%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN352+1 : TPTP v8.1.2. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.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 : Fri Sep 1 03:27:19 EDT 2023 % Result : Theorem 4.79s 1.35s % Output : Proof 6.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN352+1 : TPTP v8.1.2. Released v2.0.0. % 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Aug 26 18:21:56 EDT 2023 % 0.12/0.33 % CPUTime : % 0.51/0.60 ________ _____ % 0.51/0.60 ___ __ \_________(_)________________________________ % 0.51/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.60 % 0.51/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.60 (2023-06-19) % 0.51/0.60 % 0.51/0.60 (c) Philipp Rümmer, 2009-2023 % 0.51/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.60 Amanda Stjerna. % 0.51/0.60 Free software under BSD-3-Clause. % 0.51/0.60 % 0.51/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.60 % 0.51/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.51/0.62 Running up to 7 provers in parallel. % 0.74/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.74/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.74/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.74/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.74/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.74/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.74/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.96/0.96 Prover 4: Preprocessing ... % 1.96/0.96 Prover 1: Preprocessing ... % 2.25/1.00 Prover 2: Preprocessing ... % 2.25/1.00 Prover 3: Preprocessing ... % 2.25/1.00 Prover 6: Preprocessing ... % 2.25/1.00 Prover 5: Preprocessing ... % 2.25/1.00 Prover 0: Preprocessing ... % 2.87/1.08 Prover 1: Constructing countermodel ... % 2.87/1.08 Prover 3: Constructing countermodel ... % 2.87/1.08 Prover 4: Constructing countermodel ... % 2.87/1.08 Prover 2: Proving ... % 2.87/1.08 Prover 5: Proving ... % 2.87/1.09 Prover 6: Proving ... % 2.87/1.11 Prover 0: Proving ... % 4.79/1.35 Prover 3: proved (719ms) % 4.79/1.35 % 4.79/1.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.79/1.35 % 4.79/1.35 Prover 6: stopped % 4.79/1.35 Prover 0: stopped % 4.79/1.35 Prover 5: stopped % 4.79/1.35 Prover 2: stopped % 4.79/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.79/1.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.79/1.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.79/1.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.79/1.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.03/1.38 Prover 8: Preprocessing ... % 5.03/1.38 Prover 7: Preprocessing ... % 5.03/1.38 Prover 10: Preprocessing ... % 5.03/1.38 Prover 13: Preprocessing ... % 5.03/1.39 Prover 10: Warning: ignoring some quantifiers % 5.03/1.39 Prover 13: Warning: ignoring some quantifiers % 5.03/1.40 Prover 10: Constructing countermodel ... % 5.03/1.40 Prover 8: Warning: ignoring some quantifiers % 5.03/1.40 Prover 8: Constructing countermodel ... % 5.03/1.40 Prover 11: Preprocessing ... % 5.03/1.40 Prover 7: Warning: ignoring some quantifiers % 5.03/1.40 Prover 7: Constructing countermodel ... % 5.03/1.41 Prover 10: gave up % 5.03/1.41 Prover 13: Constructing countermodel ... % 5.03/1.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 5.03/1.42 Prover 13: gave up % 5.03/1.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 5.03/1.43 Prover 16: Preprocessing ... % 5.03/1.43 Prover 7: gave up % 5.53/1.43 Prover 11: Constructing countermodel ... % 5.53/1.44 Prover 19: Preprocessing ... % 5.53/1.44 Prover 16: Warning: ignoring some quantifiers % 5.53/1.44 Prover 16: Constructing countermodel ... % 5.79/1.47 Prover 16: gave up % 5.79/1.48 Prover 19: Warning: ignoring some quantifiers % 5.79/1.48 Prover 19: Constructing countermodel ... % 5.79/1.51 Prover 4: Found proof (size 57) % 5.79/1.51 Prover 4: proved (880ms) % 5.79/1.51 Prover 11: stopped % 5.79/1.51 Prover 8: stopped % 5.79/1.51 Prover 19: stopped % 5.79/1.51 Prover 1: stopped % 5.79/1.51 % 5.79/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.79/1.51 % 5.79/1.52 % SZS output start Proof for theBenchmark % 5.79/1.52 Assumptions after simplification: % 5.79/1.52 --------------------------------- % 5.79/1.52 % 5.79/1.52 (church_46_18_4) % 6.22/1.56 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (big_f(v0, v1) = v2 & $i(v1) & % 6.22/1.56 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (big_f(v3, v4) = v5) % 6.22/1.56 | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? % 6.22/1.56 [v9: any] : ? [v10: any] : (v2 = 0 & big_f(v6, v6) = v10 & big_f(v4, v6) % 6.22/1.56 = v8 & big_f(v3, v6) = v9 & big_f(v1, v6) = v7 & $i(v6) & ( ~ (v5 = 0) | % 6.22/1.56 v8 = 0 | v7 = 0) & ( ~ (v5 = 0) | (( ~ (v9 = 0) | ~ (v8 = 0)) & (v9 = % 6.22/1.56 0 | v8 = 0))) & (v10 = 0 | (v5 = 0 & ( ~ (v9 = 0) | ~ (v7 = 0)) & % 6.22/1.56 (v9 = 0 | v7 = 0)))))) % 6.22/1.56 % 6.22/1.56 (function-axioms) % 6.22/1.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 6.22/1.56 [v3: $i] : (v1 = v0 | ~ (big_f(v3, v2) = v1) | ~ (big_f(v3, v2) = v0)) % 6.22/1.56 % 6.22/1.56 Those formulas are unsatisfiable: % 6.22/1.56 --------------------------------- % 6.22/1.56 % 6.22/1.56 Begin of proof % 6.22/1.56 | % 6.22/1.56 | DELTA: instantiating (church_46_18_4) with fresh symbols all_3_0, all_3_1, % 6.22/1.56 | all_3_2 gives: % 6.37/1.57 | (1) big_f(all_3_2, all_3_1) = all_3_0 & $i(all_3_1) & $i(all_3_2) & ! [v0: % 6.37/1.57 | $i] : ! [v1: $i] : ! [v2: any] : ( ~ (big_f(v0, v1) = v2) | ~ % 6.37/1.57 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? % 6.37/1.57 | [v6: any] : ? [v7: any] : (all_3_0 = 0 & big_f(v3, v3) = v7 & % 6.37/1.57 | big_f(v1, v3) = v5 & big_f(v0, v3) = v6 & big_f(all_3_1, v3) = v4 & % 6.37/1.57 | $i(v3) & ( ~ (v2 = 0) | v5 = 0 | v4 = 0) & ( ~ (v2 = 0) | (( ~ (v6 % 6.37/1.57 | = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0))) & (v7 = 0 | (v2 = % 6.37/1.57 | 0 & ( ~ (v6 = 0) | ~ (v4 = 0)) & (v6 = 0 | v4 = 0))))) % 6.37/1.57 | % 6.37/1.57 | ALPHA: (1) implies: % 6.37/1.57 | (2) $i(all_3_2) % 6.37/1.57 | (3) $i(all_3_1) % 6.37/1.57 | (4) big_f(all_3_2, all_3_1) = all_3_0 % 6.37/1.57 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (big_f(v0, v1) = v2) | % 6.37/1.57 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? % 6.37/1.57 | [v6: any] : ? [v7: any] : (all_3_0 = 0 & big_f(v3, v3) = v7 & % 6.37/1.57 | big_f(v1, v3) = v5 & big_f(v0, v3) = v6 & big_f(all_3_1, v3) = v4 & % 6.37/1.57 | $i(v3) & ( ~ (v2 = 0) | v5 = 0 | v4 = 0) & ( ~ (v2 = 0) | (( ~ (v6 % 6.37/1.57 | = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0))) & (v7 = 0 | (v2 = % 6.37/1.57 | 0 & ( ~ (v6 = 0) | ~ (v4 = 0)) & (v6 = 0 | v4 = 0))))) % 6.37/1.57 | % 6.37/1.58 | GROUND_INST: instantiating (5) with all_3_2, all_3_1, all_3_0, simplifying % 6.37/1.58 | with (2), (3), (4) gives: % 6.37/1.58 | (6) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: any] % 6.37/1.58 | : (all_3_0 = 0 & big_f(v0, v0) = v4 & big_f(all_3_1, v0) = v2 & % 6.37/1.58 | big_f(all_3_1, v0) = v1 & big_f(all_3_2, v0) = v3 & $i(v0) & ( ~ (v3 % 6.37/1.58 | = 0) | ~ (v2 = 0)) & (v4 = 0 | (( ~ (v3 = 0) | ~ (v1 = 0)) & % 6.37/1.58 | (v3 = 0 | v1 = 0))) & (v3 = 0 | v2 = 0) & (v2 = 0 | v1 = 0)) % 6.37/1.58 | % 6.37/1.58 | DELTA: instantiating (6) with fresh symbols all_11_0, all_11_1, all_11_2, % 6.37/1.58 | all_11_3, all_11_4 gives: % 6.37/1.58 | (7) all_3_0 = 0 & big_f(all_11_4, all_11_4) = all_11_0 & big_f(all_3_1, % 6.37/1.58 | all_11_4) = all_11_2 & big_f(all_3_1, all_11_4) = all_11_3 & % 6.37/1.58 | big_f(all_3_2, all_11_4) = all_11_1 & $i(all_11_4) & ( ~ (all_11_1 = 0) % 6.37/1.58 | | ~ (all_11_2 = 0)) & (all_11_0 = 0 | (( ~ (all_11_1 = 0) | ~ % 6.37/1.58 | (all_11_3 = 0)) & (all_11_1 = 0 | all_11_3 = 0))) & (all_11_1 = 0 % 6.37/1.58 | | all_11_2 = 0) & (all_11_2 = 0 | all_11_3 = 0) % 6.37/1.58 | % 6.37/1.58 | ALPHA: (7) implies: % 6.37/1.58 | (8) all_3_0 = 0 % 6.37/1.58 | (9) $i(all_11_4) % 6.37/1.58 | (10) big_f(all_3_2, all_11_4) = all_11_1 % 6.37/1.58 | (11) big_f(all_3_1, all_11_4) = all_11_3 % 6.37/1.58 | (12) big_f(all_3_1, all_11_4) = all_11_2 % 6.37/1.58 | (13) all_11_2 = 0 | all_11_3 = 0 % 6.37/1.58 | (14) ~ (all_11_1 = 0) | ~ (all_11_2 = 0) % 6.37/1.58 | % 6.37/1.58 | REDUCE: (4), (8) imply: % 6.37/1.58 | (15) big_f(all_3_2, all_3_1) = 0 % 6.37/1.58 | % 6.37/1.59 | GROUND_INST: instantiating (function-axioms) with all_11_3, all_11_2, % 6.37/1.59 | all_11_4, all_3_1, simplifying with (11), (12) gives: % 6.37/1.59 | (16) all_11_2 = all_11_3 % 6.37/1.59 | % 6.37/1.59 | BETA: splitting (13) gives: % 6.37/1.59 | % 6.37/1.59 | Case 1: % 6.37/1.59 | | % 6.37/1.59 | | (17) all_11_2 = 0 % 6.37/1.59 | | % 6.37/1.59 | | COMBINE_EQS: (16), (17) imply: % 6.37/1.59 | | (18) all_11_3 = 0 % 6.37/1.59 | | % 6.37/1.59 | | BETA: splitting (14) gives: % 6.37/1.59 | | % 6.37/1.59 | | Case 1: % 6.37/1.59 | | | % 6.37/1.59 | | | (19) ~ (all_11_1 = 0) % 6.37/1.59 | | | % 6.37/1.59 | | | GROUND_INST: instantiating (5) with all_3_2, all_11_4, all_11_1, % 6.37/1.59 | | | simplifying with (2), (9), (10) gives: % 6.37/1.59 | | | (20) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 6.37/1.59 | | | any] : (all_3_0 = 0 & big_f(v0, v0) = v4 & big_f(all_11_4, v0) = % 6.37/1.59 | | | v2 & big_f(all_3_1, v0) = v1 & big_f(all_3_2, v0) = v3 & $i(v0) % 6.37/1.59 | | | & ( ~ (all_11_1 = 0) | v2 = 0 | v1 = 0) & ( ~ (all_11_1 = 0) | % 6.37/1.59 | | | (( ~ (v3 = 0) | ~ (v2 = 0)) & (v3 = 0 | v2 = 0))) & (v4 = 0 | % 6.37/1.59 | | | (all_11_1 = 0 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = % 6.37/1.59 | | | 0)))) % 6.37/1.59 | | | % 6.37/1.59 | | | DELTA: instantiating (6) with fresh symbols all_32_0, all_32_1, all_32_2, % 6.37/1.59 | | | all_32_3, all_32_4 gives: % 6.37/1.59 | | | (21) all_3_0 = 0 & big_f(all_32_4, all_32_4) = all_32_0 & % 6.37/1.59 | | | big_f(all_3_1, all_32_4) = all_32_2 & big_f(all_3_1, all_32_4) = % 6.37/1.59 | | | all_32_3 & big_f(all_3_2, all_32_4) = all_32_1 & $i(all_32_4) & ( % 6.37/1.59 | | | ~ (all_32_1 = 0) | ~ (all_32_2 = 0)) & (all_32_0 = 0 | (( ~ % 6.37/1.59 | | | (all_32_1 = 0) | ~ (all_32_3 = 0)) & (all_32_1 = 0 | % 6.37/1.59 | | | all_32_3 = 0))) & (all_32_1 = 0 | all_32_2 = 0) & (all_32_2 % 6.37/1.59 | | | = 0 | all_32_3 = 0) % 6.37/1.59 | | | % 6.37/1.59 | | | ALPHA: (21) implies: % 6.37/1.59 | | | (22) big_f(all_3_1, all_32_4) = all_32_3 % 6.37/1.59 | | | (23) big_f(all_3_1, all_32_4) = all_32_2 % 6.37/1.59 | | | (24) all_32_2 = 0 | all_32_3 = 0 % 6.37/1.59 | | | (25) ~ (all_32_1 = 0) | ~ (all_32_2 = 0) % 6.37/1.59 | | | % 6.37/1.59 | | | DELTA: instantiating (20) with fresh symbols all_34_0, all_34_1, all_34_2, % 6.37/1.59 | | | all_34_3, all_34_4 gives: % 6.37/1.59 | | | (26) all_3_0 = 0 & big_f(all_34_4, all_34_4) = all_34_0 & % 6.37/1.59 | | | big_f(all_11_4, all_34_4) = all_34_2 & big_f(all_3_1, all_34_4) = % 6.37/1.59 | | | all_34_3 & big_f(all_3_2, all_34_4) = all_34_1 & $i(all_34_4) & ( % 6.37/1.59 | | | ~ (all_11_1 = 0) | all_34_2 = 0 | all_34_3 = 0) & ( ~ (all_11_1 % 6.37/1.59 | | | = 0) | (( ~ (all_34_1 = 0) | ~ (all_34_2 = 0)) & (all_34_1 = % 6.37/1.60 | | | 0 | all_34_2 = 0))) & (all_34_0 = 0 | (all_11_1 = 0 & ( ~ % 6.37/1.60 | | | (all_34_1 = 0) | ~ (all_34_3 = 0)) & (all_34_1 = 0 | % 6.37/1.60 | | | all_34_3 = 0))) % 6.37/1.60 | | | % 6.37/1.60 | | | ALPHA: (26) implies: % 6.37/1.60 | | | (27) $i(all_34_4) % 6.37/1.60 | | | (28) big_f(all_34_4, all_34_4) = all_34_0 % 6.37/1.60 | | | (29) all_34_0 = 0 | (all_11_1 = 0 & ( ~ (all_34_1 = 0) | ~ (all_34_3 = % 6.37/1.60 | | | 0)) & (all_34_1 = 0 | all_34_3 = 0)) % 6.37/1.60 | | | % 6.37/1.60 | | | BETA: splitting (29) gives: % 6.37/1.60 | | | % 6.37/1.60 | | | Case 1: % 6.37/1.60 | | | | % 6.37/1.60 | | | | (30) all_34_0 = 0 % 6.37/1.60 | | | | % 6.37/1.60 | | | | REDUCE: (28), (30) imply: % 6.37/1.60 | | | | (31) big_f(all_34_4, all_34_4) = 0 % 6.37/1.60 | | | | % 6.37/1.60 | | | | GROUND_INST: instantiating (function-axioms) with all_32_3, all_32_2, % 6.37/1.60 | | | | all_32_4, all_3_1, simplifying with (22), (23) gives: % 6.37/1.60 | | | | (32) all_32_2 = all_32_3 % 6.37/1.60 | | | | % 6.37/1.60 | | | | BETA: splitting (24) gives: % 6.37/1.60 | | | | % 6.37/1.60 | | | | Case 1: % 6.37/1.60 | | | | | % 6.37/1.60 | | | | | (33) all_32_2 = 0 % 6.37/1.60 | | | | | % 6.37/1.60 | | | | | BETA: splitting (25) gives: % 6.37/1.60 | | | | | % 6.37/1.60 | | | | | Case 1: % 6.37/1.60 | | | | | | % 6.37/1.60 | | | | | | % 6.37/1.60 | | | | | | GROUND_INST: instantiating (5) with all_34_4, all_34_4, 0, % 6.37/1.60 | | | | | | simplifying with (27), (31) gives: % 6.37/1.60 | | | | | | (34) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 6.37/1.60 | | | | | | ? [v4: any] : (all_3_0 = 0 & big_f(v0, v0) = v4 & % 6.37/1.60 | | | | | | big_f(all_34_4, v0) = v3 & big_f(all_34_4, v0) = v2 & % 6.37/1.60 | | | | | | big_f(all_3_1, v0) = v1 & $i(v0) & ( ~ (v3 = 0) | ~ (v2 = % 6.37/1.60 | | | | | | 0)) & (v4 = 0 | (( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 % 6.37/1.60 | | | | | | | v1 = 0))) & (v3 = 0 | v2 = 0) & (v2 = 0 | v1 = 0)) % 6.37/1.60 | | | | | | % 6.37/1.60 | | | | | | DELTA: instantiating (34) with fresh symbols all_61_0, all_61_1, % 6.37/1.60 | | | | | | all_61_2, all_61_3, all_61_4 gives: % 6.37/1.60 | | | | | | (35) all_3_0 = 0 & big_f(all_61_4, all_61_4) = all_61_0 & % 6.37/1.60 | | | | | | big_f(all_34_4, all_61_4) = all_61_1 & big_f(all_34_4, % 6.37/1.60 | | | | | | all_61_4) = all_61_2 & big_f(all_3_1, all_61_4) = all_61_3 % 6.37/1.60 | | | | | | & $i(all_61_4) & ( ~ (all_61_1 = 0) | ~ (all_61_2 = 0)) & % 6.37/1.60 | | | | | | (all_61_0 = 0 | (( ~ (all_61_1 = 0) | ~ (all_61_3 = 0)) & % 6.37/1.60 | | | | | | (all_61_1 = 0 | all_61_3 = 0))) & (all_61_1 = 0 | % 6.37/1.60 | | | | | | all_61_2 = 0) & (all_61_2 = 0 | all_61_3 = 0) % 6.37/1.60 | | | | | | % 6.37/1.60 | | | | | | ALPHA: (35) implies: % 6.37/1.60 | | | | | | (36) big_f(all_34_4, all_61_4) = all_61_2 % 6.37/1.60 | | | | | | (37) big_f(all_34_4, all_61_4) = all_61_1 % 6.37/1.60 | | | | | | (38) all_61_1 = 0 | all_61_2 = 0 % 6.37/1.60 | | | | | | (39) ~ (all_61_1 = 0) | ~ (all_61_2 = 0) % 6.37/1.60 | | | | | | % 6.37/1.60 | | | | | | GROUND_INST: instantiating (function-axioms) with all_61_2, % 6.37/1.60 | | | | | | all_61_1, all_61_4, all_34_4, simplifying with (36), % 6.37/1.60 | | | | | | (37) gives: % 6.37/1.60 | | | | | | (40) all_61_1 = all_61_2 % 6.37/1.60 | | | | | | % 6.37/1.60 | | | | | | BETA: splitting (38) gives: % 6.37/1.60 | | | | | | % 6.37/1.60 | | | | | | Case 1: % 6.37/1.60 | | | | | | | % 6.37/1.60 | | | | | | | (41) all_61_1 = 0 % 6.37/1.60 | | | | | | | % 6.37/1.60 | | | | | | | COMBINE_EQS: (40), (41) imply: % 6.37/1.60 | | | | | | | (42) all_61_2 = 0 % 6.37/1.61 | | | | | | | % 6.37/1.61 | | | | | | | REF_CLOSE: (39), (41), (42) are inconsistent by sub-proof #1. % 6.37/1.61 | | | | | | | % 6.37/1.61 | | | | | | Case 2: % 6.37/1.61 | | | | | | | % 6.37/1.61 | | | | | | | (43) all_61_2 = 0 % 6.37/1.61 | | | | | | | % 6.37/1.61 | | | | | | | COMBINE_EQS: (40), (43) imply: % 6.37/1.61 | | | | | | | (44) all_61_1 = 0 % 6.37/1.61 | | | | | | | % 6.37/1.61 | | | | | | | REF_CLOSE: (39), (43), (44) are inconsistent by sub-proof #1. % 6.37/1.61 | | | | | | | % 6.37/1.61 | | | | | | End of split % 6.37/1.61 | | | | | | % 6.37/1.61 | | | | | Case 2: % 6.37/1.61 | | | | | | % 6.37/1.61 | | | | | | (45) ~ (all_32_2 = 0) % 6.37/1.61 | | | | | | % 6.37/1.61 | | | | | | REDUCE: (33), (45) imply: % 6.37/1.61 | | | | | | (46) $false % 6.37/1.61 | | | | | | % 6.37/1.61 | | | | | | CLOSE: (46) is inconsistent. % 6.37/1.61 | | | | | | % 6.37/1.61 | | | | | End of split % 6.37/1.61 | | | | | % 6.37/1.61 | | | | Case 2: % 6.37/1.61 | | | | | % 6.37/1.61 | | | | | (47) all_32_3 = 0 % 6.37/1.61 | | | | | (48) ~ (all_32_2 = 0) % 6.37/1.61 | | | | | % 6.37/1.61 | | | | | COMBINE_EQS: (32), (47) imply: % 6.37/1.61 | | | | | (49) all_32_2 = 0 % 6.37/1.61 | | | | | % 6.37/1.61 | | | | | REDUCE: (48), (49) imply: % 6.37/1.61 | | | | | (50) $false % 6.37/1.61 | | | | | % 6.37/1.61 | | | | | CLOSE: (50) is inconsistent. % 6.37/1.61 | | | | | % 6.37/1.61 | | | | End of split % 6.37/1.61 | | | | % 6.37/1.61 | | | Case 2: % 6.37/1.61 | | | | % 6.37/1.61 | | | | (51) all_11_1 = 0 & ( ~ (all_34_1 = 0) | ~ (all_34_3 = 0)) & % 6.37/1.61 | | | | (all_34_1 = 0 | all_34_3 = 0) % 6.37/1.61 | | | | % 6.37/1.61 | | | | ALPHA: (51) implies: % 6.37/1.61 | | | | (52) all_11_1 = 0 % 6.37/1.61 | | | | % 6.37/1.61 | | | | REDUCE: (19), (52) imply: % 6.37/1.61 | | | | (53) $false % 6.37/1.61 | | | | % 6.37/1.61 | | | | CLOSE: (53) is inconsistent. % 6.37/1.61 | | | | % 6.37/1.61 | | | End of split % 6.37/1.61 | | | % 6.37/1.61 | | Case 2: % 6.37/1.61 | | | % 6.37/1.61 | | | (54) ~ (all_11_2 = 0) % 6.37/1.61 | | | % 6.37/1.61 | | | REDUCE: (17), (54) imply: % 6.37/1.61 | | | (55) $false % 6.37/1.61 | | | % 6.37/1.61 | | | CLOSE: (55) is inconsistent. % 6.37/1.61 | | | % 6.37/1.61 | | End of split % 6.37/1.61 | | % 6.37/1.61 | Case 2: % 6.37/1.61 | | % 6.37/1.61 | | (56) all_11_3 = 0 % 6.37/1.61 | | (57) ~ (all_11_2 = 0) % 6.37/1.61 | | % 6.37/1.61 | | COMBINE_EQS: (16), (56) imply: % 6.37/1.61 | | (58) all_11_2 = 0 % 6.37/1.61 | | % 6.37/1.61 | | REDUCE: (57), (58) imply: % 6.37/1.61 | | (59) $false % 6.37/1.61 | | % 6.37/1.61 | | CLOSE: (59) is inconsistent. % 6.37/1.61 | | % 6.37/1.61 | End of split % 6.37/1.61 | % 6.37/1.61 End of proof % 6.37/1.61 % 6.37/1.61 Sub-proof #1 shows that the following formulas are inconsistent: % 6.37/1.61 ---------------------------------------------------------------- % 6.37/1.61 (1) ~ (all_61_1 = 0) | ~ (all_61_2 = 0) % 6.37/1.61 (2) all_61_1 = 0 % 6.37/1.61 (3) all_61_2 = 0 % 6.37/1.61 % 6.37/1.61 Begin of proof % 6.37/1.61 | % 6.37/1.61 | BETA: splitting (1) gives: % 6.37/1.61 | % 6.37/1.61 | Case 1: % 6.37/1.61 | | % 6.37/1.61 | | (4) ~ (all_61_1 = 0) % 6.37/1.61 | | % 6.37/1.61 | | REDUCE: (2), (4) imply: % 6.37/1.61 | | (5) $false % 6.37/1.61 | | % 6.37/1.61 | | CLOSE: (5) is inconsistent. % 6.37/1.61 | | % 6.37/1.61 | Case 2: % 6.37/1.61 | | % 6.37/1.61 | | (6) ~ (all_61_2 = 0) % 6.37/1.61 | | % 6.37/1.61 | | REDUCE: (3), (6) imply: % 6.37/1.61 | | (7) $false % 6.37/1.61 | | % 6.37/1.61 | | CLOSE: (7) is inconsistent. % 6.37/1.61 | | % 6.37/1.61 | End of split % 6.37/1.61 | % 6.37/1.61 End of proof % 6.37/1.61 % SZS output end Proof for theBenchmark % 6.37/1.61 % 6.37/1.61 1008ms %------------------------------------------------------------------------------