%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL664+1.005 : TPTP v9.3.1. 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 : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:54:35 PM UTC 2026 % Result : Theorem 172.96s 23.03s % Output : Proof 173.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : LCL664+1.005 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.02 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.04/0.31 % Computer : n012.cluster.edu % 0.04/0.31 % Model : x86_64 x86_64 % 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.04/0.31 % Memory : 8046.5625MB % 0.04/0.31 % OS : Linux 6.8.0-71-generic % 0.04/0.31 % CPULimit : 300 % 0.04/0.31 % WCLimit : 300 % 0.04/0.31 % DateTime : Sat Sep 5 01:40:27 UTC 2026 % 0.04/0.31 % CPUTime : % 0.04/0.32 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.24/0.49 ________ _____ % 0.24/0.49 ___ __ \_________(_)________________________________ % 0.24/0.49 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.24/0.49 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.24/0.49 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.24/0.49 % 0.24/0.49 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.24/0.49 (2023-06-19) % 0.24/0.49 % 0.24/0.49 (c) Philipp Rümmer, 2009-2023 % 0.24/0.49 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.24/0.49 Amanda Stjerna. % 0.24/0.49 Free software under BSD-3-Clause. % 0.24/0.49 % 0.24/0.49 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.24/0.49 % 0.24/0.49 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.24/0.50 Running up to 7 provers in parallel. % 0.24/0.51 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.24/0.51 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.24/0.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.24/0.51 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.24/0.51 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.24/0.51 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.24/0.51 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.42/1.32 Prover 1: Preprocessing ... % 5.42/1.32 Prover 4: Preprocessing ... % 5.42/1.36 Prover 3: Preprocessing ... % 5.42/1.37 Prover 6: Preprocessing ... % 5.42/1.38 Prover 0: Preprocessing ... % 5.42/1.38 Prover 2: Preprocessing ... % 6.23/1.44 Prover 5: Preprocessing ... % 12.49/2.21 Prover 2: Proving ... % 13.28/2.33 Prover 5: Proving ... % 14.85/2.58 Prover 6: Proving ... % 15.66/2.69 Prover 3: Constructing countermodel ... % 16.44/2.79 Prover 1: Constructing countermodel ... % 17.23/2.81 Prover 0: Proving ... % 18.02/2.97 Prover 4: Constructing countermodel ... % 74.91/10.17 Prover 2: stopped % 74.91/10.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 77.01/10.48 Prover 7: Preprocessing ... % 77.78/10.58 Prover 7: Warning: ignoring some quantifiers % 77.78/10.59 Prover 7: Constructing countermodel ... % 103.73/13.87 Prover 5: stopped % 103.73/13.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 104.49/14.01 Prover 8: Preprocessing ... % 106.82/14.24 Prover 8: Warning: ignoring some quantifiers % 106.82/14.26 Prover 8: Constructing countermodel ... % 119.27/15.85 Prover 1: stopped % 119.27/15.85 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 120.10/15.96 Prover 9: Preprocessing ... % 121.14/16.13 Prover 9: Constructing countermodel ... % 134.00/17.75 Prover 6: stopped % 134.00/17.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 135.58/17.95 Prover 10: Preprocessing ... % 135.58/18.00 Prover 10: Warning: ignoring some quantifiers % 135.58/18.01 Prover 10: Constructing countermodel ... % 172.23/22.98 Prover 10: Found proof (size 17) % 172.23/22.98 Prover 10: proved (5222ms) % 172.23/22.98 Prover 7: stopped % 172.23/22.98 Prover 8: stopped % 172.23/22.99 Prover 4: stopped % 172.23/23.00 Prover 3: stopped % 172.23/23.00 Prover 0: stopped % 172.96/23.03 Prover 9: stopped % 172.96/23.03 % 172.96/23.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 172.96/23.03 % 172.96/23.03 % SZS output start Proof for theBenchmark % 172.96/23.03 Assumptions after simplification: % 172.96/23.03 --------------------------------- % 172.96/23.03 % 172.96/23.03 (main) % 172.96/23.10 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ($i(v4) % 172.96/23.10 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & r1(v0, v4) & r1(v0, v3) & r1(v0, v2) & % 172.96/23.10 r1(v0, v1) & ~ p11(v1) & ~ p12(v2) & ~ p13(v3) & ~ p15(v4) & ! [v5: $i] % 172.96/23.10 : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ % 172.96/23.10 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v8, v9) | ~ r1(v7, v8) % 172.96/23.10 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p52(v9)) & ! [v5: $i] : % 172.96/23.10 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ % 172.96/23.10 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v8, v9) | ~ r1(v7, v8) % 172.96/23.10 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p54(v9)) & ! [v5: $i] : % 172.96/23.10 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~ $i(v9) | ~ % 172.96/23.10 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v8, v9) | ~ r1(v7, v8) % 172.96/23.10 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p56(v9)) & ! [v5: $i] : % 172.96/23.10 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) % 172.96/23.10 | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, % 172.96/23.10 v5) | p41(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p51(v9))) & ! % 172.96/23.10 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) % 172.96/23.10 | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | % 172.96/23.10 ~ r1(v0, v5) | p41(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p53(v9))) % 172.96/23.10 & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ % 172.96/23.10 $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, % 172.96/23.10 v6) | ~ r1(v0, v5) | p41(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ % 172.96/23.10 p55(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 172.96/23.10 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) % 172.96/23.10 | ~ r1(v5, v6) | ~ r1(v0, v5) | p41(v8) | ? [v9: $i] : ($i(v9) & r1(v8, % 172.96/23.10 v9) & ~ p54(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 172.96/23.10 $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ % 172.96/23.10 r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p43(v8) | ? [v9: $i] : % 172.96/23.10 ($i(v9) & r1(v8, v9) & ~ p51(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: % 172.96/23.10 $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ % 172.96/23.10 r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p43(v8) | ? % 172.96/23.10 [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p53(v9))) & ! [v5: $i] : ! [v6: $i] % 172.96/23.10 : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) % 172.96/23.10 | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p43(v8) % 172.96/23.10 | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p55(v9))) & ! [v5: $i] : ! % 172.96/23.10 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | % 172.96/23.10 ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | % 172.96/23.10 p45(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p51(v9))) & ! [v5: $i] % 172.96/23.10 : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ % 172.96/23.10 $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ % 172.96/23.10 r1(v0, v5) | p45(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p53(v9))) & % 172.96/23.10 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ % 172.96/23.10 $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, % 172.96/23.10 v6) | ~ r1(v0, v5) | p45(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ % 172.96/23.10 p55(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 172.96/23.10 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) % 172.96/23.10 | ~ r1(v5, v6) | ~ r1(v0, v5) | p42(v8) | ? [v9: $i] : ($i(v9) & r1(v8, % 172.96/23.10 v9) & ~ p52(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 172.96/23.10 $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ % 172.96/23.10 r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p42(v8) | ? [v9: $i] : % 172.96/23.10 ($i(v9) & r1(v8, v9) & ~ p54(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: % 172.96/23.10 $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ % 172.96/23.10 r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p42(v8) | ? % 172.96/23.10 [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p56(v9))) & ! [v5: $i] : ! [v6: $i] % 172.96/23.10 : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) % 172.96/23.10 | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p44(v8) % 172.96/23.10 | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p52(v9))) & ! [v5: $i] : ! % 172.96/23.10 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | % 172.96/23.10 ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | % 172.96/23.10 p44(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p54(v9))) & ! [v5: $i] % 172.96/23.10 : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ $i(v7) | ~ % 172.96/23.10 $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ % 172.96/23.11 r1(v0, v5) | p44(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ p56(v9))) & % 172.96/23.11 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ $i(v8) | ~ % 172.96/23.11 $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) | ~ r1(v5, % 172.96/23.11 v6) | ~ r1(v0, v5) | p46(v8) | ? [v9: $i] : ($i(v9) & r1(v8, v9) & ~ % 172.96/23.11 p52(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 172.96/23.11 $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ r1(v6, v7) % 172.96/23.11 | ~ r1(v5, v6) | ~ r1(v0, v5) | p46(v8) | ? [v9: $i] : ($i(v9) & r1(v8, % 172.96/23.11 v9) & ~ p54(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 172.96/23.11 $i] : ( ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v7, v8) | ~ % 172.96/23.11 r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p46(v8) | ? [v9: $i] : % 172.96/23.11 ($i(v9) & r1(v8, v9) & ~ p56(v9))) & ! [v5: $i] : ! [v6: $i] : ! [v7: % 172.96/23.11 $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | % 172.96/23.11 ~ r1(v0, v5) | p31(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ % 172.96/23.11 p43(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ % 172.96/23.11 $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | % 172.96/23.11 p31(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p45(v8))) & ! [v5: $i] % 172.96/23.11 : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, % 172.96/23.11 v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p33(v7) | ? [v8: $i] : ($i(v8) & % 172.96/23.11 r1(v7, v8) & ~ p43(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 172.96/23.11 ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ % 172.96/23.11 r1(v0, v5) | p33(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p45(v8))) & % 172.96/23.11 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) % 172.96/23.11 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p34(v7) | ? [v8: $i] : % 172.96/23.11 ($i(v8) & r1(v7, v8) & ~ p41(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: % 172.96/23.11 $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | % 172.96/23.11 ~ r1(v0, v5) | p35(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ % 172.96/23.11 p43(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ % 172.96/23.11 $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | % 172.96/23.11 p35(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p45(v8))) & ! [v5: $i] % 172.96/23.11 : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, % 172.96/23.11 v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p32(v7) | ? [v8: $i] : ($i(v8) & % 172.96/23.11 r1(v7, v8) & ~ p42(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( % 172.96/23.11 ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ % 172.96/23.11 r1(v0, v5) | p32(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p44(v8))) & % 172.96/23.11 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) % 172.96/23.11 | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p32(v7) | ? [v8: $i] : % 172.96/23.11 ($i(v8) & r1(v7, v8) & ~ p46(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: % 172.96/23.11 $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | % 172.96/23.11 ~ r1(v0, v5) | p36(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ % 172.96/23.11 p42(v8))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ % 172.96/23.11 $i(v6) | ~ $i(v5) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | % 172.96/23.11 p36(v7) | ? [v8: $i] : ($i(v8) & r1(v7, v8) & ~ p44(v8))) & ! [v5: $i] % 172.96/23.11 : ! [v6: $i] : ! [v7: $i] : ( ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ r1(v6, % 172.96/23.11 v7) | ~ r1(v5, v6) | ~ r1(v0, v5) | p36(v7) | ? [v8: $i] : ($i(v8) & % 172.96/23.11 r1(v7, v8) & ~ p46(v8))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p21(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p31(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p21(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p33(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p21(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p34(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p21(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p35(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p23(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p31(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p23(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p33(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p23(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p35(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p25(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p31(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p25(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p33(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p25(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p35(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p22(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p34(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p22(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p32(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p22(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p36(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p24(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p34(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p24(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p32(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p24(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p36(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p26(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p34(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p26(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p32(v7))) & ! [v5: $i] : ! [v6: $i] : ( ~ $i(v6) | ~ % 172.96/23.11 $i(v5) | ~ r1(v5, v6) | ~ r1(v0, v5) | p26(v6) | ? [v7: $i] : ($i(v7) & % 172.96/23.11 r1(v6, v7) & ~ p36(v7))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | % 172.96/23.11 p11(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p23(v6))) & ! [v5: $i] % 172.96/23.11 : ( ~ $i(v5) | ~ r1(v0, v5) | p11(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) % 172.96/23.11 & ~ p25(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p12(v5) | ? % 172.96/23.11 [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p21(v6))) & ! [v5: $i] : ( ~ $i(v5) % 172.96/23.11 | ~ r1(v0, v5) | p13(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ % 172.96/23.11 p23(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p13(v5) | ? [v6: % 172.96/23.11 $i] : ($i(v6) & r1(v5, v6) & ~ p25(v6))) & ! [v5: $i] : ( ~ $i(v5) | % 172.96/23.11 ~ r1(v0, v5) | p15(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p23(v6))) % 172.96/23.11 & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p15(v5) | ? [v6: $i] : ($i(v6) % 172.96/23.11 & r1(v5, v6) & ~ p25(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | % 172.96/23.11 p14(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p22(v6))) & ! [v5: $i] % 172.96/23.11 : ( ~ $i(v5) | ~ r1(v0, v5) | p14(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) % 172.96/23.11 & ~ p24(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p14(v5) | ? % 172.96/23.11 [v6: $i] : ($i(v6) & r1(v5, v6) & ~ p26(v6))) & ! [v5: $i] : ( ~ $i(v5) % 172.96/23.11 | ~ r1(v0, v5) | p16(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ % 172.96/23.11 p22(v6))) & ! [v5: $i] : ( ~ $i(v5) | ~ r1(v0, v5) | p16(v5) | ? [v6: % 172.96/23.11 $i] : ($i(v6) & r1(v5, v6) & ~ p24(v6))) & ! [v5: $i] : ( ~ $i(v5) | % 172.96/23.11 ~ r1(v0, v5) | p16(v5) | ? [v6: $i] : ($i(v6) & r1(v5, v6) & ~ % 172.96/23.11 p26(v6)))) % 172.96/23.11 % 172.96/23.11 Further assumptions not needed in the proof: % 172.96/23.11 -------------------------------------------- % 172.96/23.11 reflexivity % 172.96/23.11 % 172.96/23.11 Those formulas are unsatisfiable: % 172.96/23.11 --------------------------------- % 172.96/23.11 % 172.96/23.11 Begin of proof % 173.38/23.11 | % 173.38/23.11 | DELTA: instantiating (main) with fresh symbols all_3_0, all_3_1, all_3_2, % 173.38/23.11 | all_3_3, all_3_4 gives: % 173.38/23.15 | (1) $i(all_3_0) & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & $i(all_3_4) & % 173.38/23.15 | r1(all_3_4, all_3_0) & r1(all_3_4, all_3_1) & r1(all_3_4, all_3_2) & % 173.38/23.15 | r1(all_3_4, all_3_3) & ~ p11(all_3_3) & ~ p12(all_3_2) & ~ % 173.38/23.15 | p13(all_3_1) & ~ p15(all_3_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 173.38/23.15 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 173.38/23.15 | | ~ $i(v1) | ~ $i(v0) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, % 173.38/23.15 | v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p52(v4)) & ! [v0: $i] : % 173.38/23.15 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ % 173.38/23.15 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v3, v4) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p54(v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 173.38/23.15 | [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 173.38/23.15 | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p56(v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p41(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p51(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p41(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.15 | r1(v3, v4) & ~ p53(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p41(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p55(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p41(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.15 | r1(v3, v4) & ~ p54(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p43(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p51(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p43(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.15 | r1(v3, v4) & ~ p53(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p43(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p55(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p45(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.15 | r1(v3, v4) & ~ p51(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p45(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p53(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p45(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.15 | r1(v3, v4) & ~ p55(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p42(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p52(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p42(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.15 | r1(v3, v4) & ~ p54(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p42(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p56(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p44(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.15 | r1(v3, v4) & ~ p52(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p44(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p54(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p44(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.15 | r1(v3, v4) & ~ p56(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p46(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p52(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.15 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p46(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.15 | r1(v3, v4) & ~ p54(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p46(v3) | ? [v4: $i] : ($i(v4) & r1(v3, v4) & ~ p56(v4))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 173.38/23.15 | | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p31(v2) | ? % 173.38/23.15 | [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p43(v3))) & ! [v0: $i] : ! % 173.38/23.15 | [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, % 173.38/23.15 | v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p31(v2) | ? [v3: $i] : % 173.38/23.15 | ($i(v3) & r1(v2, v3) & ~ p45(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 173.38/23.15 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p33(v2) | ? [v3: $i] : ($i(v3) & % 173.38/23.15 | r1(v2, v3) & ~ p43(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | % 173.38/23.15 | ~ r1(all_3_4, v0) | p33(v2) | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ % 173.38/23.15 | p45(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | % 173.38/23.15 | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, % 173.38/23.15 | v0) | p34(v2) | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p41(v3))) & % 173.38/23.15 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 173.38/23.15 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p35(v2) % 173.38/23.15 | | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p43(v3))) & ! [v0: $i] : % 173.38/23.15 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p35(v2) | ? [v3: % 173.38/23.15 | $i] : ($i(v3) & r1(v2, v3) & ~ p45(v3))) & ! [v0: $i] : ! [v1: % 173.38/23.15 | $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, % 173.38/23.15 | v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p32(v2) | ? [v3: $i] : % 173.38/23.15 | ($i(v3) & r1(v2, v3) & ~ p42(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 173.38/23.15 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p32(v2) | ? [v3: $i] : ($i(v3) & % 173.38/23.15 | r1(v2, v3) & ~ p44(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 173.38/23.15 | : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | % 173.38/23.15 | ~ r1(all_3_4, v0) | p32(v2) | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ % 173.38/23.15 | p46(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | % 173.38/23.15 | ~ $i(v1) | ~ $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, % 173.38/23.15 | v0) | p36(v2) | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p42(v3))) & % 173.38/23.15 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 173.38/23.15 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p36(v2) % 173.38/23.15 | | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p44(v3))) & ! [v0: $i] : % 173.38/23.15 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p36(v2) | ? [v3: % 173.38/23.15 | $i] : ($i(v3) & r1(v2, v3) & ~ p46(v3))) & ! [v0: $i] : ! [v1: % 173.38/23.15 | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p21(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p31(v2))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p21(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ % 173.38/23.15 | p33(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p21(v1) | ? [v2: $i] : ($i(v2) & % 173.38/23.15 | r1(v1, v2) & ~ p34(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) % 173.38/23.15 | | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p21(v1) | ? [v2: % 173.38/23.15 | $i] : ($i(v2) & r1(v1, v2) & ~ p35(v2))) & ! [v0: $i] : ! [v1: % 173.38/23.15 | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p23(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p31(v2))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p23(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ % 173.38/23.15 | p33(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p23(v1) | ? [v2: $i] : ($i(v2) & % 173.38/23.15 | r1(v1, v2) & ~ p35(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) % 173.38/23.15 | | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p25(v1) | ? [v2: % 173.38/23.15 | $i] : ($i(v2) & r1(v1, v2) & ~ p31(v2))) & ! [v0: $i] : ! [v1: % 173.38/23.15 | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p25(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p33(v2))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p25(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ % 173.38/23.15 | p35(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p22(v1) | ? [v2: $i] : ($i(v2) & % 173.38/23.15 | r1(v1, v2) & ~ p34(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) % 173.38/23.15 | | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p22(v1) | ? [v2: % 173.38/23.15 | $i] : ($i(v2) & r1(v1, v2) & ~ p32(v2))) & ! [v0: $i] : ! [v1: % 173.38/23.15 | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p22(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p36(v2))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p24(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ % 173.38/23.15 | p34(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p24(v1) | ? [v2: $i] : ($i(v2) & % 173.38/23.15 | r1(v1, v2) & ~ p32(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) % 173.38/23.15 | | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p24(v1) | ? [v2: % 173.38/23.15 | $i] : ($i(v2) & r1(v1, v2) & ~ p36(v2))) & ! [v0: $i] : ! [v1: % 173.38/23.15 | $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | % 173.38/23.15 | p26(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ p34(v2))) & ! [v0: % 173.38/23.15 | $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p26(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ % 173.38/23.15 | p32(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 173.38/23.15 | r1(v0, v1) | ~ r1(all_3_4, v0) | p26(v1) | ? [v2: $i] : ($i(v2) & % 173.38/23.15 | r1(v1, v2) & ~ p36(v2))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p11(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ % 173.38/23.15 | p23(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_4, v0) | p11(v0) % 173.38/23.15 | | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p25(v1))) & ! [v0: $i] : ( % 173.38/23.15 | ~ $i(v0) | ~ r1(all_3_4, v0) | p12(v0) | ? [v1: $i] : ($i(v1) & % 173.38/23.15 | r1(v0, v1) & ~ p21(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p13(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ % 173.38/23.15 | p23(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_4, v0) | p13(v0) % 173.38/23.15 | | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p25(v1))) & ! [v0: $i] : ( % 173.38/23.15 | ~ $i(v0) | ~ r1(all_3_4, v0) | p15(v0) | ? [v1: $i] : ($i(v1) & % 173.38/23.15 | r1(v0, v1) & ~ p23(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p15(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ % 173.38/23.15 | p25(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_4, v0) | p14(v0) % 173.38/23.15 | | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p22(v1))) & ! [v0: $i] : ( % 173.38/23.15 | ~ $i(v0) | ~ r1(all_3_4, v0) | p14(v0) | ? [v1: $i] : ($i(v1) & % 173.38/23.15 | r1(v0, v1) & ~ p24(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p14(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ % 173.38/23.15 | p26(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_4, v0) | p16(v0) % 173.38/23.15 | | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ p22(v1))) & ! [v0: $i] : ( % 173.38/23.15 | ~ $i(v0) | ~ r1(all_3_4, v0) | p16(v0) | ? [v1: $i] : ($i(v1) & % 173.38/23.15 | r1(v0, v1) & ~ p24(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 173.38/23.15 | r1(all_3_4, v0) | p16(v0) | ? [v1: $i] : ($i(v1) & r1(v0, v1) & ~ % 173.38/23.15 | p26(v1))) % 173.38/23.15 | % 173.38/23.15 | ALPHA: (1) implies: % 173.38/23.15 | (2) ~ p12(all_3_2) % 173.38/23.15 | (3) r1(all_3_4, all_3_2) % 173.38/23.15 | (4) $i(all_3_2) % 173.38/23.16 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_3_4, v0) | p12(v0) | ? [v1: $i] : % 173.38/23.16 | ($i(v1) & r1(v0, v1) & ~ p21(v1))) % 173.38/23.16 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1(v0, v1) | ~ % 173.38/23.16 | r1(all_3_4, v0) | p21(v1) | ? [v2: $i] : ($i(v2) & r1(v1, v2) & ~ % 173.38/23.16 | p34(v2))) % 173.38/23.16 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 173.38/23.16 | $i(v0) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_3_4, v0) | p34(v2) % 173.38/23.16 | | ? [v3: $i] : ($i(v3) & r1(v2, v3) & ~ p41(v3))) % 173.38/23.16 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 173.38/23.16 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ % 173.38/23.16 | r1(v0, v1) | ~ r1(all_3_4, v0) | p41(v3) | ? [v4: $i] : ($i(v4) & % 173.38/23.16 | r1(v3, v4) & ~ p54(v4))) % 173.38/23.16 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 173.38/23.16 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r1(v3, % 173.38/23.16 | v4) | ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ % 173.38/23.16 | r1(all_3_4, v0) | p54(v4)) % 173.38/23.16 | % 173.38/23.16 | GROUND_INST: instantiating (5) with all_3_2, simplifying with (2), (3), (4) % 173.38/23.16 | gives: % 173.38/23.16 | (10) ? [v0: $i] : ($i(v0) & r1(all_3_2, v0) & ~ p21(v0)) % 173.38/23.16 | % 173.38/23.16 | DELTA: instantiating (10) with fresh symbol all_17_0 gives: % 173.38/23.16 | (11) $i(all_17_0) & r1(all_3_2, all_17_0) & ~ p21(all_17_0) % 173.38/23.16 | % 173.38/23.16 | ALPHA: (11) implies: % 173.38/23.16 | (12) ~ p21(all_17_0) % 173.38/23.16 | (13) r1(all_3_2, all_17_0) % 173.38/23.16 | (14) $i(all_17_0) % 173.38/23.16 | % 173.38/23.16 | GROUND_INST: instantiating (6) with all_3_2, all_17_0, simplifying with (3), % 173.38/23.16 | (4), (12), (13), (14) gives: % 173.38/23.16 | (15) ? [v0: $i] : ($i(v0) & r1(all_17_0, v0) & ~ p34(v0)) % 173.38/23.16 | % 173.38/23.16 | DELTA: instantiating (15) with fresh symbol all_52_0 gives: % 173.38/23.16 | (16) $i(all_52_0) & r1(all_17_0, all_52_0) & ~ p34(all_52_0) % 173.38/23.16 | % 173.38/23.16 | ALPHA: (16) implies: % 173.38/23.16 | (17) ~ p34(all_52_0) % 173.38/23.16 | (18) r1(all_17_0, all_52_0) % 173.38/23.16 | (19) $i(all_52_0) % 173.38/23.16 | % 173.38/23.16 | GROUND_INST: instantiating (7) with all_3_2, all_17_0, all_52_0, simplifying % 173.38/23.16 | with (3), (4), (13), (14), (17), (18), (19) gives: % 173.38/23.16 | (20) ? [v0: $i] : ($i(v0) & r1(all_52_0, v0) & ~ p41(v0)) % 173.38/23.16 | % 173.38/23.16 | DELTA: instantiating (20) with fresh symbol all_115_0 gives: % 173.38/23.16 | (21) $i(all_115_0) & r1(all_52_0, all_115_0) & ~ p41(all_115_0) % 173.38/23.16 | % 173.38/23.16 | ALPHA: (21) implies: % 173.38/23.16 | (22) ~ p41(all_115_0) % 173.38/23.16 | (23) r1(all_52_0, all_115_0) % 173.38/23.16 | (24) $i(all_115_0) % 173.38/23.16 | % 173.38/23.16 | GROUND_INST: instantiating (8) with all_3_2, all_17_0, all_52_0, all_115_0, % 173.38/23.16 | simplifying with (3), (4), (13), (14), (18), (19), (22), (23), % 173.38/23.16 | (24) gives: % 173.38/23.16 | (25) ? [v0: $i] : ($i(v0) & r1(all_115_0, v0) & ~ p54(v0)) % 173.38/23.16 | % 173.38/23.16 | DELTA: instantiating (25) with fresh symbol all_362_0 gives: % 173.38/23.16 | (26) $i(all_362_0) & r1(all_115_0, all_362_0) & ~ p54(all_362_0) % 173.38/23.16 | % 173.38/23.16 | ALPHA: (26) implies: % 173.38/23.16 | (27) ~ p54(all_362_0) % 173.38/23.16 | (28) r1(all_115_0, all_362_0) % 173.38/23.16 | (29) $i(all_362_0) % 173.38/23.16 | % 173.38/23.16 | GROUND_INST: instantiating (9) with all_3_2, all_17_0, all_52_0, all_115_0, % 173.38/23.16 | all_362_0, simplifying with (3), (4), (13), (14), (18), (19), % 173.38/23.16 | (23), (24), (27), (28), (29) gives: % 173.38/23.16 | (30) $false % 173.38/23.16 | % 173.38/23.16 | CLOSE: (30) is inconsistent. % 173.38/23.16 | % 173.38/23.16 End of proof % 173.38/23.17 % SZS output end Proof for theBenchmark % 173.38/23.17 % 173.38/23.17 22675ms %------------------------------------------------------------------------------