST: instantiating (3) with all_20_2, all_20_1, all_20_0, simplifying % 10.81/2.22 | with (14), (15), (17) gives: % 10.81/2.22 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_0) = v0 & % 10.81/2.22 | converse(all_20_1) = v2 & converse(all_20_2) = v1 & join(v1, v2) = % 10.81/2.22 | v0 & $i(v2) & $i(v1) & $i(v0)) % 10.81/2.22 | % 10.81/2.22 | GROUND_INST: instantiating (converse_cancellativity) with all_20_7, all_20_6, % 10.81/2.22 | all_20_2, simplifying with (10), (11), (18) gives: % 10.81/2.22 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 10.81/2.22 | (converse(all_20_7) = v0 & composition(v0, v1) = v2 & % 10.81/2.22 | complement(all_20_2) = v1 & complement(all_20_6) = v3 & join(v2, v3) % 10.81/2.22 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.81/2.22 | % 10.81/2.22 | GROUND_INST: instantiating (4) with all_20_7, all_20_6, all_20_2, simplifying % 10.81/2.22 | with (10), (11), (18) gives: % 10.81/2.22 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_2) = v0 & % 10.81/2.22 | converse(all_20_6) = v1 & converse(all_20_7) = v2 & composition(v1, % 10.81/2.22 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 10.81/2.22 | % 10.81/2.22 | GROUND_INST: instantiating (converse_cancellativity) with all_20_7, all_20_5, % 10.81/2.22 | all_20_1, simplifying with (10), (12), (19) gives: % 10.81/2.22 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 10.81/2.22 | (converse(all_20_7) = v0 & composition(v0, v1) = v2 & % 10.81/2.22 | complement(all_20_1) = v1 & complement(all_20_5) = v3 & join(v2, v3) % 10.81/2.22 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.81/2.22 | % 10.81/2.22 | GROUND_INST: instantiating (4) with all_20_7, all_20_5, all_20_1, simplifying % 10.81/2.22 | with (10), (12), (19) gives: % 10.81/2.22 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_1) = v0 & % 10.81/2.22 | converse(all_20_5) = v1 & converse(all_20_7) = v2 & composition(v1, % 10.81/2.22 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 10.81/2.22 | % 10.81/2.22 | GROUND_INST: instantiating (converse_cancellativity) with all_20_7, all_20_4, % 10.81/2.22 | all_20_3, simplifying with (10), (20), (22) gives: % 10.81/2.22 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 10.81/2.22 | (converse(all_20_7) = v0 & composition(v0, v1) = v2 & % 10.81/2.22 | complement(all_20_3) = v1 & complement(all_20_4) = v3 & join(v2, v3) % 10.81/2.22 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.81/2.22 | % 10.81/2.22 | GROUND_INST: instantiating (4) with all_20_7, all_20_4, all_20_3, simplifying % 10.81/2.22 | with (10), (20), (22) gives: % 10.81/2.22 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_3) = v0 & % 10.81/2.22 | converse(all_20_4) = v1 & converse(all_20_7) = v2 & composition(v1, % 10.81/2.22 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 10.81/2.22 | % 10.81/2.22 | DELTA: instantiating (23) with fresh symbols all_28_0, all_28_1, all_28_2 % 10.81/2.22 | gives: % 10.81/2.22 | (33) converse(all_20_4) = all_28_2 & converse(all_20_5) = all_28_0 & % 10.81/2.22 | converse(all_20_6) = all_28_1 & join(all_28_1, all_28_0) = all_28_2 & % 10.81/2.22 | $i(all_28_0) & $i(all_28_1) & $i(all_28_2) % 10.81/2.22 | % 10.81/2.22 | ALPHA: (33) implies: % 10.81/2.22 | (34) join(all_28_1, all_28_0) = all_28_2 % 10.81/2.22 | (35) converse(all_20_6) = all_28_1 % 10.81/2.22 | (36) converse(all_20_5) = all_28_0 % 10.81/2.22 | (37) converse(all_20_4) = all_28_2 % 10.81/2.22 | % 10.81/2.22 | DELTA: instantiating (32) with fresh symbols all_30_0, all_30_1, all_30_2 % 10.81/2.22 | gives: % 10.81/2.23 | (38) converse(all_20_3) = all_30_2 & converse(all_20_4) = all_30_1 & % 10.81/2.23 | converse(all_20_7) = all_30_0 & composition(all_30_1, all_30_0) = % 10.81/2.23 | all_30_2 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) % 10.81/2.23 | % 10.81/2.23 | ALPHA: (38) implies: % 10.81/2.23 | (39) composition(all_30_1, all_30_0) = all_30_2 % 10.81/2.23 | (40) converse(all_20_7) = all_30_0 % 10.81/2.23 | (41) converse(all_20_4) = all_30_1 % 10.81/2.23 | (42) converse(all_20_3) = all_30_2 % 10.81/2.23 | % 10.81/2.23 | DELTA: instantiating (30) with fresh symbols all_32_0, all_32_1, all_32_2 % 10.81/2.23 | gives: % 10.81/2.23 | (43) converse(all_20_1) = all_32_2 & converse(all_20_5) = all_32_1 & % 10.81/2.23 | converse(all_20_7) = all_32_0 & composition(all_32_1, all_32_0) = % 10.81/2.23 | all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) % 10.81/2.23 | % 10.81/2.23 | ALPHA: (43) implies: % 10.81/2.23 | (44) $i(all_32_1) % 10.81/2.23 | (45) $i(all_32_0) % 10.81/2.23 | (46) composition(all_32_1, all_32_0) = all_32_2 % 10.81/2.23 | (47) converse(all_20_7) = all_32_0 % 10.81/2.23 | (48) converse(all_20_5) = all_32_1 % 10.81/2.23 | (49) converse(all_20_1) = all_32_2 % 10.81/2.23 | % 10.81/2.23 | DELTA: instantiating (26) with fresh symbols all_34_0, all_34_1, all_34_2 % 10.81/2.23 | gives: % 10.81/2.23 | (50) converse(all_20_0) = all_34_2 & converse(all_20_1) = all_34_0 & % 10.81/2.23 | converse(all_20_2) = all_34_1 & join(all_34_1, all_34_0) = all_34_2 & % 10.81/2.23 | $i(all_34_0) & $i(all_34_1) & $i(all_34_2) % 10.81/2.23 | % 10.81/2.23 | ALPHA: (50) implies: % 10.81/2.23 | (51) $i(all_34_0) % 10.81/2.23 | (52) join(all_34_1, all_34_0) = all_34_2 % 10.81/2.23 | (53) converse(all_20_2) = all_34_1 % 10.81/2.23 | (54) converse(all_20_1) = all_34_0 % 10.81/2.23 | (55) converse(all_20_0) = all_34_2 % 10.81/2.23 | % 10.81/2.23 | DELTA: instantiating (28) with fresh symbols all_36_0, all_36_1, all_36_2 % 10.81/2.23 | gives: % 10.81/2.23 | (56) converse(all_20_2) = all_36_2 & converse(all_20_6) = all_36_1 & % 10.81/2.23 | converse(all_20_7) = all_36_0 & composition(all_36_1, all_36_0) = % 10.81/2.23 | all_36_2 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) % 10.81/2.23 | % 10.81/2.23 | ALPHA: (56) implies: % 10.81/2.23 | (57) $i(all_36_2) % 10.81/2.23 | (58) $i(all_36_1) % 10.81/2.23 | (59) composition(all_36_1, all_36_0) = all_36_2 % 10.81/2.23 | (60) converse(all_20_7) = all_36_0 % 10.81/2.23 | (61) converse(all_20_6) = all_36_1 % 10.81/2.23 | (62) converse(all_20_2) = all_36_2 % 10.81/2.23 | % 10.81/2.23 | DELTA: instantiating (31) with fresh symbols all_38_0, all_38_1, all_38_2, % 10.81/2.23 | all_38_3 gives: % 10.81/2.23 | (63) converse(all_20_7) = all_38_3 & composition(all_38_3, all_38_2) = % 10.81/2.23 | all_38_1 & complement(all_20_3) = all_38_2 & complement(all_20_4) = % 10.81/2.23 | all_38_0 & join(all_38_1, all_38_0) = all_38_0 & $i(all_38_0) & % 10.81/2.23 | $i(all_38_1) & $i(all_38_2) & $i(all_38_3) % 10.81/2.23 | % 10.81/2.23 | ALPHA: (63) implies: % 10.81/2.23 | (64) converse(all_20_7) = all_38_3 % 10.81/2.23 | % 10.81/2.23 | DELTA: instantiating (29) with fresh symbols all_40_0, all_40_1, all_40_2, % 10.81/2.23 | all_40_3 gives: % 10.81/2.23 | (65) converse(all_20_7) = all_40_3 & composition(all_40_3, all_40_2) = % 10.81/2.23 | all_40_1 & complement(all_20_1) = all_40_2 & complement(all_20_5) = % 10.81/2.23 | all_40_0 & join(all_40_1, all_40_0) = all_40_0 & $i(all_40_0) & % 10.81/2.23 | $i(all_40_1) & $i(all_40_2) & $i(all_40_3) % 10.81/2.23 | % 10.81/2.23 | ALPHA: (65) implies: % 10.81/2.23 | (66) converse(all_20_7) = all_40_3 % 10.81/2.23 | % 10.81/2.23 | DELTA: instantiating (27) with fresh symbols all_42_0, all_42_1, all_42_2, % 10.81/2.23 | all_42_3 gives: % 10.81/2.23 | (67) converse(all_20_7) = all_42_3 & composition(all_42_3, all_42_2) = % 10.81/2.23 | all_42_1 & complement(all_20_2) = all_42_2 & complement(all_20_6) = % 10.81/2.23 | all_42_0 & join(all_42_1, all_42_0) = all_42_0 & $i(all_42_0) & % 10.81/2.23 | $i(all_42_1) & $i(all_42_2) & $i(all_42_3) % 10.81/2.23 | % 10.81/2.23 | ALPHA: (67) implies: % 10.81/2.23 | (68) converse(all_20_7) = all_42_3 % 10.81/2.23 | % 10.81/2.23 | GROUND_INST: instantiating (5) with all_38_3, all_40_3, all_20_7, simplifying % 10.81/2.23 | with (64), (66) gives: % 10.81/2.23 | (69) all_40_3 = all_38_3 % 10.81/2.23 | % 10.81/2.23 | GROUND_INST: instantiating (5) with all_36_0, all_40_3, all_20_7, simplifying % 10.81/2.23 | with (60), (66) gives: % 10.81/2.23 | (70) all_40_3 = all_36_0 % 10.81/2.23 | % 10.81/2.23 | GROUND_INST: instantiating (5) with all_32_0, all_40_3, all_20_7, simplifying % 10.81/2.23 | with (47), (66) gives: % 10.81/2.23 | (71) all_40_3 = all_32_0 % 10.81/2.23 | % 10.81/2.23 | GROUND_INST: instantiating (5) with all_38_3, all_42_3, all_20_7, simplifying % 10.81/2.23 | with (64), (68) gives: % 10.81/2.23 | (72) all_42_3 = all_38_3 % 10.81/2.23 | % 10.81/2.24 | GROUND_INST: instantiating (5) with all_30_0, all_42_3, all_20_7, simplifying % 10.81/2.24 | with (40), (68) gives: % 10.81/2.24 | (73) all_42_3 = all_30_0 % 10.81/2.24 | % 10.81/2.24 | GROUND_INST: instantiating (5) with all_28_1, all_36_1, all_20_6, simplifying % 10.81/2.24 | with (35), (61) gives: % 10.81/2.24 | (74) all_36_1 = all_28_1 % 10.81/2.24 | % 10.81/2.24 | GROUND_INST: instantiating (5) with all_28_0, all_32_1, all_20_5, simplifying % 10.81/2.24 | with (36), (48) gives: % 10.81/2.24 | (75) all_32_1 = all_28_0 % 10.81/2.24 | % 10.81/2.24 | GROUND_INST: instantiating (5) with all_28_2, all_30_1, all_20_4, simplifying % 10.81/2.24 | with (37), (41) gives: % 10.81/2.24 | (76) all_30_1 = all_28_2 % 10.81/2.24 | % 10.81/2.24 | GROUND_INST: instantiating (5) with all_34_1, all_36_2, all_20_2, simplifying % 10.81/2.24 | with (53), (62) gives: % 10.81/2.24 | (77) all_36_2 = all_34_1 % 10.81/2.24 | % 10.81/2.24 | GROUND_INST: instantiating (5) with all_32_2, all_34_0, all_20_1, simplifying % 10.81/2.24 | with (49), (54) gives: % 10.81/2.24 | (78) all_34_0 = all_32_2 % 10.81/2.24 | % 10.81/2.24 | COMBINE_EQS: (72), (73) imply: % 10.81/2.24 | (79) all_38_3 = all_30_0 % 10.81/2.24 | % 10.81/2.24 | SIMP: (79) implies: % 10.81/2.24 | (80) all_38_3 = all_30_0 % 10.81/2.24 | % 10.81/2.24 | COMBINE_EQS: (70), (71) imply: % 10.81/2.24 | (81) all_36_0 = all_32_0 % 10.81/2.24 | % 10.81/2.24 | COMBINE_EQS: (69), (70) imply: % 10.81/2.24 | (82) all_38_3 = all_36_0 % 10.81/2.24 | % 10.81/2.24 | SIMP: (82) implies: % 10.81/2.24 | (83) all_38_3 = all_36_0 % 10.81/2.24 | % 10.81/2.24 | COMBINE_EQS: (80), (83) imply: % 10.81/2.24 | (84) all_36_0 = all_30_0 % 10.81/2.24 | % 10.81/2.24 | SIMP: (84) implies: % 10.81/2.24 | (85) all_36_0 = all_30_0 % 10.81/2.24 | % 10.81/2.24 | COMBINE_EQS: (81), (85) imply: % 10.81/2.24 | (86) all_32_0 = all_30_0 % 10.81/2.24 | % 10.81/2.24 | SIMP: (86) implies: % 10.81/2.24 | (87) all_32_0 = all_30_0 % 10.81/2.24 | % 10.81/2.24 | REDUCE: (59), (74), (77), (85) imply: % 10.81/2.24 | (88) composition(all_28_1, all_30_0) = all_34_1 % 10.81/2.24 | % 10.81/2.24 | REDUCE: (46), (75), (87) imply: % 10.81/2.24 | (89) composition(all_28_0, all_30_0) = all_32_2 % 10.81/2.24 | % 10.81/2.24 | REDUCE: (39), (76) imply: % 10.81/2.24 | (90) composition(all_28_2, all_30_0) = all_30_2 % 10.81/2.24 | % 10.81/2.24 | REDUCE: (52), (78) imply: % 10.81/2.24 | (91) join(all_34_1, all_32_2) = all_34_2 % 10.81/2.24 | % 10.81/2.24 | REDUCE: (58), (74) imply: % 10.81/2.24 | (92) $i(all_28_1) % 10.81/2.24 | % 10.81/2.24 | REDUCE: (57), (77) imply: % 10.81/2.24 | (93) $i(all_34_1) % 10.81/2.24 | % 10.81/2.24 | REDUCE: (51), (78) imply: % 10.81/2.24 | (94) $i(all_32_2) % 10.81/2.24 | % 10.81/2.24 | REDUCE: (45), (87) imply: % 10.81/2.24 | (95) $i(all_30_0) % 10.81/2.24 | % 10.81/2.24 | REDUCE: (44), (75) imply: % 10.81/2.24 | (96) $i(all_28_0) % 10.81/2.24 | % 10.81/2.24 | GROUND_INST: instantiating (1) with all_28_0, all_28_1, all_28_2, simplifying % 10.81/2.24 | with (34), (92), (96) gives: % 10.81/2.24 | (97) join(all_28_0, all_28_1) = all_28_2 & $i(all_28_2) % 10.81/2.24 | % 10.81/2.24 | ALPHA: (97) implies: % 10.81/2.24 | (98) $i(all_28_2) % 10.81/2.24 | % 10.81/2.24 | GROUND_INST: instantiating (3) with all_34_1, all_32_2, all_34_2, simplifying % 10.81/2.24 | with (91), (93), (94) gives: % 10.81/2.24 | (99) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_34_1) = v1 & % 10.99/2.24 | converse(all_34_2) = v0 & converse(all_32_2) = v2 & join(v1, v2) = % 10.99/2.24 | v0 & $i(v2) & $i(v1) & $i(v0)) % 10.99/2.24 | % 10.99/2.24 | GROUND_INST: instantiating (4) with all_28_2, all_30_0, all_30_2, simplifying % 10.99/2.24 | with (90), (95), (98) gives: % 10.99/2.24 | (100) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_30_0) = v1 & % 10.99/2.24 | converse(all_30_2) = v0 & converse(all_28_2) = v2 & composition(v1, % 10.99/2.24 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 10.99/2.24 | % 10.99/2.25 | GROUND_INST: instantiating (2) with all_28_1, all_28_0, all_30_0, all_34_1, % 10.99/2.25 | all_32_2, all_34_2, simplifying with (88), (89), (91), (92), % 10.99/2.25 | (95), (96) gives: % 10.99/2.25 | (101) ? [v0: $i] : (composition(v0, all_30_0) = all_34_2 & join(all_28_1, % 10.99/2.25 | all_28_0) = v0 & $i(v0) & $i(all_34_2)) % 10.99/2.25 | % 10.99/2.25 | GROUND_INST: instantiating (converse_idempotence) with all_20_3, all_30_2, % 10.99/2.25 | simplifying with (13), (42) gives: % 10.99/2.25 | (102) converse(all_30_2) = all_20_3 % 10.99/2.25 | % 10.99/2.25 | GROUND_INST: instantiating (converse_idempotence) with all_20_0, all_34_2, % 10.99/2.25 | simplifying with (25), (55) gives: % 10.99/2.25 | (103) converse(all_34_2) = all_20_0 % 10.99/2.25 | % 10.99/2.25 | DELTA: instantiating (101) with fresh symbol all_60_0 gives: % 10.99/2.25 | (104) composition(all_60_0, all_30_0) = all_34_2 & join(all_28_1, all_28_0) % 10.99/2.25 | = all_60_0 & $i(all_60_0) & $i(all_34_2) % 10.99/2.25 | % 10.99/2.25 | ALPHA: (104) implies: % 10.99/2.25 | (105) join(all_28_1, all_28_0) = all_60_0 % 10.99/2.25 | (106) composition(all_60_0, all_30_0) = all_34_2 % 10.99/2.25 | % 10.99/2.25 | DELTA: instantiating (100) with fresh symbols all_86_0, all_86_1, all_86_2 % 10.99/2.25 | gives: % 10.99/2.25 | (107) converse(all_30_0) = all_86_1 & converse(all_30_2) = all_86_2 & % 10.99/2.25 | converse(all_28_2) = all_86_0 & composition(all_86_1, all_86_0) = % 10.99/2.25 | all_86_2 & $i(all_86_0) & $i(all_86_1) & $i(all_86_2) % 10.99/2.25 | % 10.99/2.25 | ALPHA: (107) implies: % 10.99/2.25 | (108) converse(all_30_2) = all_86_2 % 10.99/2.25 | % 10.99/2.25 | DELTA: instantiating (99) with fresh symbols all_88_0, all_88_1, all_88_2 % 10.99/2.25 | gives: % 10.99/2.25 | (109) converse(all_34_1) = all_88_1 & converse(all_34_2) = all_88_2 & % 10.99/2.25 | converse(all_32_2) = all_88_0 & join(all_88_1, all_88_0) = all_88_2 & % 10.99/2.25 | $i(all_88_0) & $i(all_88_1) & $i(all_88_2) % 10.99/2.25 | % 10.99/2.25 | ALPHA: (109) implies: % 10.99/2.25 | (110) converse(all_34_2) = all_88_2 % 10.99/2.25 | % 10.99/2.25 | GROUND_INST: instantiating (6) with all_28_2, all_60_0, all_28_0, all_28_1, % 10.99/2.25 | simplifying with (34), (105) gives: % 10.99/2.25 | (111) all_60_0 = all_28_2 % 10.99/2.25 | % 10.99/2.25 | GROUND_INST: instantiating (5) with all_20_3, all_86_2, all_30_2, simplifying % 10.99/2.25 | with (102), (108) gives: % 10.99/2.25 | (112) all_86_2 = all_20_3 % 10.99/2.25 | % 10.99/2.25 | GROUND_INST: instantiating (5) with all_20_0, all_88_2, all_34_2, simplifying % 10.99/2.25 | with (103), (110) gives: % 10.99/2.25 | (113) all_88_2 = all_20_0 % 10.99/2.25 | % 10.99/2.25 | REDUCE: (106), (111) imply: % 10.99/2.25 | (114) composition(all_28_2, all_30_0) = all_34_2 % 10.99/2.25 | % 10.99/2.25 | GROUND_INST: instantiating (7) with all_30_2, all_34_2, all_30_0, all_28_2, % 10.99/2.25 | simplifying with (90), (114) gives: % 10.99/2.25 | (115) all_34_2 = all_30_2 % 10.99/2.25 | % 10.99/2.25 | REDUCE: (103), (115) imply: % 10.99/2.25 | (116) converse(all_30_2) = all_20_0 % 10.99/2.25 | % 10.99/2.25 | GROUND_INST: instantiating (5) with all_20_3, all_20_0, all_30_2, simplifying % 10.99/2.25 | with (102), (116) gives: % 10.99/2.25 | (117) all_20_0 = all_20_3 % 10.99/2.25 | % 10.99/2.25 | REDUCE: (9), (117) imply: % 10.99/2.25 | (118) $false % 10.99/2.25 | % 10.99/2.25 | CLOSE: (118) is inconsistent. % 10.99/2.25 | % 10.99/2.25 End of proof % 10.99/2.25 % SZS output end Proof for theBenchmark % 10.99/2.25 % 10.99/2.25 1639ms %------------------------------------------------------------------------------