%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : REL009+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 14.13s 2.67s % Output : Proof 14.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : REL009+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n012.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Aug 25 20:29:56 EDT 2023 % 0.18/0.34 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.62 Running up to 7 provers in parallel. % 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 2.06/1.05 Prover 1: Preprocessing ... % 2.06/1.05 Prover 4: Preprocessing ... % 2.93/1.09 Prover 5: Preprocessing ... % 2.93/1.09 Prover 3: Preprocessing ... % 2.93/1.09 Prover 0: Preprocessing ... % 2.93/1.10 Prover 2: Preprocessing ... % 2.93/1.11 Prover 6: Preprocessing ... % 4.89/1.38 Prover 6: Constructing countermodel ... % 4.89/1.40 Prover 1: Constructing countermodel ... % 4.89/1.41 Prover 3: Constructing countermodel ... % 4.89/1.44 Prover 0: Proving ... % 4.89/1.46 Prover 4: Constructing countermodel ... % 4.89/1.48 Prover 5: Proving ... % 5.42/1.55 Prover 2: Proving ... % 14.13/2.66 Prover 4: Found proof (size 126) % 14.13/2.66 Prover 4: proved (2029ms) % 14.13/2.66 Prover 6: stopped % 14.13/2.66 Prover 5: stopped % 14.13/2.66 Prover 0: stopped % 14.13/2.66 Prover 2: stopped % 14.13/2.66 Prover 1: stopped % 14.13/2.67 Prover 3: stopped % 14.13/2.67 % 14.13/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.13/2.67 % 14.58/2.69 % SZS output start Proof for theBenchmark % 14.58/2.70 Assumptions after simplification: % 14.58/2.70 --------------------------------- % 14.58/2.70 % 14.58/2.70 (composition_distributivity) % 14.58/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.58/2.73 $i] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) = v3) | ~ % 14.58/2.73 (join(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 14.58/2.73 (composition(v6, v2) = v5 & join(v0, v1) = v6 & $i(v6) & $i(v5))) & ! [v0: % 14.58/2.73 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 14.58/2.73 (composition(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 14.58/2.73 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (composition(v1, v2) = v6 & % 14.58/2.73 composition(v0, v2) = v5 & join(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 14.58/2.73 % 14.58/2.73 (converse_additivity) % 14.58/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 14.58/2.73 (converse(v1) = v3) | ~ (converse(v0) = v2) | ~ (join(v2, v3) = v4) | ~ % 14.58/2.73 $i(v1) | ~ $i(v0) | ? [v5: $i] : (converse(v5) = v4 & join(v0, v1) = v5 & % 14.58/2.73 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 14.58/2.73 (join(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 14.58/2.73 [v5: $i] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & % 14.58/2.73 join(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 14.58/2.73 % 14.58/2.73 (converse_cancellativity) % 14.58/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (composition(v0, v1) = v2) | ~ % 14.58/2.73 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 14.58/2.73 (converse(v0) = v3 & composition(v3, v4) = v5 & complement(v2) = v4 & % 14.58/2.73 complement(v1) = v6 & join(v5, v6) = v6 & $i(v6) & $i(v5) & $i(v4) & % 14.58/2.73 $i(v3))) % 14.58/2.73 % 14.58/2.73 (converse_idempotence) % 14.58/2.73 ! [v0: $i] : ! [v1: $i] : ( ~ (converse(v0) = v1) | ~ $i(v0) | converse(v1) % 14.58/2.73 = v0) % 14.58/2.73 % 14.58/2.73 (converse_multiplicativity) % 14.58/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 14.58/2.74 (converse(v1) = v2) | ~ (converse(v0) = v3) | ~ (composition(v2, v3) = v4) % 14.58/2.74 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (converse(v5) = v4 & composition(v0, % 14.58/2.74 v1) = v5 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.58/2.74 ( ~ (composition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 14.58/2.74 $i] : ? [v5: $i] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) % 14.58/2.74 = v5 & composition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 14.58/2.74 % 14.58/2.74 (goals) % 14.58/2.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.58/2.74 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (composition(v2, v1) = v7 & % 14.58/2.74 composition(v2, v0) = v6 & composition(v1, v2) = v4 & composition(v0, v2) = % 14.58/2.74 v3 & join(v6, v7) = v8 & join(v3, v4) = v5 & join(v0, v1) = v1 & $i(v8) & % 14.58/2.74 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ % 14.58/2.74 (v8 = v7) | ~ (v5 = v4))) % 14.58/2.74 % 14.58/2.74 (maddux1_join_commutativity) % 14.58/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v1, v0) = v2) | ~ $i(v1) % 14.58/2.74 | ~ $i(v0) | (join(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! % 14.58/2.74 [v2: $i] : ( ~ (join(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (join(v1, v0) = % 14.58/2.74 v2 & $i(v2))) % 14.58/2.74 % 14.58/2.74 (function-axioms) % 14.58/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.58/2.74 (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) & ! [v0: $i] : % 14.58/2.74 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (meet(v3, v2) = v1) | % 14.58/2.74 ~ (meet(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 14.58/2.74 $i] : (v1 = v0 | ~ (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) & ! [v0: % 14.58/2.74 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) = v1) | ~ % 14.58/2.74 (converse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 14.58/2.74 ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) % 14.58/2.74 % 14.58/2.74 Further assumptions not needed in the proof: % 14.58/2.74 -------------------------------------------- % 14.58/2.74 composition_associativity, composition_identity, dedekind_law, def_top, % 14.58/2.74 def_zero, maddux2_join_associativity, maddux3_a_kind_of_de_Morgan, % 14.58/2.74 maddux4_definiton_of_meet, modular_law_1, modular_law_2 % 14.58/2.74 % 14.58/2.74 Those formulas are unsatisfiable: % 14.58/2.74 --------------------------------- % 14.58/2.74 % 14.58/2.74 Begin of proof % 14.58/2.75 | % 14.58/2.75 | ALPHA: (maddux1_join_commutativity) implies: % 14.58/2.75 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v1, v0) = v2) | ~ % 14.58/2.75 | $i(v1) | ~ $i(v0) | (join(v0, v1) = v2 & $i(v2))) % 14.58/2.75 | % 14.58/2.75 | ALPHA: (composition_distributivity) implies: % 14.58/2.75 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 14.58/2.75 | ~ (composition(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ~ $i(v2) | % 14.58/2.75 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (composition(v1, % 14.58/2.75 | v2) = v6 & composition(v0, v2) = v5 & join(v5, v6) = v4 & $i(v6) % 14.58/2.75 | & $i(v5) & $i(v4))) % 14.58/2.75 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 14.58/2.75 | ! [v5: $i] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) = % 14.58/2.75 | v3) | ~ (join(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.58/2.75 | ? [v6: $i] : (composition(v6, v2) = v5 & join(v0, v1) = v6 & $i(v6) & % 14.58/2.75 | $i(v5))) % 14.58/2.75 | % 14.58/2.75 | ALPHA: (converse_additivity) implies: % 14.58/2.75 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v0, v1) = v2) | ~ % 14.58/2.75 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 14.58/2.75 | (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, % 14.58/2.75 | v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 14.58/2.75 | % 14.58/2.75 | ALPHA: (converse_multiplicativity) implies: % 14.58/2.75 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (composition(v0, v1) = % 14.58/2.75 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.58/2.75 | $i] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & % 14.58/2.75 | composition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 14.58/2.75 | % 14.58/2.75 | ALPHA: (function-axioms) implies: % 14.58/2.75 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) = % 14.58/2.75 | v1) | ~ (converse(v2) = v0)) % 14.58/2.75 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.58/2.75 | (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) % 14.58/2.75 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.58/2.75 | (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) % 14.58/2.75 | % 14.58/2.75 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2, % 14.58/2.75 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7, all_20_8 gives: % 14.58/2.76 | (9) composition(all_20_6, all_20_7) = all_20_1 & composition(all_20_6, % 14.58/2.76 | all_20_8) = all_20_2 & composition(all_20_7, all_20_6) = all_20_4 & % 14.58/2.76 | composition(all_20_8, all_20_6) = all_20_5 & join(all_20_2, all_20_1) = % 14.58/2.76 | all_20_0 & join(all_20_5, all_20_4) = all_20_3 & join(all_20_8, % 14.58/2.76 | all_20_7) = all_20_7 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & % 14.58/2.76 | $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & $i(all_20_6) & % 14.58/2.76 | $i(all_20_7) & $i(all_20_8) & ( ~ (all_20_0 = all_20_1) | ~ (all_20_3 % 14.58/2.76 | = all_20_4)) % 14.58/2.76 | % 14.58/2.76 | ALPHA: (9) implies: % 14.58/2.76 | (10) $i(all_20_8) % 14.58/2.76 | (11) $i(all_20_7) % 14.58/2.76 | (12) $i(all_20_6) % 14.58/2.76 | (13) $i(all_20_2) % 14.58/2.76 | (14) $i(all_20_1) % 14.58/2.76 | (15) join(all_20_8, all_20_7) = all_20_7 % 14.58/2.76 | (16) join(all_20_5, all_20_4) = all_20_3 % 14.58/2.76 | (17) join(all_20_2, all_20_1) = all_20_0 % 14.58/2.76 | (18) composition(all_20_8, all_20_6) = all_20_5 % 14.58/2.76 | (19) composition(all_20_7, all_20_6) = all_20_4 % 14.58/2.76 | (20) composition(all_20_6, all_20_8) = all_20_2 % 14.58/2.76 | (21) composition(all_20_6, all_20_7) = all_20_1 % 14.58/2.76 | (22) ~ (all_20_0 = all_20_1) | ~ (all_20_3 = all_20_4) % 14.58/2.76 | % 14.58/2.76 | GROUND_INST: instantiating (4) with all_20_8, all_20_7, all_20_7, simplifying % 14.58/2.76 | with (10), (11), (15) gives: % 14.58/2.76 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_7) = v2 & % 14.58/2.76 | converse(all_20_7) = v0 & converse(all_20_8) = v1 & join(v1, v2) = % 14.58/2.76 | v0 & $i(v2) & $i(v1) & $i(v0)) % 14.58/2.76 | % 14.58/2.76 | GROUND_INST: instantiating (1) with all_20_1, all_20_2, all_20_0, simplifying % 14.58/2.76 | with (13), (14), (17) gives: % 14.58/2.76 | (24) join(all_20_1, all_20_2) = all_20_0 & $i(all_20_0) % 14.58/2.76 | % 14.58/2.76 | ALPHA: (24) implies: % 14.58/2.76 | (25) $i(all_20_0) % 14.58/2.76 | % 14.58/2.76 | GROUND_INST: instantiating (4) with all_20_2, all_20_1, all_20_0, simplifying % 14.58/2.76 | with (13), (14), (17) gives: % 14.58/2.76 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_0) = v0 & % 14.58/2.76 | converse(all_20_1) = v2 & converse(all_20_2) = v1 & join(v1, v2) = % 14.58/2.76 | v0 & $i(v2) & $i(v1) & $i(v0)) % 14.58/2.76 | % 14.58/2.76 | GROUND_INST: instantiating (converse_cancellativity) with all_20_8, all_20_6, % 14.58/2.76 | all_20_5, simplifying with (10), (12), (18) gives: % 14.58/2.76 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 14.58/2.76 | (converse(all_20_8) = v0 & composition(v0, v1) = v2 & % 14.58/2.76 | complement(all_20_5) = v1 & complement(all_20_6) = v3 & join(v2, v3) % 14.58/2.76 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.58/2.76 | % 14.58/2.76 | GROUND_INST: instantiating (5) with all_20_8, all_20_6, all_20_5, simplifying % 14.58/2.76 | with (10), (12), (18) gives: % 14.58/2.76 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_5) = v0 & % 14.58/2.76 | converse(all_20_6) = v1 & converse(all_20_8) = v2 & composition(v1, % 14.58/2.76 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 14.58/2.76 | % 14.58/2.76 | GROUND_INST: instantiating (3) with all_20_8, all_20_7, all_20_6, all_20_5, % 14.58/2.76 | all_20_4, all_20_3, simplifying with (10), (11), (12), (16), % 14.58/2.76 | (18), (19) gives: % 14.58/2.76 | (29) ? [v0: $i] : (composition(v0, all_20_6) = all_20_3 & join(all_20_8, % 14.58/2.76 | all_20_7) = v0 & $i(v0) & $i(all_20_3)) % 14.58/2.76 | % 14.96/2.77 | GROUND_INST: instantiating (2) with all_20_8, all_20_7, all_20_6, all_20_7, % 14.96/2.77 | all_20_4, simplifying with (10), (11), (12), (15), (19) gives: % 14.96/2.77 | (30) ? [v0: $i] : ? [v1: $i] : (composition(all_20_7, all_20_6) = v1 & % 14.96/2.77 | composition(all_20_8, all_20_6) = v0 & join(v0, v1) = all_20_4 & % 14.96/2.77 | $i(v1) & $i(v0) & $i(all_20_4)) % 14.96/2.77 | % 14.96/2.77 | GROUND_INST: instantiating (converse_cancellativity) with all_20_7, all_20_6, % 14.96/2.77 | all_20_4, simplifying with (11), (12), (19) gives: % 14.96/2.77 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 14.96/2.77 | (converse(all_20_7) = v0 & composition(v0, v1) = v2 & % 14.96/2.77 | complement(all_20_4) = v1 & complement(all_20_6) = v3 & join(v2, v3) % 14.96/2.77 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.96/2.77 | % 14.96/2.77 | GROUND_INST: instantiating (5) with all_20_7, all_20_6, all_20_4, simplifying % 14.96/2.77 | with (11), (12), (19) gives: % 14.96/2.77 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_4) = v0 & % 14.96/2.77 | converse(all_20_6) = v1 & converse(all_20_7) = v2 & composition(v1, % 14.96/2.77 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 14.96/2.77 | % 14.96/2.77 | GROUND_INST: instantiating (converse_cancellativity) with all_20_6, all_20_8, % 14.96/2.77 | all_20_2, simplifying with (10), (12), (20) gives: % 14.96/2.77 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 14.96/2.77 | (converse(all_20_6) = v0 & composition(v0, v1) = v2 & % 14.96/2.77 | complement(all_20_2) = v1 & complement(all_20_8) = v3 & join(v2, v3) % 14.96/2.77 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.96/2.77 | % 14.96/2.77 | GROUND_INST: instantiating (5) with all_20_6, all_20_8, all_20_2, simplifying % 14.96/2.77 | with (10), (12), (20) gives: % 14.96/2.77 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_2) = v0 & % 14.96/2.77 | converse(all_20_6) = v2 & converse(all_20_8) = v1 & composition(v1, % 14.96/2.77 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 14.96/2.77 | % 14.96/2.77 | GROUND_INST: instantiating (converse_cancellativity) with all_20_6, all_20_7, % 14.96/2.77 | all_20_1, simplifying with (11), (12), (21) gives: % 14.96/2.77 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 14.96/2.77 | (converse(all_20_6) = v0 & composition(v0, v1) = v2 & % 14.96/2.77 | complement(all_20_1) = v1 & complement(all_20_7) = v3 & join(v2, v3) % 14.96/2.77 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.96/2.77 | % 14.96/2.77 | GROUND_INST: instantiating (5) with all_20_6, all_20_7, all_20_1, simplifying % 14.96/2.77 | with (11), (12), (21) gives: % 14.96/2.77 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_20_1) = v0 & % 14.96/2.77 | converse(all_20_6) = v2 & converse(all_20_7) = v1 & composition(v1, % 14.96/2.77 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 14.96/2.77 | % 14.96/2.77 | DELTA: instantiating (29) with fresh symbol all_30_0 gives: % 14.96/2.77 | (37) composition(all_30_0, all_20_6) = all_20_3 & join(all_20_8, all_20_7) % 14.96/2.77 | = all_30_0 & $i(all_30_0) & $i(all_20_3) % 14.96/2.77 | % 14.96/2.77 | ALPHA: (37) implies: % 14.96/2.77 | (38) join(all_20_8, all_20_7) = all_30_0 % 14.96/2.77 | (39) composition(all_30_0, all_20_6) = all_20_3 % 14.96/2.77 | % 14.96/2.77 | DELTA: instantiating (30) with fresh symbols all_32_0, all_32_1 gives: % 14.96/2.77 | (40) composition(all_20_7, all_20_6) = all_32_0 & composition(all_20_8, % 14.96/2.77 | all_20_6) = all_32_1 & join(all_32_1, all_32_0) = all_20_4 & % 14.96/2.77 | $i(all_32_0) & $i(all_32_1) & $i(all_20_4) % 14.96/2.77 | % 14.96/2.77 | ALPHA: (40) implies: % 14.96/2.77 | (41) composition(all_20_7, all_20_6) = all_32_0 % 14.96/2.77 | % 14.96/2.77 | DELTA: instantiating (28) with fresh symbols all_34_0, all_34_1, all_34_2 % 14.96/2.77 | gives: % 14.96/2.77 | (42) converse(all_20_5) = all_34_2 & converse(all_20_6) = all_34_1 & % 14.96/2.77 | converse(all_20_8) = all_34_0 & composition(all_34_1, all_34_0) = % 14.96/2.77 | all_34_2 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) % 14.96/2.77 | % 14.96/2.77 | ALPHA: (42) implies: % 14.96/2.77 | (43) converse(all_20_8) = all_34_0 % 14.96/2.78 | (44) converse(all_20_6) = all_34_1 % 14.96/2.78 | % 14.96/2.78 | DELTA: instantiating (34) with fresh symbols all_36_0, all_36_1, all_36_2 % 14.96/2.78 | gives: % 14.96/2.78 | (45) converse(all_20_2) = all_36_2 & converse(all_20_6) = all_36_0 & % 14.96/2.78 | converse(all_20_8) = all_36_1 & composition(all_36_1, all_36_0) = % 14.96/2.78 | all_36_2 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) % 14.96/2.78 | % 14.96/2.78 | ALPHA: (45) implies: % 14.96/2.78 | (46) $i(all_36_1) % 14.96/2.78 | (47) $i(all_36_0) % 14.96/2.78 | (48) composition(all_36_1, all_36_0) = all_36_2 % 14.96/2.78 | (49) converse(all_20_8) = all_36_1 % 14.96/2.78 | (50) converse(all_20_6) = all_36_0 % 14.96/2.78 | (51) converse(all_20_2) = all_36_2 % 14.96/2.78 | % 14.96/2.78 | DELTA: instantiating (32) with fresh symbols all_38_0, all_38_1, all_38_2 % 14.96/2.78 | gives: % 14.96/2.78 | (52) converse(all_20_4) = all_38_2 & converse(all_20_6) = all_38_1 & % 14.96/2.78 | converse(all_20_7) = all_38_0 & composition(all_38_1, all_38_0) = % 14.96/2.78 | all_38_2 & $i(all_38_0) & $i(all_38_1) & $i(all_38_2) % 14.96/2.78 | % 14.96/2.78 | ALPHA: (52) implies: % 14.96/2.78 | (53) converse(all_20_7) = all_38_0 % 14.96/2.78 | (54) converse(all_20_6) = all_38_1 % 14.96/2.78 | % 14.96/2.78 | DELTA: instantiating (36) with fresh symbols all_40_0, all_40_1, all_40_2 % 14.96/2.78 | gives: % 14.96/2.78 | (55) converse(all_20_1) = all_40_2 & converse(all_20_6) = all_40_0 & % 14.96/2.78 | converse(all_20_7) = all_40_1 & composition(all_40_1, all_40_0) = % 14.96/2.78 | all_40_2 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) % 14.96/2.78 | % 14.96/2.78 | ALPHA: (55) implies: % 14.96/2.78 | (56) $i(all_40_1) % 14.96/2.78 | (57) composition(all_40_1, all_40_0) = all_40_2 % 14.96/2.78 | (58) converse(all_20_7) = all_40_1 % 14.96/2.78 | (59) converse(all_20_6) = all_40_0 % 14.96/2.78 | (60) converse(all_20_1) = all_40_2 % 14.96/2.78 | % 14.96/2.78 | DELTA: instantiating (26) with fresh symbols all_42_0, all_42_1, all_42_2 % 14.96/2.78 | gives: % 14.96/2.78 | (61) converse(all_20_0) = all_42_2 & converse(all_20_1) = all_42_0 & % 14.96/2.78 | converse(all_20_2) = all_42_1 & join(all_42_1, all_42_0) = all_42_2 & % 14.96/2.78 | $i(all_42_0) & $i(all_42_1) & $i(all_42_2) % 14.96/2.78 | % 14.96/2.78 | ALPHA: (61) implies: % 14.96/2.78 | (62) $i(all_42_1) % 14.96/2.78 | (63) $i(all_42_0) % 14.96/2.78 | (64) join(all_42_1, all_42_0) = all_42_2 % 14.96/2.78 | (65) converse(all_20_2) = all_42_1 % 14.96/2.78 | (66) converse(all_20_1) = all_42_0 % 14.96/2.78 | (67) converse(all_20_0) = all_42_2 % 14.96/2.78 | % 14.96/2.78 | DELTA: instantiating (23) with fresh symbols all_44_0, all_44_1, all_44_2 % 14.96/2.78 | gives: % 14.96/2.78 | (68) converse(all_20_7) = all_44_0 & converse(all_20_7) = all_44_2 & % 14.96/2.78 | converse(all_20_8) = all_44_1 & join(all_44_1, all_44_0) = all_44_2 & % 14.96/2.78 | $i(all_44_0) & $i(all_44_1) & $i(all_44_2) % 14.96/2.78 | % 14.96/2.78 | ALPHA: (68) implies: % 14.96/2.78 | (69) join(all_44_1, all_44_0) = all_44_2 % 14.96/2.78 | (70) converse(all_20_8) = all_44_1 % 14.96/2.78 | (71) converse(all_20_7) = all_44_2 % 14.96/2.78 | (72) converse(all_20_7) = all_44_0 % 14.96/2.78 | % 14.96/2.78 | DELTA: instantiating (27) with fresh symbols all_48_0, all_48_1, all_48_2, % 14.96/2.78 | all_48_3 gives: % 14.96/2.78 | (73) converse(all_20_8) = all_48_3 & composition(all_48_3, all_48_2) = % 14.96/2.78 | all_48_1 & complement(all_20_5) = all_48_2 & complement(all_20_6) = % 14.96/2.78 | all_48_0 & join(all_48_1, all_48_0) = all_48_0 & $i(all_48_0) & % 14.96/2.78 | $i(all_48_1) & $i(all_48_2) & $i(all_48_3) % 14.96/2.78 | % 14.96/2.78 | ALPHA: (73) implies: % 14.96/2.78 | (74) converse(all_20_8) = all_48_3 % 14.96/2.78 | % 14.96/2.78 | DELTA: instantiating (31) with fresh symbols all_50_0, all_50_1, all_50_2, % 14.96/2.78 | all_50_3 gives: % 14.96/2.78 | (75) converse(all_20_7) = all_50_3 & composition(all_50_3, all_50_2) = % 14.96/2.78 | all_50_1 & complement(all_20_4) = all_50_2 & complement(all_20_6) = % 14.96/2.78 | all_50_0 & join(all_50_1, all_50_0) = all_50_0 & $i(all_50_0) & % 14.96/2.78 | $i(all_50_1) & $i(all_50_2) & $i(all_50_3) % 14.96/2.78 | % 14.96/2.78 | ALPHA: (75) implies: % 14.96/2.78 | (76) converse(all_20_7) = all_50_3 % 14.96/2.78 | % 14.96/2.78 | DELTA: instantiating (35) with fresh symbols all_52_0, all_52_1, all_52_2, % 14.96/2.78 | all_52_3 gives: % 14.96/2.78 | (77) converse(all_20_6) = all_52_3 & composition(all_52_3, all_52_2) = % 14.96/2.78 | all_52_1 & complement(all_20_1) = all_52_2 & complement(all_20_7) = % 14.96/2.79 | all_52_0 & join(all_52_1, all_52_0) = all_52_0 & $i(all_52_0) & % 14.96/2.79 | $i(all_52_1) & $i(all_52_2) & $i(all_52_3) % 14.96/2.79 | % 14.96/2.79 | ALPHA: (77) implies: % 14.96/2.79 | (78) converse(all_20_6) = all_52_3 % 14.96/2.79 | % 14.96/2.79 | DELTA: instantiating (33) with fresh symbols all_54_0, all_54_1, all_54_2, % 14.96/2.79 | all_54_3 gives: % 14.96/2.79 | (79) converse(all_20_6) = all_54_3 & composition(all_54_3, all_54_2) = % 14.96/2.79 | all_54_1 & complement(all_20_2) = all_54_2 & complement(all_20_8) = % 14.96/2.79 | all_54_0 & join(all_54_1, all_54_0) = all_54_0 & $i(all_54_0) & % 14.96/2.79 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) % 14.96/2.79 | % 14.96/2.79 | ALPHA: (79) implies: % 14.96/2.79 | (80) converse(all_20_6) = all_54_3 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (7) with all_20_7, all_30_0, all_20_7, all_20_8, % 14.96/2.79 | simplifying with (15), (38) gives: % 14.96/2.79 | (81) all_30_0 = all_20_7 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (8) with all_20_4, all_32_0, all_20_6, all_20_7, % 14.96/2.79 | simplifying with (19), (41) gives: % 14.96/2.79 | (82) all_32_0 = all_20_4 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_36_1, all_44_1, all_20_8, simplifying % 14.96/2.79 | with (49), (70) gives: % 14.96/2.79 | (83) all_44_1 = all_36_1 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_44_1, all_48_3, all_20_8, simplifying % 14.96/2.79 | with (70), (74) gives: % 14.96/2.79 | (84) all_48_3 = all_44_1 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_34_0, all_48_3, all_20_8, simplifying % 14.96/2.79 | with (43), (74) gives: % 14.96/2.79 | (85) all_48_3 = all_34_0 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_40_1, all_44_2, all_20_7, simplifying % 14.96/2.79 | with (58), (71) gives: % 14.96/2.79 | (86) all_44_2 = all_40_1 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_44_2, all_44_0, all_20_7, simplifying % 14.96/2.79 | with (71), (72) gives: % 14.96/2.79 | (87) all_44_0 = all_44_2 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_44_0, all_50_3, all_20_7, simplifying % 14.96/2.79 | with (72), (76) gives: % 14.96/2.79 | (88) all_50_3 = all_44_0 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_38_0, all_50_3, all_20_7, simplifying % 14.96/2.79 | with (53), (76) gives: % 14.96/2.79 | (89) all_50_3 = all_38_0 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_40_0, all_52_3, all_20_6, simplifying % 14.96/2.79 | with (59), (78) gives: % 14.96/2.79 | (90) all_52_3 = all_40_0 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_38_1, all_52_3, all_20_6, simplifying % 14.96/2.79 | with (54), (78) gives: % 14.96/2.79 | (91) all_52_3 = all_38_1 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_34_1, all_52_3, all_20_6, simplifying % 14.96/2.79 | with (44), (78) gives: % 14.96/2.79 | (92) all_52_3 = all_34_1 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_40_0, all_54_3, all_20_6, simplifying % 14.96/2.79 | with (59), (80) gives: % 14.96/2.79 | (93) all_54_3 = all_40_0 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_36_0, all_54_3, all_20_6, simplifying % 14.96/2.79 | with (50), (80) gives: % 14.96/2.79 | (94) all_54_3 = all_36_0 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_36_2, all_42_1, all_20_2, simplifying % 14.96/2.79 | with (51), (65) gives: % 14.96/2.79 | (95) all_42_1 = all_36_2 % 14.96/2.79 | % 14.96/2.79 | GROUND_INST: instantiating (6) with all_40_2, all_42_0, all_20_1, simplifying % 14.96/2.79 | with (60), (66) gives: % 14.96/2.79 | (96) all_42_0 = all_40_2 % 14.96/2.79 | % 14.96/2.79 | COMBINE_EQS: (93), (94) imply: % 14.96/2.79 | (97) all_40_0 = all_36_0 % 14.96/2.79 | % 14.96/2.79 | SIMP: (97) implies: % 14.96/2.79 | (98) all_40_0 = all_36_0 % 14.96/2.79 | % 14.96/2.79 | COMBINE_EQS: (90), (91) imply: % 14.96/2.79 | (99) all_40_0 = all_38_1 % 14.96/2.79 | % 14.96/2.79 | SIMP: (99) implies: % 14.96/2.79 | (100) all_40_0 = all_38_1 % 14.96/2.79 | % 14.96/2.79 | COMBINE_EQS: (91), (92) imply: % 14.96/2.79 | (101) all_38_1 = all_34_1 % 14.96/2.79 | % 14.96/2.79 | COMBINE_EQS: (88), (89) imply: % 14.96/2.79 | (102) all_44_0 = all_38_0 % 14.96/2.79 | % 14.96/2.79 | SIMP: (102) implies: % 14.96/2.79 | (103) all_44_0 = all_38_0 % 14.96/2.79 | % 14.96/2.79 | COMBINE_EQS: (84), (85) imply: % 14.96/2.79 | (104) all_44_1 = all_34_0 % 14.96/2.79 | % 14.96/2.79 | SIMP: (104) implies: % 14.96/2.79 | (105) all_44_1 = all_34_0 % 14.96/2.79 | % 14.96/2.79 | COMBINE_EQS: (87), (103) imply: % 14.96/2.80 | (106) all_44_2 = all_38_0 % 14.96/2.80 | % 14.96/2.80 | SIMP: (106) implies: % 14.96/2.80 | (107) all_44_2 = all_38_0 % 14.96/2.80 | % 14.96/2.80 | COMBINE_EQS: (83), (105) imply: % 14.96/2.80 | (108) all_36_1 = all_34_0 % 14.96/2.80 | % 14.96/2.80 | COMBINE_EQS: (86), (107) imply: % 14.96/2.80 | (109) all_40_1 = all_38_0 % 14.96/2.80 | % 14.96/2.80 | COMBINE_EQS: (98), (100) imply: % 14.96/2.80 | (110) all_38_1 = all_36_0 % 14.96/2.80 | % 14.96/2.80 | SIMP: (110) implies: % 14.96/2.80 | (111) all_38_1 = all_36_0 % 14.96/2.80 | % 14.96/2.80 | COMBINE_EQS: (101), (111) imply: % 14.96/2.80 | (112) all_36_0 = all_34_1 % 14.96/2.80 | % 14.96/2.80 | COMBINE_EQS: (98), (112) imply: % 14.96/2.80 | (113) all_40_0 = all_34_1 % 14.96/2.80 | % 14.96/2.80 | REDUCE: (57), (109), (113) imply: % 14.96/2.80 | (114) composition(all_38_0, all_34_1) = all_40_2 % 14.96/2.80 | % 14.96/2.80 | REDUCE: (48), (108), (112) imply: % 14.96/2.80 | (115) composition(all_34_0, all_34_1) = all_36_2 % 14.96/2.80 | % 14.96/2.80 | REDUCE: (39), (81) imply: % 14.96/2.80 | (116) composition(all_20_7, all_20_6) = all_20_3 % 14.96/2.80 | % 14.96/2.80 | REDUCE: (69), (103), (105), (107) imply: % 14.96/2.80 | (117) join(all_34_0, all_38_0) = all_38_0 % 14.96/2.80 | % 14.96/2.80 | REDUCE: (64), (95), (96) imply: % 14.96/2.80 | (118) join(all_36_2, all_40_2) = all_42_2 % 14.96/2.80 | % 14.96/2.80 | REDUCE: (63), (96) imply: % 14.96/2.80 | (119) $i(all_40_2) % 14.96/2.80 | % 14.96/2.80 | REDUCE: (62), (95) imply: % 14.96/2.80 | (120) $i(all_36_2) % 14.96/2.80 | % 14.96/2.80 | REDUCE: (56), (109) imply: % 14.96/2.80 | (121) $i(all_38_0) % 14.96/2.80 | % 14.96/2.80 | REDUCE: (47), (112) imply: % 14.96/2.80 | (122) $i(all_34_1) % 14.96/2.80 | % 14.96/2.80 | REDUCE: (46), (108) imply: % 14.96/2.80 | (123) $i(all_34_0) % 14.96/2.80 | % 14.96/2.80 | GROUND_INST: instantiating (8) with all_20_4, all_20_3, all_20_6, all_20_7, % 14.96/2.80 | simplifying with (19), (116) gives: % 14.96/2.80 | (124) all_20_3 = all_20_4 % 14.96/2.80 | % 14.96/2.80 | BETA: splitting (22) gives: % 14.96/2.80 | % 14.96/2.80 | Case 1: % 14.96/2.80 | | % 14.96/2.80 | | (125) ~ (all_20_0 = all_20_1) % 14.96/2.80 | | % 14.96/2.80 | | GROUND_INST: instantiating (4) with all_36_2, all_40_2, all_42_2, % 14.96/2.80 | | simplifying with (118), (119), (120) gives: % 14.96/2.80 | | (126) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_42_2) = v0 % 14.96/2.80 | | & converse(all_40_2) = v2 & converse(all_36_2) = v1 & join(v1, % 14.96/2.80 | | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 14.96/2.80 | | % 14.96/2.80 | | GROUND_INST: instantiating (3) with all_34_0, all_38_0, all_34_1, all_36_2, % 14.96/2.80 | | all_40_2, all_42_2, simplifying with (114), (115), (118), % 14.96/2.80 | | (121), (122), (123) gives: % 14.96/2.80 | | (127) ? [v0: $i] : (composition(v0, all_34_1) = all_42_2 & % 14.96/2.80 | | join(all_34_0, all_38_0) = v0 & $i(v0) & $i(all_42_2)) % 14.96/2.80 | | % 14.96/2.80 | | GROUND_INST: instantiating (2) with all_34_0, all_38_0, all_34_1, all_38_0, % 14.96/2.80 | | all_40_2, simplifying with (114), (117), (121), (122), (123) % 14.96/2.80 | | gives: % 14.96/2.80 | | (128) ? [v0: $i] : ? [v1: $i] : (composition(all_38_0, all_34_1) = v1 & % 14.96/2.80 | | composition(all_34_0, all_34_1) = v0 & join(v0, v1) = all_40_2 & % 14.96/2.80 | | $i(v1) & $i(v0) & $i(all_40_2)) % 14.96/2.80 | | % 14.96/2.80 | | GROUND_INST: instantiating (5) with all_38_0, all_34_1, all_40_2, % 14.96/2.80 | | simplifying with (114), (121), (122) gives: % 14.96/2.80 | | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_40_2) = v0 % 14.96/2.80 | | & converse(all_38_0) = v2 & converse(all_34_1) = v1 & % 14.96/2.80 | | composition(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 14.96/2.80 | | % 14.96/2.81 | | GROUND_INST: instantiating (converse_idempotence) with all_20_1, all_40_2, % 14.96/2.81 | | simplifying with (14), (60) gives: % 14.96/2.81 | | (130) converse(all_40_2) = all_20_1 % 14.96/2.81 | | % 14.96/2.81 | | GROUND_INST: instantiating (converse_idempotence) with all_20_0, all_42_2, % 14.96/2.81 | | simplifying with (25), (67) gives: % 14.96/2.81 | | (131) converse(all_42_2) = all_20_0 % 14.96/2.81 | | % 14.96/2.81 | | DELTA: instantiating (127) with fresh symbol all_106_0 gives: % 14.96/2.81 | | (132) composition(all_106_0, all_34_1) = all_42_2 & join(all_34_0, % 14.96/2.81 | | all_38_0) = all_106_0 & $i(all_106_0) & $i(all_42_2) % 14.96/2.81 | | % 14.96/2.81 | | ALPHA: (132) implies: % 14.96/2.81 | | (133) join(all_34_0, all_38_0) = all_106_0 % 14.96/2.81 | | (134) composition(all_106_0, all_34_1) = all_42_2 % 14.96/2.81 | | % 14.96/2.81 | | DELTA: instantiating (128) with fresh symbols all_112_0, all_112_1 gives: % 14.96/2.81 | | (135) composition(all_38_0, all_34_1) = all_112_0 & composition(all_34_0, % 14.96/2.81 | | all_34_1) = all_112_1 & join(all_112_1, all_112_0) = all_40_2 & % 14.96/2.81 | | $i(all_112_0) & $i(all_112_1) & $i(all_40_2) % 14.96/2.81 | | % 14.96/2.81 | | ALPHA: (135) implies: % 14.96/2.81 | | (136) composition(all_38_0, all_34_1) = all_112_0 % 14.96/2.81 | | % 14.96/2.81 | | DELTA: instantiating (129) with fresh symbols all_114_0, all_114_1, % 14.96/2.81 | | all_114_2 gives: % 14.96/2.81 | | (137) converse(all_40_2) = all_114_2 & converse(all_38_0) = all_114_0 & % 14.96/2.81 | | converse(all_34_1) = all_114_1 & composition(all_114_1, all_114_0) % 14.96/2.81 | | = all_114_2 & $i(all_114_0) & $i(all_114_1) & $i(all_114_2) % 14.96/2.81 | | % 14.96/2.81 | | ALPHA: (137) implies: % 14.96/2.81 | | (138) converse(all_40_2) = all_114_2 % 14.96/2.81 | | % 14.96/2.81 | | DELTA: instantiating (126) with fresh symbols all_128_0, all_128_1, % 14.96/2.81 | | all_128_2 gives: % 14.96/2.81 | | (139) converse(all_42_2) = all_128_2 & converse(all_40_2) = all_128_0 & % 14.96/2.81 | | converse(all_36_2) = all_128_1 & join(all_128_1, all_128_0) = % 14.96/2.81 | | all_128_2 & $i(all_128_0) & $i(all_128_1) & $i(all_128_2) % 14.96/2.81 | | % 14.96/2.81 | | ALPHA: (139) implies: % 14.96/2.81 | | (140) converse(all_40_2) = all_128_0 % 14.96/2.81 | | (141) converse(all_42_2) = all_128_2 % 14.96/2.81 | | % 14.96/2.81 | | GROUND_INST: instantiating (7) with all_38_0, all_106_0, all_38_0, all_34_0, % 14.96/2.81 | | simplifying with (117), (133) gives: % 14.96/2.81 | | (142) all_106_0 = all_38_0 % 14.96/2.81 | | % 14.96/2.81 | | GROUND_INST: instantiating (8) with all_40_2, all_112_0, all_34_1, all_38_0, % 14.96/2.81 | | simplifying with (114), (136) gives: % 14.96/2.81 | | (143) all_112_0 = all_40_2 % 14.96/2.81 | | % 14.96/2.81 | | GROUND_INST: instantiating (6) with all_114_2, all_128_0, all_40_2, % 14.96/2.81 | | simplifying with (138), (140) gives: % 14.96/2.81 | | (144) all_128_0 = all_114_2 % 14.96/2.81 | | % 14.96/2.81 | | GROUND_INST: instantiating (6) with all_20_1, all_128_0, all_40_2, % 14.96/2.81 | | simplifying with (130), (140) gives: % 14.96/2.81 | | (145) all_128_0 = all_20_1 % 14.96/2.81 | | % 14.96/2.81 | | GROUND_INST: instantiating (6) with all_20_0, all_128_2, all_42_2, % 14.96/2.81 | | simplifying with (131), (141) gives: % 14.96/2.81 | | (146) all_128_2 = all_20_0 % 14.96/2.81 | | % 14.96/2.81 | | COMBINE_EQS: (144), (145) imply: % 14.96/2.81 | | (147) all_114_2 = all_20_1 % 14.96/2.81 | | % 14.96/2.81 | | SIMP: (147) implies: % 14.96/2.81 | | (148) all_114_2 = all_20_1 % 14.96/2.81 | | % 14.96/2.81 | | REDUCE: (134), (142) imply: % 14.96/2.81 | | (149) composition(all_38_0, all_34_1) = all_42_2 % 14.96/2.81 | | % 14.96/2.81 | | GROUND_INST: instantiating (8) with all_40_2, all_42_2, all_34_1, all_38_0, % 14.96/2.81 | | simplifying with (114), (149) gives: % 14.96/2.81 | | (150) all_42_2 = all_40_2 % 14.96/2.81 | | % 14.96/2.81 | | REDUCE: (131), (150) imply: % 14.96/2.81 | | (151) converse(all_40_2) = all_20_0 % 14.96/2.81 | | % 14.96/2.81 | | GROUND_INST: instantiating (6) with all_20_1, all_20_0, all_40_2, % 14.96/2.81 | | simplifying with (130), (151) gives: % 14.96/2.81 | | (152) all_20_0 = all_20_1 % 14.96/2.81 | | % 14.96/2.81 | | REDUCE: (125), (152) imply: % 14.96/2.81 | | (153) $false % 14.96/2.81 | | % 14.96/2.81 | | CLOSE: (153) is inconsistent. % 14.96/2.81 | | % 14.96/2.81 | Case 2: % 14.96/2.81 | | % 14.96/2.81 | | (154) ~ (all_20_3 = all_20_4) % 14.96/2.81 | | % 14.96/2.81 | | REDUCE: (124), (154) imply: % 14.96/2.81 | | (155) $false % 14.96/2.81 | | % 14.96/2.81 | | CLOSE: (155) is inconsistent. % 14.96/2.81 | | % 14.96/2.81 | End of split % 14.96/2.81 | % 14.96/2.81 End of proof % 14.96/2.81 % SZS output end Proof for theBenchmark % 14.96/2.81 % 14.96/2.81 2209ms %------------------------------------------------------------------------------