%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV415+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 22:56:15 EDT 2023 % Result : Theorem 15.46s 2.87s % Output : Proof 22.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.13 % Problem : SWV415+2 : TPTP v8.1.2. Released v3.3.0. % 0.09/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n004.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 06:05:37 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.60/1.24 Prover 4: Preprocessing ... % 3.60/1.24 Prover 1: Preprocessing ... % 4.12/1.28 Prover 2: Preprocessing ... % 4.12/1.28 Prover 5: Preprocessing ... % 4.12/1.28 Prover 0: Preprocessing ... % 4.12/1.28 Prover 6: Preprocessing ... % 4.12/1.28 Prover 3: Preprocessing ... % 9.72/2.09 Prover 1: Warning: ignoring some quantifiers % 10.61/2.22 Prover 1: Constructing countermodel ... % 11.05/2.24 Prover 5: Proving ... % 11.05/2.25 Prover 6: Proving ... % 11.05/2.25 Prover 3: Warning: ignoring some quantifiers % 11.21/2.29 Prover 3: Constructing countermodel ... % 11.92/2.36 Prover 0: Proving ... % 11.92/2.38 Prover 4: Constructing countermodel ... % 11.92/2.42 Prover 2: Proving ... % 13.70/2.70 Prover 1: gave up % 13.70/2.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.54/2.72 Prover 3: gave up % 14.54/2.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.80/2.80 Prover 7: Preprocessing ... % 14.80/2.81 Prover 8: Preprocessing ... % 15.46/2.87 Prover 0: proved (2231ms) % 15.46/2.87 % 15.46/2.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.46/2.87 % 15.46/2.88 Prover 5: stopped % 15.46/2.88 Prover 6: stopped % 15.46/2.89 Prover 2: stopped % 15.87/2.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.87/2.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.87/2.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.87/2.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.87/2.95 Prover 13: Preprocessing ... % 16.35/2.96 Prover 11: Preprocessing ... % 16.40/2.97 Prover 10: Preprocessing ... % 16.40/2.99 Prover 7: Warning: ignoring some quantifiers % 16.40/3.00 Prover 16: Preprocessing ... % 16.77/3.01 Prover 7: Constructing countermodel ... % 17.07/3.13 Prover 8: Warning: ignoring some quantifiers % 17.78/3.14 Prover 10: Warning: ignoring some quantifiers % 17.78/3.16 Prover 10: Constructing countermodel ... % 17.78/3.17 Prover 16: Warning: ignoring some quantifiers % 17.78/3.18 Prover 8: Constructing countermodel ... % 18.22/3.20 Prover 16: Constructing countermodel ... % 18.22/3.28 Prover 13: Warning: ignoring some quantifiers % 18.74/3.32 Prover 13: Constructing countermodel ... % 19.14/3.35 Prover 11: Constructing countermodel ... % 21.52/3.64 Prover 11: Found proof (size 47) % 21.52/3.64 Prover 11: proved (752ms) % 21.52/3.64 Prover 16: stopped % 21.52/3.64 Prover 10: stopped % 21.52/3.64 Prover 4: stopped % 21.52/3.64 Prover 13: stopped % 21.52/3.64 Prover 8: stopped % 21.52/3.64 Prover 7: stopped % 21.52/3.64 % 21.52/3.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.52/3.64 % 21.52/3.65 % SZS output start Proof for theBenchmark % 21.52/3.65 Assumptions after simplification: % 21.52/3.65 --------------------------------- % 21.52/3.65 % 21.52/3.65 (ax42) % 21.52/3.68 $i(bottom) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.52/3.68 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (insert_pqp(v0, v3) = % 21.52/3.68 v4) | ~ (triple(v4, v6, v2) = v7) | ~ (pair(v3, bottom) = v5) | ~ % 21.52/3.68 (insert_slb(v1, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.52/3.68 ? [v8: $i] : (triple(v0, v1, v2) = v8 & insert_cpq(v8, v3) = v7 & $i(v8) & % 21.52/3.68 $i(v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.52/3.68 $i] : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = % 21.52/3.68 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? % 21.52/3.68 [v7: $i] : ? [v8: $i] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, v2) = v5 % 21.52/3.68 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8 & $i(v8) & $i(v7) & % 21.52/3.68 $i(v6) & $i(v5))) % 21.52/3.68 % 21.52/3.68 (ax50) % 21.52/3.68 $i(create_slb) & $i(bottom) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.52/3.68 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.52/3.68 findmin_cpq_res(v2) = bottom) % 21.52/3.68 % 21.52/3.68 (ax54) % 21.52/3.68 $i(create_slb) & $i(create_pq) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.52/3.68 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | i(v2) = % 21.52/3.68 create_pq) % 21.52/3.68 % 21.52/3.68 (ax55) % 21.83/3.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.83/3.69 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~ % 21.83/3.69 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | % 21.83/3.69 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] % 21.83/3.69 : (i(v9) = v10 & i(v7) = v8 & triple(v0, v1, v2) = v9 & insert_pq(v10, v3) = % 21.83/3.69 v8 & $i(v10) & $i(v9) & $i(v8))) % 21.83/3.69 % 21.83/3.69 (big2_induction) % 21.83/3.69 $i(create_slb) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 21.83/3.69 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 21.83/3.69 : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 21.83/3.69 ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? % 21.83/3.69 [v20: $i] : ($i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v6) & $i(v5) & $i(v4) % 21.83/3.69 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ! [v21: $i] : ! [v22: $i] : ! % 21.83/3.69 [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ! % 21.83/3.69 [v28: $i] : ! [v29: $i] : (v29 = v27 | ~ (i(v28) = v29) | ~ (i(v26) = % 21.83/3.69 v27) | ~ (triple(v22, v23, v25) = v28) | ~ (triple(v21, v23, v24) = % 21.83/3.69 v26) | ~ $i(v25) | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21)) % 21.83/3.69 | ( ~ (v20 = v18) & i(v19) = v20 & i(v17) = v18 & triple(v14, create_slb, % 21.83/3.69 v16) = v19 & triple(v13, create_slb, v15) = v17 & $i(v20) & $i(v19) & % 21.83/3.69 $i(v18) & $i(v17)) | ( ~ (v12 = v10) & i(v11) = v12 & i(v9) = v10 & % 21.83/3.69 triple(v2, v8, v4) = v11 & triple(v1, v8, v3) = v9 & pair(v5, v6) = v7 & % 21.83/3.69 insert_slb(v0, v7) = v8 & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) % 21.83/3.69 & $i(v7) & ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : % 21.83/3.69 ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ! [v28: $i] : (v28 = v26 | % 21.83/3.69 ~ (i(v27) = v28) | ~ (i(v25) = v26) | ~ (triple(v22, v0, v24) = v27) % 21.83/3.69 | ~ (triple(v21, v0, v23) = v25) | ~ $i(v24) | ~ $i(v23) | ~ % 21.83/3.69 $i(v22) | ~ $i(v21))))) % 21.83/3.69 % 21.83/3.69 (co2) % 21.83/3.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 21.83/3.69 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v6) & i(v5) = v6 & % 21.83/3.69 i(v4) = v7 & triple(v0, v1, v2) = v4 & insert_cpq(v4, v3) = v5 & % 21.83/3.69 insert_pq(v7, v3) = v8 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 21.83/3.69 & $i(v2) & $i(v1) & $i(v0)) % 21.83/3.69 % 21.83/3.69 (function-axioms) % 21.83/3.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 21.83/3.70 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 21.83/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.83/3.70 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 21.83/3.70 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.83/3.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.83/3.70 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) & % 21.83/3.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 21.83/3.70 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~ % 21.83/3.70 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.83/3.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.83/3.70 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0: % 21.83/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.83/3.70 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) = % 21.83/3.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 21.83/3.70 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] : % 21.83/3.70 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) = % 21.83/3.70 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.83/3.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.83/3.70 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i] % 21.83/3.70 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2) % 21.83/3.70 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 21.83/3.70 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~ % 21.83/3.70 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.83/3.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 21.83/3.70 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 21.83/3.70 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 21.83/3.70 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.83/3.70 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 21.83/3.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 21.83/3.70 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 21.83/3.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.83/3.70 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 21.83/3.70 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.83/3.70 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 21.83/3.70 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 21.83/3.70 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.83/3.70 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ % 21.83/3.70 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.83/3.70 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ % 21.83/3.70 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.83/3.70 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ % 21.83/3.70 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.83/3.70 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ % 21.83/3.70 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.83/3.70 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = % 21.83/3.70 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.83/3.70 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~ % 21.83/3.70 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.83/3.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.83/3.70 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] : % 21.83/3.70 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) = % 21.83/3.70 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.83/3.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.83/3.70 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 21.83/3.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 21.83/3.70 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 21.83/3.70 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 21.83/3.70 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] : % 21.83/3.70 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) = % 21.83/3.70 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.83/3.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~ % 21.83/3.70 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 21.83/3.70 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.83/3.70 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) % 21.83/3.70 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 21.83/3.70 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : % 21.83/3.70 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ % 21.83/3.70 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.83/3.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) % 21.83/3.70 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.83/3.70 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! % 21.83/3.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = % 21.83/3.70 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 21.83/3.70 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) % 21.83/3.70 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.83/3.70 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = % 21.83/3.70 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.83/3.71 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0)) % 21.83/3.71 % 21.83/3.71 Further assumptions not needed in the proof: % 21.83/3.71 -------------------------------------------- % 21.83/3.71 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22, % 21.83/3.71 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, % 21.83/3.71 ax36, ax37, ax38, ax39, ax40, ax41, ax43, ax44, ax45, ax46, ax47, ax48, ax49, % 21.83/3.71 ax51, ax52, ax53, ax56, ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax7, ax8, ax9, % 21.83/3.71 bottom_smallest, reflexivity, stricly_smaller_definition, totality, transitivity % 21.83/3.71 % 21.83/3.71 Those formulas are unsatisfiable: % 21.83/3.71 --------------------------------- % 21.83/3.71 % 21.83/3.71 Begin of proof % 21.83/3.71 | % 21.83/3.71 | ALPHA: (ax42) implies: % 21.83/3.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.83/3.71 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (insert_cpq(v4, v3) = % 21.83/3.71 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 21.83/3.71 | ? [v7: $i] : ? [v8: $i] : (insert_pqp(v0, v3) = v6 & triple(v6, v8, % 21.83/3.71 | v2) = v5 & pair(v3, bottom) = v7 & insert_slb(v1, v7) = v8 & % 21.83/3.71 | $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 21.83/3.71 | % 21.83/3.71 | ALPHA: (ax50) implies: % 21.83/3.71 | (2) $i(bottom) % 21.83/3.71 | % 21.83/3.71 | ALPHA: (ax54) implies: % 21.83/3.71 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb, % 21.83/3.71 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | i(v2) = create_pq) % 21.83/3.71 | % 21.83/3.71 | ALPHA: (big2_induction) implies: % 21.83/3.71 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 21.83/3.71 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 21.83/3.71 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 21.83/3.71 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 21.83/3.71 | $i] : ? [v20: $i] : ($i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v6) % 21.83/3.71 | & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ! [v21: $i] % 21.83/3.71 | : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! % 21.83/3.71 | [v26: $i] : ! [v27: $i] : ! [v28: $i] : ! [v29: $i] : (v29 = v27 % 21.83/3.71 | | ~ (i(v28) = v29) | ~ (i(v26) = v27) | ~ (triple(v22, v23, % 21.83/3.71 | v25) = v28) | ~ (triple(v21, v23, v24) = v26) | ~ $i(v25) | % 21.83/3.71 | ~ $i(v24) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21)) | ( ~ (v20 = % 21.83/3.71 | v18) & i(v19) = v20 & i(v17) = v18 & triple(v14, create_slb, % 21.83/3.71 | v16) = v19 & triple(v13, create_slb, v15) = v17 & $i(v20) & % 21.83/3.71 | $i(v19) & $i(v18) & $i(v17)) | ( ~ (v12 = v10) & i(v11) = v12 & % 21.83/3.71 | i(v9) = v10 & triple(v2, v8, v4) = v11 & triple(v1, v8, v3) = v9 % 21.83/3.71 | & pair(v5, v6) = v7 & insert_slb(v0, v7) = v8 & $i(v12) & $i(v11) % 21.83/3.71 | & $i(v10) & $i(v9) & $i(v8) & $i(v7) & ! [v21: $i] : ! [v22: % 21.83/3.71 | $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] % 21.83/3.71 | : ! [v27: $i] : ! [v28: $i] : (v28 = v26 | ~ (i(v27) = v28) | % 21.83/3.71 | ~ (i(v25) = v26) | ~ (triple(v22, v0, v24) = v27) | ~ % 21.83/3.71 | (triple(v21, v0, v23) = v25) | ~ $i(v24) | ~ $i(v23) | ~ % 21.83/3.71 | $i(v22) | ~ $i(v21))))) % 21.83/3.71 | % 21.83/3.71 | ALPHA: (function-axioms) implies: % 21.83/3.71 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) | % 21.83/3.71 | ~ (i(v2) = v0)) % 21.83/3.71 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.83/3.72 | (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) % 21.83/3.72 | % 21.83/3.72 | DELTA: instantiating (co2) with fresh symbols all_68_0, all_68_1, all_68_2, % 21.83/3.72 | all_68_3, all_68_4, all_68_5, all_68_6, all_68_7, all_68_8 gives: % 21.83/3.72 | (7) ~ (all_68_0 = all_68_2) & i(all_68_3) = all_68_2 & i(all_68_4) = % 21.83/3.72 | all_68_1 & triple(all_68_8, all_68_7, all_68_6) = all_68_4 & % 21.83/3.72 | insert_cpq(all_68_4, all_68_5) = all_68_3 & insert_pq(all_68_1, % 21.83/3.72 | all_68_5) = all_68_0 & $i(all_68_0) & $i(all_68_1) & $i(all_68_2) & % 21.83/3.72 | $i(all_68_3) & $i(all_68_4) & $i(all_68_5) & $i(all_68_6) & % 21.83/3.72 | $i(all_68_7) & $i(all_68_8) % 21.83/3.72 | % 21.83/3.72 | ALPHA: (7) implies: % 21.83/3.72 | (8) ~ (all_68_0 = all_68_2) % 21.83/3.72 | (9) $i(all_68_8) % 21.83/3.72 | (10) $i(all_68_7) % 21.83/3.72 | (11) $i(all_68_6) % 21.83/3.72 | (12) $i(all_68_5) % 21.83/3.72 | (13) insert_pq(all_68_1, all_68_5) = all_68_0 % 21.83/3.72 | (14) insert_cpq(all_68_4, all_68_5) = all_68_3 % 21.83/3.72 | (15) triple(all_68_8, all_68_7, all_68_6) = all_68_4 % 21.83/3.72 | (16) i(all_68_4) = all_68_1 % 21.83/3.72 | (17) i(all_68_3) = all_68_2 % 21.83/3.72 | % 21.83/3.72 | DELTA: instantiating (4) with fresh symbols all_70_0, all_70_1, all_70_2, % 21.83/3.72 | all_70_3, all_70_4, all_70_5, all_70_6, all_70_7, all_70_8, all_70_9, % 21.83/3.72 | all_70_10, all_70_11, all_70_12, all_70_13, all_70_14, all_70_15, % 21.83/3.72 | all_70_16, all_70_17, all_70_18, all_70_19, all_70_20 gives: % 21.83/3.72 | (18) $i(all_70_4) & $i(all_70_5) & $i(all_70_6) & $i(all_70_7) & % 21.83/3.72 | $i(all_70_14) & $i(all_70_15) & $i(all_70_16) & $i(all_70_17) & % 21.83/3.72 | $i(all_70_18) & $i(all_70_19) & $i(all_70_20) & ( ! [v0: $i] : ! [v1: % 21.83/3.72 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 21.83/3.72 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v8 = v6 | ~ (i(v7) = v8) | % 21.83/3.72 | ~ (i(v5) = v6) | ~ (triple(v1, v2, v4) = v7) | ~ (triple(v0, v2, % 21.83/3.72 | v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.83/3.72 | $i(v0)) | ( ~ (all_70_0 = all_70_2) & i(all_70_1) = all_70_0 & % 21.83/3.72 | i(all_70_3) = all_70_2 & triple(all_70_6, create_slb, all_70_4) = % 21.83/3.72 | all_70_1 & triple(all_70_7, create_slb, all_70_5) = all_70_3 & % 21.83/3.72 | $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & $i(all_70_3)) | ( ~ % 21.83/3.72 | (all_70_8 = all_70_10) & i(all_70_9) = all_70_8 & i(all_70_11) = % 21.83/3.72 | all_70_10 & triple(all_70_18, all_70_12, all_70_16) = all_70_9 & % 21.83/3.72 | triple(all_70_19, all_70_12, all_70_17) = all_70_11 & % 21.83/3.72 | pair(all_70_15, all_70_14) = all_70_13 & insert_slb(all_70_20, % 21.83/3.72 | all_70_13) = all_70_12 & $i(all_70_8) & $i(all_70_9) & % 21.83/3.72 | $i(all_70_10) & $i(all_70_11) & $i(all_70_12) & $i(all_70_13) & ! % 21.83/3.72 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.83/3.72 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (i(v6) = % 21.83/3.72 | v7) | ~ (i(v4) = v5) | ~ (triple(v1, all_70_20, v3) = v6) | % 21.83/3.72 | ~ (triple(v0, all_70_20, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.83/3.72 | $i(v1) | ~ $i(v0)))) % 21.83/3.72 | % 21.83/3.72 | ALPHA: (18) implies: % 21.83/3.72 | (19) $i(all_70_20) % 21.83/3.72 | (20) $i(all_70_19) % 21.83/3.72 | (21) $i(all_70_18) % 21.83/3.72 | (22) $i(all_70_17) % 21.83/3.72 | (23) $i(all_70_16) % 21.83/3.72 | (24) $i(all_70_15) % 21.83/3.72 | (25) $i(all_70_14) % 21.83/3.72 | (26) $i(all_70_7) % 21.83/3.72 | (27) $i(all_70_6) % 21.83/3.72 | (28) $i(all_70_5) % 21.83/3.72 | (29) $i(all_70_4) % 21.83/3.73 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.83/3.73 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v8 = v6 | ~ % 21.83/3.73 | (i(v7) = v8) | ~ (i(v5) = v6) | ~ (triple(v1, v2, v4) = v7) | ~ % 21.83/3.73 | (triple(v0, v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.83/3.73 | $i(v1) | ~ $i(v0)) | ( ~ (all_70_0 = all_70_2) & i(all_70_1) = % 21.83/3.73 | all_70_0 & i(all_70_3) = all_70_2 & triple(all_70_6, create_slb, % 21.83/3.73 | all_70_4) = all_70_1 & triple(all_70_7, create_slb, all_70_5) = % 21.83/3.73 | all_70_3 & $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & % 21.83/3.73 | $i(all_70_3)) | ( ~ (all_70_8 = all_70_10) & i(all_70_9) = all_70_8 % 21.83/3.73 | & i(all_70_11) = all_70_10 & triple(all_70_18, all_70_12, all_70_16) % 21.83/3.73 | = all_70_9 & triple(all_70_19, all_70_12, all_70_17) = all_70_11 & % 21.83/3.73 | pair(all_70_15, all_70_14) = all_70_13 & insert_slb(all_70_20, % 21.83/3.73 | all_70_13) = all_70_12 & $i(all_70_8) & $i(all_70_9) & % 21.83/3.73 | $i(all_70_10) & $i(all_70_11) & $i(all_70_12) & $i(all_70_13) & ! % 21.83/3.73 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.83/3.73 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (i(v6) = v7) % 21.83/3.73 | | ~ (i(v4) = v5) | ~ (triple(v1, all_70_20, v3) = v6) | ~ % 21.83/3.73 | (triple(v0, all_70_20, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.83/3.73 | $i(v1) | ~ $i(v0))) % 21.83/3.73 | % 21.83/3.73 | GROUND_INST: instantiating (1) with all_68_8, all_68_7, all_68_6, all_68_5, % 21.83/3.73 | all_68_4, all_68_3, simplifying with (9), (10), (11), (12), (14), % 21.83/3.73 | (15) gives: % 21.83/3.73 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (insert_pqp(all_68_8, % 21.83/3.73 | all_68_5) = v0 & triple(v0, v2, all_68_6) = all_68_3 & % 21.83/3.73 | pair(all_68_5, bottom) = v1 & insert_slb(all_68_7, v1) = v2 & $i(v2) % 21.83/3.73 | & $i(v1) & $i(v0) & $i(all_68_3)) % 21.83/3.73 | % 21.83/3.73 | DELTA: instantiating (31) with fresh symbols all_86_0, all_86_1, all_86_2 % 21.83/3.73 | gives: % 21.83/3.73 | (32) insert_pqp(all_68_8, all_68_5) = all_86_2 & triple(all_86_2, all_86_0, % 21.83/3.73 | all_68_6) = all_68_3 & pair(all_68_5, bottom) = all_86_1 & % 21.83/3.73 | insert_slb(all_68_7, all_86_1) = all_86_0 & $i(all_86_0) & % 21.83/3.73 | $i(all_86_1) & $i(all_86_2) & $i(all_68_3) % 21.83/3.73 | % 21.83/3.73 | ALPHA: (32) implies: % 21.83/3.73 | (33) $i(all_86_2) % 21.83/3.73 | (34) insert_slb(all_68_7, all_86_1) = all_86_0 % 21.83/3.73 | (35) pair(all_68_5, bottom) = all_86_1 % 21.83/3.73 | (36) triple(all_86_2, all_86_0, all_68_6) = all_68_3 % 21.83/3.73 | % 21.83/3.73 | GROUND_INST: instantiating (ax55) with all_86_2, all_68_7, all_68_6, all_68_5, % 21.83/3.73 | bottom, all_86_1, all_86_0, all_68_3, simplifying with (2), (10), % 21.83/3.73 | (11), (12), (33), (34), (35), (36) gives: % 21.83/3.73 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (i(v1) = v2 & i(all_68_3) = % 21.83/3.73 | v0 & triple(all_86_2, all_68_7, all_68_6) = v1 & insert_pq(v2, % 21.83/3.73 | all_68_5) = v0 & $i(v2) & $i(v1) & $i(v0)) % 21.83/3.73 | % 21.83/3.73 | DELTA: instantiating (37) with fresh symbols all_95_0, all_95_1, all_95_2 % 21.83/3.73 | gives: % 21.83/3.73 | (38) i(all_95_1) = all_95_0 & i(all_68_3) = all_95_2 & triple(all_86_2, % 21.83/3.73 | all_68_7, all_68_6) = all_95_1 & insert_pq(all_95_0, all_68_5) = % 21.83/3.73 | all_95_2 & $i(all_95_0) & $i(all_95_1) & $i(all_95_2) % 21.83/3.73 | % 21.83/3.73 | ALPHA: (38) implies: % 21.83/3.73 | (39) insert_pq(all_95_0, all_68_5) = all_95_2 % 21.83/3.73 | (40) triple(all_86_2, all_68_7, all_68_6) = all_95_1 % 21.83/3.73 | (41) i(all_68_3) = all_95_2 % 21.83/3.73 | (42) i(all_95_1) = all_95_0 % 21.83/3.73 | % 21.83/3.73 | GROUND_INST: instantiating (5) with all_68_2, all_95_2, all_68_3, simplifying % 21.83/3.73 | with (17), (41) gives: % 21.83/3.73 | (43) all_95_2 = all_68_2 % 21.83/3.73 | % 21.83/3.73 | REDUCE: (39), (43) imply: % 21.83/3.73 | (44) insert_pq(all_95_0, all_68_5) = all_68_2 % 21.83/3.73 | % 21.83/3.73 | BETA: splitting (30) gives: % 21.83/3.73 | % 21.83/3.73 | Case 1: % 21.83/3.73 | | % 21.83/3.73 | | (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 21.83/3.73 | | : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v8 = v6 | % 21.83/3.73 | | ~ (i(v7) = v8) | ~ (i(v5) = v6) | ~ (triple(v1, v2, v4) = v7) | % 21.83/3.73 | | ~ (triple(v0, v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 21.83/3.73 | | ~ $i(v1) | ~ $i(v0)) % 21.83/3.73 | | % 21.83/3.74 | | GROUND_INST: instantiating (45) with all_68_8, all_86_2, all_68_7, all_68_6, % 21.83/3.74 | | all_68_6, all_68_4, all_68_1, all_95_1, all_95_0, simplifying % 21.83/3.74 | | with (9), (10), (11), (15), (16), (33), (40), (42) gives: % 21.83/3.74 | | (46) all_95_0 = all_68_1 % 21.83/3.74 | | % 21.83/3.74 | | REDUCE: (44), (46) imply: % 21.83/3.74 | | (47) insert_pq(all_68_1, all_68_5) = all_68_2 % 21.83/3.74 | | % 21.83/3.74 | | GROUND_INST: instantiating (6) with all_68_0, all_68_2, all_68_5, all_68_1, % 21.83/3.74 | | simplifying with (13), (47) gives: % 21.83/3.74 | | (48) all_68_0 = all_68_2 % 21.83/3.74 | | % 21.83/3.74 | | REDUCE: (8), (48) imply: % 21.83/3.74 | | (49) $false % 21.83/3.74 | | % 21.83/3.74 | | CLOSE: (49) is inconsistent. % 21.83/3.74 | | % 21.83/3.74 | Case 2: % 21.83/3.74 | | % 21.83/3.74 | | (50) ( ~ (all_70_0 = all_70_2) & i(all_70_1) = all_70_0 & i(all_70_3) = % 21.83/3.74 | | all_70_2 & triple(all_70_6, create_slb, all_70_4) = all_70_1 & % 21.83/3.74 | | triple(all_70_7, create_slb, all_70_5) = all_70_3 & $i(all_70_0) & % 21.83/3.74 | | $i(all_70_1) & $i(all_70_2) & $i(all_70_3)) | ( ~ (all_70_8 = % 21.83/3.74 | | all_70_10) & i(all_70_9) = all_70_8 & i(all_70_11) = all_70_10 & % 21.83/3.74 | | triple(all_70_18, all_70_12, all_70_16) = all_70_9 & % 21.83/3.74 | | triple(all_70_19, all_70_12, all_70_17) = all_70_11 & % 21.83/3.74 | | pair(all_70_15, all_70_14) = all_70_13 & insert_slb(all_70_20, % 21.83/3.74 | | all_70_13) = all_70_12 & $i(all_70_8) & $i(all_70_9) & % 21.83/3.74 | | $i(all_70_10) & $i(all_70_11) & $i(all_70_12) & $i(all_70_13) & ! % 21.83/3.74 | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.83/3.74 | | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (i(v6) = % 21.83/3.74 | | v7) | ~ (i(v4) = v5) | ~ (triple(v1, all_70_20, v3) = v6) | % 21.83/3.74 | | ~ (triple(v0, all_70_20, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.83/3.74 | | $i(v1) | ~ $i(v0))) % 21.83/3.74 | | % 21.83/3.74 | | BETA: splitting (50) gives: % 21.83/3.74 | | % 21.83/3.74 | | Case 1: % 21.83/3.74 | | | % 21.83/3.74 | | | (51) ~ (all_70_0 = all_70_2) & i(all_70_1) = all_70_0 & i(all_70_3) = % 21.83/3.74 | | | all_70_2 & triple(all_70_6, create_slb, all_70_4) = all_70_1 & % 21.83/3.74 | | | triple(all_70_7, create_slb, all_70_5) = all_70_3 & $i(all_70_0) & % 21.83/3.74 | | | $i(all_70_1) & $i(all_70_2) & $i(all_70_3) % 21.83/3.74 | | | % 21.83/3.74 | | | ALPHA: (51) implies: % 21.83/3.74 | | | (52) ~ (all_70_0 = all_70_2) % 21.83/3.74 | | | (53) triple(all_70_7, create_slb, all_70_5) = all_70_3 % 21.83/3.74 | | | (54) triple(all_70_6, create_slb, all_70_4) = all_70_1 % 21.83/3.74 | | | (55) i(all_70_3) = all_70_2 % 21.83/3.74 | | | (56) i(all_70_1) = all_70_0 % 21.83/3.74 | | | % 21.83/3.74 | | | GROUND_INST: instantiating (3) with all_70_7, all_70_5, all_70_3, % 21.83/3.74 | | | simplifying with (26), (28), (53) gives: % 21.83/3.74 | | | (57) i(all_70_3) = create_pq % 21.83/3.74 | | | % 21.83/3.74 | | | GROUND_INST: instantiating (3) with all_70_6, all_70_4, all_70_1, % 21.83/3.74 | | | simplifying with (27), (29), (54) gives: % 21.83/3.74 | | | (58) i(all_70_1) = create_pq % 21.83/3.74 | | | % 21.83/3.74 | | | GROUND_INST: instantiating (5) with all_70_2, create_pq, all_70_3, % 21.83/3.74 | | | simplifying with (55), (57) gives: % 21.83/3.74 | | | (59) all_70_2 = create_pq % 21.83/3.74 | | | % 21.83/3.75 | | | GROUND_INST: instantiating (5) with all_70_0, create_pq, all_70_1, % 21.83/3.75 | | | simplifying with (56), (58) gives: % 21.83/3.75 | | | (60) all_70_0 = create_pq % 21.83/3.75 | | | % 21.83/3.75 | | | REDUCE: (52), (59), (60) imply: % 21.83/3.75 | | | (61) $false % 21.83/3.75 | | | % 21.83/3.75 | | | CLOSE: (61) is inconsistent. % 21.83/3.75 | | | % 21.83/3.75 | | Case 2: % 21.83/3.75 | | | % 21.83/3.75 | | | (62) ~ (all_70_8 = all_70_10) & i(all_70_9) = all_70_8 & i(all_70_11) % 21.83/3.75 | | | = all_70_10 & triple(all_70_18, all_70_12, all_70_16) = all_70_9 & % 21.83/3.75 | | | triple(all_70_19, all_70_12, all_70_17) = all_70_11 & % 21.83/3.75 | | | pair(all_70_15, all_70_14) = all_70_13 & insert_slb(all_70_20, % 21.83/3.75 | | | all_70_13) = all_70_12 & $i(all_70_8) & $i(all_70_9) & % 21.83/3.75 | | | $i(all_70_10) & $i(all_70_11) & $i(all_70_12) & $i(all_70_13) & ! % 21.83/3.75 | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.83/3.75 | | | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (i(v6) = % 21.83/3.75 | | | v7) | ~ (i(v4) = v5) | ~ (triple(v1, all_70_20, v3) = v6) | % 21.83/3.75 | | | ~ (triple(v0, all_70_20, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.83/3.75 | | | $i(v1) | ~ $i(v0)) % 21.83/3.75 | | | % 21.83/3.75 | | | ALPHA: (62) implies: % 21.83/3.75 | | | (63) ~ (all_70_8 = all_70_10) % 21.83/3.75 | | | (64) insert_slb(all_70_20, all_70_13) = all_70_12 % 21.83/3.75 | | | (65) pair(all_70_15, all_70_14) = all_70_13 % 21.83/3.75 | | | (66) triple(all_70_19, all_70_12, all_70_17) = all_70_11 % 21.83/3.75 | | | (67) triple(all_70_18, all_70_12, all_70_16) = all_70_9 % 21.83/3.75 | | | (68) i(all_70_11) = all_70_10 % 21.83/3.75 | | | (69) i(all_70_9) = all_70_8 % 21.83/3.75 | | | (70) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.83/3.75 | | | $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 21.83/3.75 | | | (i(v6) = v7) | ~ (i(v4) = v5) | ~ (triple(v1, all_70_20, v3) = % 21.83/3.75 | | | v6) | ~ (triple(v0, all_70_20, v2) = v4) | ~ $i(v3) | ~ % 21.83/3.75 | | | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 21.83/3.75 | | | % 21.83/3.75 | | | GROUND_INST: instantiating (ax55) with all_70_19, all_70_20, all_70_17, % 21.83/3.75 | | | all_70_15, all_70_14, all_70_13, all_70_12, all_70_11, % 21.83/3.75 | | | simplifying with (19), (20), (22), (24), (25), (64), (65), % 21.83/3.75 | | | (66) gives: % 21.83/3.75 | | | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (i(v1) = v2 & % 21.83/3.75 | | | i(all_70_11) = v0 & triple(all_70_19, all_70_20, all_70_17) = v1 % 21.83/3.75 | | | & insert_pq(v2, all_70_15) = v0 & $i(v2) & $i(v1) & $i(v0)) % 21.83/3.75 | | | % 21.83/3.75 | | | GROUND_INST: instantiating (ax55) with all_70_18, all_70_20, all_70_16, % 21.83/3.75 | | | all_70_15, all_70_14, all_70_13, all_70_12, all_70_9, % 21.83/3.75 | | | simplifying with (19), (21), (23), (24), (25), (64), (65), % 21.83/3.75 | | | (67) gives: % 21.83/3.75 | | | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (i(v1) = v2 & % 21.83/3.75 | | | i(all_70_9) = v0 & triple(all_70_18, all_70_20, all_70_16) = v1 % 21.83/3.75 | | | & insert_pq(v2, all_70_15) = v0 & $i(v2) & $i(v1) & $i(v0)) % 21.83/3.75 | | | % 21.83/3.75 | | | DELTA: instantiating (71) with fresh symbols all_138_0, all_138_1, % 21.83/3.75 | | | all_138_2 gives: % 21.83/3.75 | | | (73) i(all_138_1) = all_138_0 & i(all_70_11) = all_138_2 & % 21.83/3.75 | | | triple(all_70_19, all_70_20, all_70_17) = all_138_1 & % 21.83/3.75 | | | insert_pq(all_138_0, all_70_15) = all_138_2 & $i(all_138_0) & % 21.83/3.75 | | | $i(all_138_1) & $i(all_138_2) % 21.83/3.75 | | | % 21.83/3.75 | | | ALPHA: (73) implies: % 21.83/3.75 | | | (74) insert_pq(all_138_0, all_70_15) = all_138_2 % 21.83/3.75 | | | (75) triple(all_70_19, all_70_20, all_70_17) = all_138_1 % 21.83/3.75 | | | (76) i(all_70_11) = all_138_2 % 22.16/3.75 | | | (77) i(all_138_1) = all_138_0 % 22.16/3.75 | | | % 22.16/3.75 | | | DELTA: instantiating (72) with fresh symbols all_140_0, all_140_1, % 22.16/3.75 | | | all_140_2 gives: % 22.16/3.75 | | | (78) i(all_140_1) = all_140_0 & i(all_70_9) = all_140_2 & % 22.16/3.75 | | | triple(all_70_18, all_70_20, all_70_16) = all_140_1 & % 22.16/3.75 | | | insert_pq(all_140_0, all_70_15) = all_140_2 & $i(all_140_0) & % 22.16/3.75 | | | $i(all_140_1) & $i(all_140_2) % 22.16/3.75 | | | % 22.16/3.75 | | | ALPHA: (78) implies: % 22.16/3.75 | | | (79) insert_pq(all_140_0, all_70_15) = all_140_2 % 22.16/3.75 | | | (80) triple(all_70_18, all_70_20, all_70_16) = all_140_1 % 22.16/3.75 | | | (81) i(all_70_9) = all_140_2 % 22.16/3.75 | | | (82) i(all_140_1) = all_140_0 % 22.16/3.75 | | | % 22.16/3.75 | | | GROUND_INST: instantiating (5) with all_70_10, all_138_2, all_70_11, % 22.16/3.75 | | | simplifying with (68), (76) gives: % 22.16/3.75 | | | (83) all_138_2 = all_70_10 % 22.16/3.75 | | | % 22.16/3.75 | | | GROUND_INST: instantiating (5) with all_70_8, all_140_2, all_70_9, % 22.16/3.75 | | | simplifying with (69), (81) gives: % 22.16/3.75 | | | (84) all_140_2 = all_70_8 % 22.16/3.75 | | | % 22.16/3.75 | | | REDUCE: (79), (84) imply: % 22.16/3.75 | | | (85) insert_pq(all_140_0, all_70_15) = all_70_8 % 22.16/3.75 | | | % 22.16/3.75 | | | REDUCE: (74), (83) imply: % 22.16/3.75 | | | (86) insert_pq(all_138_0, all_70_15) = all_70_10 % 22.16/3.75 | | | % 22.16/3.76 | | | GROUND_INST: instantiating (70) with all_70_19, all_70_18, all_70_17, % 22.16/3.76 | | | all_70_16, all_138_1, all_138_0, all_140_1, all_140_0, % 22.16/3.76 | | | simplifying with (20), (21), (22), (23), (75), (77), (80), % 22.16/3.76 | | | (82) gives: % 22.16/3.76 | | | (87) all_140_0 = all_138_0 % 22.16/3.76 | | | % 22.16/3.76 | | | REDUCE: (85), (87) imply: % 22.16/3.76 | | | (88) insert_pq(all_138_0, all_70_15) = all_70_8 % 22.16/3.76 | | | % 22.16/3.76 | | | GROUND_INST: instantiating (6) with all_70_10, all_70_8, all_70_15, % 22.16/3.76 | | | all_138_0, simplifying with (86), (88) gives: % 22.16/3.76 | | | (89) all_70_8 = all_70_10 % 22.16/3.76 | | | % 22.16/3.76 | | | REDUCE: (63), (89) imply: % 22.16/3.76 | | | (90) $false % 22.16/3.76 | | | % 22.16/3.76 | | | CLOSE: (90) is inconsistent. % 22.16/3.76 | | | % 22.16/3.76 | | End of split % 22.16/3.76 | | % 22.16/3.76 | End of split % 22.16/3.76 | % 22.16/3.76 End of proof % 22.16/3.76 % SZS output end Proof for theBenchmark % 22.16/3.76 % 22.16/3.76 3136ms %------------------------------------------------------------------------------