%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : REL008+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 13:42:45 EDT 2023 % Result : Theorem 8.16s 1.93s % Output : Proof 12.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : REL008+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n026.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 : Fri Aug 25 21:06:03 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.69 ________ _____ % 0.21/0.69 ___ __ \_________(_)________________________________ % 0.21/0.69 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.69 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.69 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.69 % 0.21/0.69 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.69 (2023-06-19) % 0.21/0.69 % 0.21/0.69 (c) Philipp Rümmer, 2009-2023 % 0.21/0.69 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.69 Amanda Stjerna. % 0.21/0.69 Free software under BSD-3-Clause. % 0.21/0.69 % 0.21/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.69 % 0.21/0.70 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.71 Running up to 7 provers in parallel. % 0.21/0.72 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.72 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.72 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.72 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.73 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.59/1.11 Prover 4: Preprocessing ... % 2.59/1.12 Prover 1: Preprocessing ... % 2.59/1.16 Prover 5: Preprocessing ... % 2.59/1.16 Prover 6: Preprocessing ... % 2.59/1.16 Prover 0: Preprocessing ... % 2.59/1.16 Prover 2: Preprocessing ... % 2.59/1.16 Prover 3: Preprocessing ... % 4.54/1.41 Prover 1: Constructing countermodel ... % 4.54/1.44 Prover 6: Constructing countermodel ... % 4.54/1.44 Prover 3: Constructing countermodel ... % 4.54/1.45 Prover 4: Constructing countermodel ... % 5.26/1.50 Prover 5: Proving ... % 5.26/1.50 Prover 0: Proving ... % 5.26/1.58 Prover 2: Proving ... % 5.26/1.58 Prover 1: gave up % 5.26/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.26/1.59 Prover 3: gave up % 5.26/1.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.70/1.63 Prover 7: Preprocessing ... % 6.21/1.65 Prover 8: Preprocessing ... % 6.21/1.70 Prover 6: gave up % 6.68/1.70 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.68/1.72 Prover 9: Preprocessing ... % 6.68/1.76 Prover 8: Warning: ignoring some quantifiers % 7.09/1.77 Prover 8: Constructing countermodel ... % 7.09/1.82 Prover 7: Constructing countermodel ... % 7.09/1.85 Prover 9: Constructing countermodel ... % 8.16/1.90 Prover 8: gave up % 8.16/1.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.16/1.92 Prover 0: proved (1199ms) % 8.16/1.92 % 8.16/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.16/1.93 % 8.16/1.93 Prover 9: stopped % 8.40/1.94 Prover 2: stopped % 8.40/1.94 Prover 5: stopped % 8.40/1.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.40/1.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.40/1.94 Prover 10: Preprocessing ... % 8.40/1.95 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.40/1.95 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.40/1.97 Prover 19: Preprocessing ... % 8.40/1.97 Prover 13: Preprocessing ... % 8.40/1.98 Prover 16: Preprocessing ... % 8.40/1.99 Prover 11: Preprocessing ... % 8.40/2.02 Prover 10: Constructing countermodel ... % 9.09/2.05 Prover 10: gave up % 9.09/2.05 Prover 16: Warning: ignoring some quantifiers % 9.09/2.05 Prover 19: Warning: ignoring some quantifiers % 9.09/2.06 Prover 16: Constructing countermodel ... % 9.09/2.07 Prover 19: Constructing countermodel ... % 9.09/2.07 Prover 11: Constructing countermodel ... % 9.09/2.08 Prover 13: Warning: ignoring some quantifiers % 9.09/2.08 Prover 13: Constructing countermodel ... % 9.54/2.12 Prover 19: gave up % 11.36/2.41 Prover 4: Found proof (size 87) % 11.36/2.41 Prover 4: proved (1690ms) % 11.36/2.41 Prover 7: stopped % 11.36/2.41 Prover 13: stopped % 11.36/2.41 Prover 16: stopped % 11.36/2.42 Prover 11: stopped % 11.36/2.42 % 11.36/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.36/2.42 % 11.36/2.43 % SZS output start Proof for theBenchmark % 11.36/2.44 Assumptions after simplification: % 11.36/2.44 --------------------------------- % 11.36/2.44 % 11.36/2.44 (composition_distributivity) % 11.95/2.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 11.95/2.47 $i] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) = v3) | ~ % 11.95/2.47 (join(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 11.95/2.47 (composition(v6, v2) = v5 & join(v0, v1) = v6 & $i(v6) & $i(v5))) & ! [v0: % 11.95/2.47 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 11.95/2.47 (composition(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 11.95/2.47 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (composition(v1, v2) = v6 & % 11.95/2.47 composition(v0, v2) = v5 & join(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 11.95/2.47 % 11.95/2.47 (converse_additivity) % 11.95/2.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 11.95/2.47 (converse(v1) = v3) | ~ (converse(v0) = v2) | ~ (join(v2, v3) = v4) | ~ % 11.95/2.47 $i(v1) | ~ $i(v0) | ? [v5: $i] : (converse(v5) = v4 & join(v0, v1) = v5 & % 11.95/2.47 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.95/2.48 (join(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 11.95/2.48 [v5: $i] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & % 11.95/2.48 join(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 11.95/2.48 % 11.95/2.48 (converse_cancellativity) % 11.95/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (composition(v0, v1) = v2) | ~ % 11.95/2.48 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 11.95/2.48 (converse(v0) = v3 & composition(v3, v4) = v5 & complement(v2) = v4 & % 11.95/2.48 complement(v1) = v6 & join(v5, v6) = v6 & $i(v6) & $i(v5) & $i(v4) & % 11.95/2.48 $i(v3))) % 11.95/2.48 % 11.95/2.48 (converse_idempotence) % 11.95/2.48 ! [v0: $i] : ! [v1: $i] : ( ~ (converse(v0) = v1) | ~ $i(v0) | converse(v1) % 11.95/2.48 = v0) % 11.95/2.48 % 11.95/2.48 (converse_multiplicativity) % 11.95/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 11.95/2.48 (converse(v1) = v2) | ~ (converse(v0) = v3) | ~ (composition(v2, v3) = v4) % 11.95/2.48 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (converse(v5) = v4 & composition(v0, % 11.95/2.48 v1) = v5 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 11.95/2.48 ( ~ (composition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 11.95/2.48 $i] : ? [v5: $i] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) % 11.95/2.48 = v5 & composition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 11.95/2.48 % 11.95/2.48 (goals) % 11.95/2.48 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 11.95/2.48 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v4) & composition(v0, v3) = v4 & % 11.95/2.48 composition(v0, v2) = v6 & composition(v0, v1) = v5 & join(v5, v6) = v7 & % 11.95/2.48 join(v1, v2) = v3 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 11.95/2.48 $i(v1) & $i(v0)) % 11.95/2.48 % 11.95/2.48 (maddux1_join_commutativity) % 11.95/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v1, v0) = v2) | ~ $i(v1) % 11.95/2.49 | ~ $i(v0) | (join(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! % 11.95/2.49 [v2: $i] : ( ~ (join(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (join(v1, v0) = % 11.95/2.49 v2 & $i(v2))) % 11.95/2.49 % 11.95/2.49 (function-axioms) % 11.95/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.95/2.49 (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) & ! [v0: $i] : % 11.95/2.49 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (meet(v3, v2) = v1) | % 11.95/2.49 ~ (meet(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.95/2.49 $i] : (v1 = v0 | ~ (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) & ! [v0: % 11.95/2.49 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) = v1) | ~ % 11.95/2.49 (converse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 11.95/2.49 ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) % 11.95/2.49 % 11.95/2.49 Further assumptions not needed in the proof: % 11.95/2.49 -------------------------------------------- % 11.95/2.49 composition_associativity, composition_identity, def_top, def_zero, % 11.95/2.49 maddux2_join_associativity, maddux3_a_kind_of_de_Morgan, % 11.95/2.49 maddux4_definiton_of_meet % 11.95/2.49 % 11.95/2.49 Those formulas are unsatisfiable: % 11.95/2.49 --------------------------------- % 11.95/2.49 % 11.95/2.49 Begin of proof % 11.95/2.49 | % 11.95/2.49 | ALPHA: (maddux1_join_commutativity) implies: % 11.95/2.49 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v1, v0) = v2) | ~ % 11.95/2.49 | $i(v1) | ~ $i(v0) | (join(v0, v1) = v2 & $i(v2))) % 11.95/2.49 | % 11.95/2.49 | ALPHA: (composition_distributivity) implies: % 11.95/2.49 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 11.95/2.49 | ! [v5: $i] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) = % 11.95/2.49 | v3) | ~ (join(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 11.95/2.49 | ? [v6: $i] : (composition(v6, v2) = v5 & join(v0, v1) = v6 & $i(v6) & % 11.95/2.49 | $i(v5))) % 11.95/2.49 | % 11.95/2.49 | ALPHA: (converse_additivity) implies: % 11.95/2.49 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v0, v1) = v2) | ~ % 11.95/2.49 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 11.95/2.49 | (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, % 11.95/2.49 | v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 11.95/2.49 | % 11.95/2.49 | ALPHA: (converse_multiplicativity) implies: % 11.95/2.50 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (composition(v0, v1) = % 11.95/2.50 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 11.95/2.50 | $i] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & % 11.95/2.50 | composition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3))) % 11.95/2.50 | % 11.95/2.50 | ALPHA: (function-axioms) implies: % 11.95/2.50 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) = % 11.95/2.50 | v1) | ~ (converse(v2) = v0)) % 11.95/2.50 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.95/2.50 | (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) % 11.95/2.50 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.95/2.50 | (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) % 11.95/2.50 | % 11.95/2.50 | DELTA: instantiating (goals) with fresh symbols all_17_0, all_17_1, all_17_2, % 11.95/2.50 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7 gives: % 11.95/2.50 | (8) ~ (all_17_0 = all_17_3) & composition(all_17_7, all_17_4) = all_17_3 & % 11.95/2.50 | composition(all_17_7, all_17_5) = all_17_1 & composition(all_17_7, % 11.95/2.50 | all_17_6) = all_17_2 & join(all_17_2, all_17_1) = all_17_0 & % 11.95/2.50 | join(all_17_6, all_17_5) = all_17_4 & $i(all_17_0) & $i(all_17_1) & % 11.95/2.50 | $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & $i(all_17_5) & % 11.95/2.50 | $i(all_17_6) & $i(all_17_7) % 11.95/2.50 | % 11.95/2.50 | ALPHA: (8) implies: % 11.95/2.50 | (9) ~ (all_17_0 = all_17_3) % 11.95/2.50 | (10) $i(all_17_7) % 11.95/2.50 | (11) $i(all_17_6) % 11.95/2.50 | (12) $i(all_17_5) % 11.95/2.50 | (13) $i(all_17_3) % 11.95/2.50 | (14) $i(all_17_2) % 11.95/2.50 | (15) $i(all_17_1) % 11.95/2.50 | (16) join(all_17_6, all_17_5) = all_17_4 % 11.95/2.50 | (17) join(all_17_2, all_17_1) = all_17_0 % 11.95/2.50 | (18) composition(all_17_7, all_17_6) = all_17_2 % 11.95/2.50 | (19) composition(all_17_7, all_17_5) = all_17_1 % 11.95/2.50 | (20) composition(all_17_7, all_17_4) = all_17_3 % 11.95/2.50 | % 11.95/2.50 | GROUND_INST: instantiating (1) with all_17_5, all_17_6, all_17_4, simplifying % 11.95/2.50 | with (11), (12), (16) gives: % 11.95/2.50 | (21) join(all_17_5, all_17_6) = all_17_4 & $i(all_17_4) % 11.95/2.50 | % 11.95/2.50 | ALPHA: (21) implies: % 11.95/2.50 | (22) $i(all_17_4) % 11.95/2.50 | % 11.95/2.50 | GROUND_INST: instantiating (3) with all_17_6, all_17_5, all_17_4, simplifying % 11.95/2.50 | with (11), (12), (16) gives: % 11.95/2.50 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_4) = v0 & % 11.95/2.50 | converse(all_17_5) = v2 & converse(all_17_6) = v1 & join(v1, v2) = % 11.95/2.50 | v0 & $i(v2) & $i(v1) & $i(v0)) % 11.95/2.50 | % 11.95/2.50 | GROUND_INST: instantiating (1) with all_17_1, all_17_2, all_17_0, simplifying % 11.95/2.50 | with (14), (15), (17) gives: % 11.95/2.50 | (24) join(all_17_1, all_17_2) = all_17_0 & $i(all_17_0) % 11.95/2.50 | % 11.95/2.50 | ALPHA: (24) implies: % 11.95/2.50 | (25) $i(all_17_0) % 11.95/2.50 | % 11.95/2.51 | GROUND_INST: instantiating (3) with all_17_2, all_17_1, all_17_0, simplifying % 11.95/2.51 | with (14), (15), (17) gives: % 11.95/2.51 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_0) = v0 & % 11.95/2.51 | converse(all_17_1) = v2 & converse(all_17_2) = v1 & join(v1, v2) = % 11.95/2.51 | v0 & $i(v2) & $i(v1) & $i(v0)) % 11.95/2.51 | % 11.95/2.51 | GROUND_INST: instantiating (converse_cancellativity) with all_17_7, all_17_6, % 11.95/2.51 | all_17_2, simplifying with (10), (11), (18) gives: % 11.95/2.51 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 11.95/2.51 | (converse(all_17_7) = v0 & composition(v0, v1) = v2 & % 11.95/2.51 | complement(all_17_2) = v1 & complement(all_17_6) = v3 & join(v2, v3) % 11.95/2.51 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.95/2.51 | % 11.95/2.51 | GROUND_INST: instantiating (4) with all_17_7, all_17_6, all_17_2, simplifying % 11.95/2.51 | with (10), (11), (18) gives: % 11.95/2.51 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_2) = v0 & % 11.95/2.51 | converse(all_17_6) = v1 & converse(all_17_7) = v2 & composition(v1, % 11.95/2.51 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 11.95/2.51 | % 11.95/2.51 | GROUND_INST: instantiating (converse_cancellativity) with all_17_7, all_17_5, % 11.95/2.51 | all_17_1, simplifying with (10), (12), (19) gives: % 11.95/2.51 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 11.95/2.51 | (converse(all_17_7) = v0 & composition(v0, v1) = v2 & % 11.95/2.51 | complement(all_17_1) = v1 & complement(all_17_5) = v3 & join(v2, v3) % 11.95/2.51 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.95/2.51 | % 11.95/2.51 | GROUND_INST: instantiating (4) with all_17_7, all_17_5, all_17_1, simplifying % 11.95/2.51 | with (10), (12), (19) gives: % 11.95/2.51 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_1) = v0 & % 11.95/2.51 | converse(all_17_5) = v1 & converse(all_17_7) = v2 & composition(v1, % 11.95/2.51 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 11.95/2.51 | % 11.95/2.51 | GROUND_INST: instantiating (converse_cancellativity) with all_17_7, all_17_4, % 11.95/2.51 | all_17_3, simplifying with (10), (20), (22) gives: % 11.95/2.51 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 11.95/2.51 | (converse(all_17_7) = v0 & composition(v0, v1) = v2 & % 11.95/2.51 | complement(all_17_3) = v1 & complement(all_17_4) = v3 & join(v2, v3) % 11.95/2.51 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.95/2.51 | % 11.95/2.51 | GROUND_INST: instantiating (4) with all_17_7, all_17_4, all_17_3, simplifying % 11.95/2.51 | with (10), (20), (22) gives: % 11.95/2.51 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_3) = v0 & % 11.95/2.51 | converse(all_17_4) = v1 & converse(all_17_7) = v2 & composition(v1, % 11.95/2.51 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 11.95/2.51 | % 11.95/2.51 | DELTA: instantiating (23) with fresh symbols all_25_0, all_25_1, all_25_2 % 11.95/2.51 | gives: % 11.95/2.51 | (33) converse(all_17_4) = all_25_2 & converse(all_17_5) = all_25_0 & % 11.95/2.51 | converse(all_17_6) = all_25_1 & join(all_25_1, all_25_0) = all_25_2 & % 11.95/2.51 | $i(all_25_0) & $i(all_25_1) & $i(all_25_2) % 11.95/2.51 | % 11.95/2.51 | ALPHA: (33) implies: % 11.95/2.51 | (34) join(all_25_1, all_25_0) = all_25_2 % 11.95/2.51 | (35) converse(all_17_6) = all_25_1 % 11.95/2.51 | (36) converse(all_17_5) = all_25_0 % 11.95/2.51 | (37) converse(all_17_4) = all_25_2 % 11.95/2.51 | % 11.95/2.51 | DELTA: instantiating (32) with fresh symbols all_27_0, all_27_1, all_27_2 % 11.95/2.51 | gives: % 11.95/2.51 | (38) converse(all_17_3) = all_27_2 & converse(all_17_4) = all_27_1 & % 11.95/2.51 | converse(all_17_7) = all_27_0 & composition(all_27_1, all_27_0) = % 11.95/2.52 | all_27_2 & $i(all_27_0) & $i(all_27_1) & $i(all_27_2) % 11.95/2.52 | % 11.95/2.52 | ALPHA: (38) implies: % 11.95/2.52 | (39) composition(all_27_1, all_27_0) = all_27_2 % 11.95/2.52 | (40) converse(all_17_7) = all_27_0 % 11.95/2.52 | (41) converse(all_17_4) = all_27_1 % 11.95/2.52 | (42) converse(all_17_3) = all_27_2 % 11.95/2.52 | % 11.95/2.52 | DELTA: instantiating (30) with fresh symbols all_29_0, all_29_1, all_29_2 % 11.95/2.52 | gives: % 11.95/2.52 | (43) converse(all_17_1) = all_29_2 & converse(all_17_5) = all_29_1 & % 11.95/2.52 | converse(all_17_7) = all_29_0 & composition(all_29_1, all_29_0) = % 11.95/2.52 | all_29_2 & $i(all_29_0) & $i(all_29_1) & $i(all_29_2) % 11.95/2.52 | % 11.95/2.52 | ALPHA: (43) implies: % 11.95/2.52 | (44) $i(all_29_1) % 11.95/2.52 | (45) $i(all_29_0) % 11.95/2.52 | (46) composition(all_29_1, all_29_0) = all_29_2 % 11.95/2.52 | (47) converse(all_17_7) = all_29_0 % 11.95/2.52 | (48) converse(all_17_5) = all_29_1 % 11.95/2.52 | (49) converse(all_17_1) = all_29_2 % 11.95/2.52 | % 11.95/2.52 | DELTA: instantiating (26) with fresh symbols all_31_0, all_31_1, all_31_2 % 11.95/2.52 | gives: % 11.95/2.52 | (50) converse(all_17_0) = all_31_2 & converse(all_17_1) = all_31_0 & % 11.95/2.52 | converse(all_17_2) = all_31_1 & join(all_31_1, all_31_0) = all_31_2 & % 11.95/2.52 | $i(all_31_0) & $i(all_31_1) & $i(all_31_2) % 11.95/2.52 | % 11.95/2.52 | ALPHA: (50) implies: % 11.95/2.52 | (51) $i(all_31_0) % 11.95/2.52 | (52) join(all_31_1, all_31_0) = all_31_2 % 11.95/2.52 | (53) converse(all_17_2) = all_31_1 % 11.95/2.52 | (54) converse(all_17_1) = all_31_0 % 11.95/2.52 | (55) converse(all_17_0) = all_31_2 % 11.95/2.52 | % 11.95/2.52 | DELTA: instantiating (28) with fresh symbols all_33_0, all_33_1, all_33_2 % 11.95/2.52 | gives: % 11.95/2.52 | (56) converse(all_17_2) = all_33_2 & converse(all_17_6) = all_33_1 & % 11.95/2.52 | converse(all_17_7) = all_33_0 & composition(all_33_1, all_33_0) = % 11.95/2.52 | all_33_2 & $i(all_33_0) & $i(all_33_1) & $i(all_33_2) % 11.95/2.52 | % 11.95/2.52 | ALPHA: (56) implies: % 11.95/2.52 | (57) $i(all_33_2) % 11.95/2.52 | (58) $i(all_33_1) % 11.95/2.52 | (59) composition(all_33_1, all_33_0) = all_33_2 % 11.95/2.52 | (60) converse(all_17_7) = all_33_0 % 11.95/2.52 | (61) converse(all_17_6) = all_33_1 % 11.95/2.52 | (62) converse(all_17_2) = all_33_2 % 11.95/2.52 | % 11.95/2.52 | DELTA: instantiating (31) with fresh symbols all_35_0, all_35_1, all_35_2, % 11.95/2.52 | all_35_3 gives: % 11.95/2.52 | (63) converse(all_17_7) = all_35_3 & composition(all_35_3, all_35_2) = % 11.95/2.52 | all_35_1 & complement(all_17_3) = all_35_2 & complement(all_17_4) = % 11.95/2.52 | all_35_0 & join(all_35_1, all_35_0) = all_35_0 & $i(all_35_0) & % 11.95/2.52 | $i(all_35_1) & $i(all_35_2) & $i(all_35_3) % 11.95/2.52 | % 11.95/2.52 | ALPHA: (63) implies: % 11.95/2.52 | (64) converse(all_17_7) = all_35_3 % 11.95/2.52 | % 11.95/2.52 | DELTA: instantiating (29) with fresh symbols all_37_0, all_37_1, all_37_2, % 11.95/2.52 | all_37_3 gives: % 11.95/2.52 | (65) converse(all_17_7) = all_37_3 & composition(all_37_3, all_37_2) = % 11.95/2.52 | all_37_1 & complement(all_17_1) = all_37_2 & complement(all_17_5) = % 11.95/2.52 | all_37_0 & join(all_37_1, all_37_0) = all_37_0 & $i(all_37_0) & % 11.95/2.52 | $i(all_37_1) & $i(all_37_2) & $i(all_37_3) % 11.95/2.52 | % 11.95/2.52 | ALPHA: (65) implies: % 11.95/2.52 | (66) converse(all_17_7) = all_37_3 % 11.95/2.52 | % 11.95/2.52 | DELTA: instantiating (27) with fresh symbols all_39_0, all_39_1, all_39_2, % 11.95/2.52 | all_39_3 gives: % 11.95/2.52 | (67) converse(all_17_7) = all_39_3 & composition(all_39_3, all_39_2) = % 11.95/2.52 | all_39_1 & complement(all_17_2) = all_39_2 & complement(all_17_6) = % 11.95/2.52 | all_39_0 & join(all_39_1, all_39_0) = all_39_0 & $i(all_39_0) & % 11.95/2.52 | $i(all_39_1) & $i(all_39_2) & $i(all_39_3) % 11.95/2.52 | % 11.95/2.52 | ALPHA: (67) implies: % 11.95/2.52 | (68) converse(all_17_7) = all_39_3 % 11.95/2.52 | % 11.95/2.52 | GROUND_INST: instantiating (5) with all_35_3, all_37_3, all_17_7, simplifying % 11.95/2.52 | with (64), (66) gives: % 11.95/2.52 | (69) all_37_3 = all_35_3 % 11.95/2.52 | % 11.95/2.52 | GROUND_INST: instantiating (5) with all_33_0, all_37_3, all_17_7, simplifying % 11.95/2.52 | with (60), (66) gives: % 11.95/2.52 | (70) all_37_3 = all_33_0 % 11.95/2.52 | % 11.95/2.53 | GROUND_INST: instantiating (5) with all_29_0, all_37_3, all_17_7, simplifying % 11.95/2.53 | with (47), (66) gives: % 11.95/2.53 | (71) all_37_3 = all_29_0 % 11.95/2.53 | % 11.95/2.53 | GROUND_INST: instantiating (5) with all_35_3, all_39_3, all_17_7, simplifying % 11.95/2.53 | with (64), (68) gives: % 11.95/2.53 | (72) all_39_3 = all_35_3 % 11.95/2.53 | % 11.95/2.53 | GROUND_INST: instantiating (5) with all_27_0, all_39_3, all_17_7, simplifying % 11.95/2.53 | with (40), (68) gives: % 12.24/2.53 | (73) all_39_3 = all_27_0 % 12.24/2.53 | % 12.24/2.53 | GROUND_INST: instantiating (5) with all_25_1, all_33_1, all_17_6, simplifying % 12.24/2.53 | with (35), (61) gives: % 12.24/2.53 | (74) all_33_1 = all_25_1 % 12.24/2.53 | % 12.24/2.53 | GROUND_INST: instantiating (5) with all_25_0, all_29_1, all_17_5, simplifying % 12.24/2.53 | with (36), (48) gives: % 12.24/2.53 | (75) all_29_1 = all_25_0 % 12.24/2.53 | % 12.24/2.53 | GROUND_INST: instantiating (5) with all_25_2, all_27_1, all_17_4, simplifying % 12.24/2.53 | with (37), (41) gives: % 12.24/2.53 | (76) all_27_1 = all_25_2 % 12.24/2.53 | % 12.24/2.53 | GROUND_INST: instantiating (5) with all_31_1, all_33_2, all_17_2, simplifying % 12.24/2.53 | with (53), (62) gives: % 12.24/2.53 | (77) all_33_2 = all_31_1 % 12.24/2.53 | % 12.24/2.53 | GROUND_INST: instantiating (5) with all_29_2, all_31_0, all_17_1, simplifying % 12.24/2.53 | with (49), (54) gives: % 12.24/2.53 | (78) all_31_0 = all_29_2 % 12.24/2.53 | % 12.24/2.53 | COMBINE_EQS: (72), (73) imply: % 12.24/2.53 | (79) all_35_3 = all_27_0 % 12.24/2.53 | % 12.24/2.53 | SIMP: (79) implies: % 12.24/2.53 | (80) all_35_3 = all_27_0 % 12.24/2.53 | % 12.24/2.53 | COMBINE_EQS: (70), (71) imply: % 12.24/2.53 | (81) all_33_0 = all_29_0 % 12.24/2.53 | % 12.24/2.53 | COMBINE_EQS: (69), (70) imply: % 12.24/2.53 | (82) all_35_3 = all_33_0 % 12.24/2.53 | % 12.24/2.53 | SIMP: (82) implies: % 12.24/2.53 | (83) all_35_3 = all_33_0 % 12.24/2.53 | % 12.24/2.53 | COMBINE_EQS: (80), (83) imply: % 12.24/2.53 | (84) all_33_0 = all_27_0 % 12.24/2.53 | % 12.24/2.53 | SIMP: (84) implies: % 12.24/2.53 | (85) all_33_0 = all_27_0 % 12.24/2.53 | % 12.24/2.53 | COMBINE_EQS: (81), (85) imply: % 12.24/2.53 | (86) all_29_0 = all_27_0 % 12.24/2.53 | % 12.24/2.53 | SIMP: (86) implies: % 12.24/2.53 | (87) all_29_0 = all_27_0 % 12.24/2.53 | % 12.24/2.53 | REDUCE: (59), (74), (77), (85) imply: % 12.24/2.53 | (88) composition(all_25_1, all_27_0) = all_31_1 % 12.24/2.53 | % 12.24/2.53 | REDUCE: (46), (75), (87) imply: % 12.24/2.53 | (89) composition(all_25_0, all_27_0) = all_29_2 % 12.24/2.53 | % 12.24/2.53 | REDUCE: (39), (76) imply: % 12.24/2.53 | (90) composition(all_25_2, all_27_0) = all_27_2 % 12.24/2.53 | % 12.24/2.53 | REDUCE: (52), (78) imply: % 12.24/2.53 | (91) join(all_31_1, all_29_2) = all_31_2 % 12.24/2.53 | % 12.24/2.53 | REDUCE: (58), (74) imply: % 12.24/2.53 | (92) $i(all_25_1) % 12.24/2.53 | % 12.24/2.53 | REDUCE: (57), (77) imply: % 12.24/2.53 | (93) $i(all_31_1) % 12.24/2.53 | % 12.24/2.53 | REDUCE: (51), (78) imply: % 12.24/2.53 | (94) $i(all_29_2) % 12.24/2.53 | % 12.24/2.53 | REDUCE: (45), (87) imply: % 12.24/2.53 | (95) $i(all_27_0) % 12.24/2.53 | % 12.24/2.53 | REDUCE: (44), (75) imply: % 12.24/2.53 | (96) $i(all_25_0) % 12.24/2.53 | % 12.24/2.53 | GROUND_INST: instantiating (1) with all_25_0, all_25_1, all_25_2, simplifying % 12.24/2.53 | with (34), (92), (96) gives: % 12.24/2.53 | (97) join(all_25_0, all_25_1) = all_25_2 & $i(all_25_2) % 12.24/2.53 | % 12.24/2.53 | ALPHA: (97) implies: % 12.24/2.53 | (98) $i(all_25_2) % 12.24/2.53 | % 12.24/2.53 | GROUND_INST: instantiating (3) with all_31_1, all_29_2, all_31_2, simplifying % 12.24/2.53 | with (91), (93), (94) gives: % 12.24/2.54 | (99) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_31_1) = v1 & % 12.24/2.54 | converse(all_31_2) = v0 & converse(all_29_2) = v2 & join(v1, v2) = % 12.24/2.54 | v0 & $i(v2) & $i(v1) & $i(v0)) % 12.24/2.54 | % 12.24/2.54 | GROUND_INST: instantiating (4) with all_25_2, all_27_0, all_27_2, simplifying % 12.24/2.54 | with (90), (95), (98) gives: % 12.24/2.54 | (100) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_27_0) = v1 & % 12.24/2.54 | converse(all_27_2) = v0 & converse(all_25_2) = v2 & composition(v1, % 12.24/2.54 | v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 12.24/2.54 | % 12.24/2.54 | GROUND_INST: instantiating (2) with all_25_1, all_25_0, all_27_0, all_31_1, % 12.24/2.54 | all_29_2, all_31_2, simplifying with (88), (89), (91), (92), % 12.24/2.54 | (95), (96) gives: % 12.24/2.54 | (101) ? [v0: $i] : (composition(v0, all_27_0) = all_31_2 & join(all_25_1, % 12.24/2.54 | all_25_0) = v0 & $i(v0) & $i(all_31_2)) % 12.24/2.54 | % 12.24/2.54 | GROUND_INST: instantiating (converse_idempotence) with all_17_3, all_27_2, % 12.24/2.54 | simplifying with (13), (42) gives: % 12.24/2.54 | (102) converse(all_27_2) = all_17_3 % 12.24/2.54 | % 12.24/2.54 | GROUND_INST: instantiating (converse_idempotence) with all_17_0, all_31_2, % 12.24/2.54 | simplifying with (25), (55) gives: % 12.24/2.54 | (103) converse(all_31_2) = all_17_0 % 12.24/2.54 | % 12.24/2.54 | DELTA: instantiating (101) with fresh symbol all_57_0 gives: % 12.24/2.54 | (104) composition(all_57_0, all_27_0) = all_31_2 & join(all_25_1, all_25_0) % 12.24/2.54 | = all_57_0 & $i(all_57_0) & $i(all_31_2) % 12.24/2.54 | % 12.24/2.54 | ALPHA: (104) implies: % 12.24/2.54 | (105) join(all_25_1, all_25_0) = all_57_0 % 12.24/2.54 | (106) composition(all_57_0, all_27_0) = all_31_2 % 12.24/2.54 | % 12.24/2.54 | DELTA: instantiating (100) with fresh symbols all_83_0, all_83_1, all_83_2 % 12.24/2.54 | gives: % 12.24/2.54 | (107) converse(all_27_0) = all_83_1 & converse(all_27_2) = all_83_2 & % 12.24/2.54 | converse(all_25_2) = all_83_0 & composition(all_83_1, all_83_0) = % 12.24/2.54 | all_83_2 & $i(all_83_0) & $i(all_83_1) & $i(all_83_2) % 12.24/2.54 | % 12.24/2.54 | ALPHA: (107) implies: % 12.24/2.54 | (108) converse(all_27_2) = all_83_2 % 12.24/2.54 | % 12.24/2.54 | DELTA: instantiating (99) with fresh symbols all_85_0, all_85_1, all_85_2 % 12.24/2.54 | gives: % 12.24/2.54 | (109) converse(all_31_1) = all_85_1 & converse(all_31_2) = all_85_2 & % 12.24/2.54 | converse(all_29_2) = all_85_0 & join(all_85_1, all_85_0) = all_85_2 & % 12.24/2.54 | $i(all_85_0) & $i(all_85_1) & $i(all_85_2) % 12.24/2.54 | % 12.24/2.54 | ALPHA: (109) implies: % 12.24/2.54 | (110) converse(all_31_2) = all_85_2 % 12.24/2.54 | % 12.24/2.54 | GROUND_INST: instantiating (6) with all_25_2, all_57_0, all_25_0, all_25_1, % 12.24/2.54 | simplifying with (34), (105) gives: % 12.24/2.54 | (111) all_57_0 = all_25_2 % 12.24/2.54 | % 12.24/2.54 | GROUND_INST: instantiating (5) with all_17_3, all_83_2, all_27_2, simplifying % 12.24/2.54 | with (102), (108) gives: % 12.24/2.54 | (112) all_83_2 = all_17_3 % 12.24/2.54 | % 12.24/2.54 | GROUND_INST: instantiating (5) with all_17_0, all_85_2, all_31_2, simplifying % 12.24/2.54 | with (103), (110) gives: % 12.24/2.54 | (113) all_85_2 = all_17_0 % 12.24/2.54 | % 12.24/2.54 | REDUCE: (106), (111) imply: % 12.24/2.54 | (114) composition(all_25_2, all_27_0) = all_31_2 % 12.24/2.54 | % 12.24/2.54 | GROUND_INST: instantiating (7) with all_27_2, all_31_2, all_27_0, all_25_2, % 12.24/2.54 | simplifying with (90), (114) gives: % 12.24/2.54 | (115) all_31_2 = all_27_2 % 12.24/2.54 | % 12.24/2.54 | REDUCE: (103), (115) imply: % 12.24/2.54 | (116) converse(all_27_2) = all_17_0 % 12.24/2.54 | % 12.24/2.54 | GROUND_INST: instantiating (5) with all_17_3, all_17_0, all_27_2, simplifying % 12.24/2.54 | with (102), (116) gives: % 12.24/2.54 | (117) all_17_0 = all_17_3 % 12.24/2.54 | % 12.24/2.54 | REDUCE: (9), (117) imply: % 12.24/2.54 | (118) $false % 12.24/2.55 | % 12.24/2.55 | CLOSE: (118) is inconsistent. % 12.24/2.55 | % 12.24/2.55 End of proof % 12.24/2.55 % SZS output end Proof for theBenchmark % 12.24/2.55 % 12.24/2.55 1849ms %------------------------------------------------------------------------------