%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n029.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 15:27:02 EDT 2023 % Result : Theorem 5.64s 2.02s % Output : Proof 7.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.15 % Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.16 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.37 % Computer : n029.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Sat Aug 26 14:34:25 EDT 2023 % 0.15/0.37 % CPUTime : % 0.22/0.68 ________ _____ % 0.22/0.68 ___ __ \_________(_)________________________________ % 0.22/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.68 % 0.22/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.68 (2023-06-19) % 0.22/0.68 % 0.22/0.68 (c) Philipp Rümmer, 2009-2023 % 0.22/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.68 Amanda Stjerna. % 0.22/0.69 Free software under BSD-3-Clause. % 0.22/0.69 % 0.22/0.69 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.69 % 0.22/0.69 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.71 Running up to 7 provers in parallel. % 0.22/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.76 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.60/1.10 Prover 1: Preprocessing ... % 1.60/1.11 Prover 4: Preprocessing ... % 2.27/1.20 Prover 5: Preprocessing ... % 2.27/1.20 Prover 6: Preprocessing ... % 2.27/1.20 Prover 0: Preprocessing ... % 2.27/1.20 Prover 2: Preprocessing ... % 2.27/1.20 Prover 3: Preprocessing ... % 3.75/1.59 Prover 3: Warning: ignoring some quantifiers % 3.93/1.59 Prover 1: Warning: ignoring some quantifiers % 3.93/1.61 Prover 5: Proving ... % 3.93/1.63 Prover 3: Constructing countermodel ... % 4.15/1.63 Prover 6: Proving ... % 4.15/1.64 Prover 1: Constructing countermodel ... % 4.21/1.65 Prover 4: Warning: ignoring some quantifiers % 4.21/1.68 Prover 4: Constructing countermodel ... % 4.21/1.68 Prover 2: Proving ... % 4.51/1.75 Prover 0: Proving ... % 5.64/2.02 Prover 3: proved (1279ms) % 5.64/2.02 % 5.64/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.64/2.02 % 5.64/2.03 Prover 5: stopped % 5.64/2.04 Prover 2: stopped % 5.64/2.05 Prover 0: stopped % 5.64/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.64/2.07 Prover 6: stopped % 5.64/2.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.64/2.09 Prover 7: Preprocessing ... % 5.64/2.09 Prover 8: Preprocessing ... % 5.64/2.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.64/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.64/2.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.64/2.12 Prover 10: Preprocessing ... % 5.64/2.12 Prover 13: Preprocessing ... % 5.64/2.12 Prover 11: Preprocessing ... % 6.11/2.15 Prover 7: Warning: ignoring some quantifiers % 6.11/2.16 Prover 7: Constructing countermodel ... % 6.11/2.18 Prover 1: Found proof (size 43) % 6.11/2.18 Prover 1: proved (1463ms) % 6.11/2.18 Prover 7: stopped % 6.11/2.18 Prover 13: Warning: ignoring some quantifiers % 6.11/2.19 Prover 4: Found proof (size 48) % 6.11/2.19 Prover 4: proved (1450ms) % 6.11/2.19 Prover 11: stopped % 6.86/2.20 Prover 13: Constructing countermodel ... % 6.86/2.21 Prover 8: Warning: ignoring some quantifiers % 6.86/2.21 Prover 10: Warning: ignoring some quantifiers % 6.86/2.21 Prover 13: stopped % 6.86/2.21 Prover 8: Constructing countermodel ... % 6.86/2.22 Prover 8: stopped % 6.86/2.22 Prover 10: Constructing countermodel ... % 6.86/2.22 Prover 10: stopped % 6.86/2.22 % 6.86/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.86/2.22 % 6.86/2.24 % SZS output start Proof for theBenchmark % 6.86/2.24 Assumptions after simplification: % 6.86/2.24 --------------------------------- % 6.86/2.24 % 6.86/2.24 (commutativity_k2_tarski) % 7.04/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 7.04/2.30 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 7.04/2.30 % 7.04/2.30 (commutativity_k3_xboole_0) % 7.04/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 7.04/2.30 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 7.04/2.30 % 7.04/2.30 (d1_tarski) % 7.04/2.31 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | % 7.04/2.31 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & % 7.04/2.31 $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0: $i] % 7.04/2.31 : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: % 7.04/2.31 $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 = % 7.04/2.31 0 | ~ (in(v0, v1) = v2)))) % 7.04/2.31 % 7.04/2.31 (d2_tarski) % 7.04/2.32 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 7.04/2.32 (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 7.04/2.32 $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = % 7.04/2.32 v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0: $i] % 7.04/2.32 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | % 7.04/2.32 ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, % 7.04/2.32 v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1) & ~ (v3 = v0))) & ! [v3: $i] % 7.04/2.32 : (v3 = v1 | v3 = v0 | ~ (in(v3, v2) = 0) | ~ $i(v3)))) % 7.04/2.32 % 7.04/2.32 (d3_xboole_0) % 7.04/2.33 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 7.04/2.33 (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 7.04/2.33 [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 & % 7.04/2.33 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) | % 7.04/2.33 ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] % 7.04/2.33 : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 7.04/2.33 ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) % 7.04/2.33 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ % 7.04/2.33 (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) % 7.04/2.33 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, % 7.04/2.34 v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 7.04/2.34 % 7.04/2.34 (t59_zfmisc_1) % 7.04/2.34 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v1 % 7.04/2.34 = v0) & singleton(v0) = v4 & set_intersection2(v3, v2) = v4 & % 7.04/2.34 unordered_pair(v0, v1) = v3 & in(v1, v2) = 0 & $i(v4) & $i(v3) & $i(v2) & % 7.04/2.34 $i(v1) & $i(v0)) % 7.04/2.34 % 7.04/2.34 (function-axioms) % 7.04/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.04/2.35 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 7.04/2.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.04/2.35 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 7.04/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 7.04/2.35 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 7.04/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.04/2.35 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 7.04/2.35 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 7.04/2.35 % 7.04/2.35 Further assumptions not needed in the proof: % 7.04/2.35 -------------------------------------------- % 7.04/2.35 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0 % 7.04/2.35 % 7.04/2.35 Those formulas are unsatisfiable: % 7.04/2.35 --------------------------------- % 7.04/2.35 % 7.04/2.35 Begin of proof % 7.04/2.35 | % 7.04/2.35 | ALPHA: (d1_tarski) implies: % 7.04/2.35 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 7.04/2.35 | $i(v0) | ( ! [v2: $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & % 7.04/2.35 | ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2)))) % 7.04/2.35 | % 7.04/2.35 | ALPHA: (d2_tarski) implies: % 7.41/2.35 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 7.41/2.35 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: % 7.41/2.35 | int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1) % 7.41/2.35 | & ~ (v3 = v0))) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 7.41/2.35 | (in(v3, v2) = 0) | ~ $i(v3)))) % 7.41/2.36 | % 7.41/2.36 | ALPHA: (d3_xboole_0) implies: % 7.41/2.36 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, % 7.41/2.36 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! % 7.41/2.36 | [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? % 7.41/2.36 | [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | % 7.41/2.36 | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) | % 7.41/2.36 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & % 7.41/2.36 | in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 7.41/2.36 | % 7.41/2.36 | ALPHA: (function-axioms) implies: % 7.41/2.36 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.41/2.36 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 7.41/2.36 | % 7.41/2.36 | DELTA: instantiating (t59_zfmisc_1) with fresh symbols all_17_0, all_17_1, % 7.41/2.36 | all_17_2, all_17_3, all_17_4 gives: % 7.41/2.36 | (5) ~ (all_17_3 = all_17_4) & singleton(all_17_4) = all_17_0 & % 7.41/2.36 | set_intersection2(all_17_1, all_17_2) = all_17_0 & % 7.41/2.36 | unordered_pair(all_17_4, all_17_3) = all_17_1 & in(all_17_3, all_17_2) % 7.41/2.36 | = 0 & $i(all_17_0) & $i(all_17_1) & $i(all_17_2) & $i(all_17_3) & % 7.41/2.36 | $i(all_17_4) % 7.41/2.36 | % 7.41/2.36 | ALPHA: (5) implies: % 7.41/2.37 | (6) ~ (all_17_3 = all_17_4) % 7.41/2.37 | (7) $i(all_17_4) % 7.41/2.37 | (8) $i(all_17_3) % 7.41/2.37 | (9) $i(all_17_2) % 7.41/2.37 | (10) $i(all_17_0) % 7.41/2.37 | (11) in(all_17_3, all_17_2) = 0 % 7.41/2.37 | (12) unordered_pair(all_17_4, all_17_3) = all_17_1 % 7.41/2.37 | (13) set_intersection2(all_17_1, all_17_2) = all_17_0 % 7.41/2.37 | (14) singleton(all_17_4) = all_17_0 % 7.41/2.37 | % 7.41/2.37 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_17_4, all_17_3, % 7.41/2.37 | all_17_1, simplifying with (7), (8), (12) gives: % 7.41/2.37 | (15) unordered_pair(all_17_3, all_17_4) = all_17_1 & $i(all_17_1) % 7.41/2.37 | % 7.41/2.37 | ALPHA: (15) implies: % 7.41/2.37 | (16) $i(all_17_1) % 7.41/2.37 | (17) unordered_pair(all_17_3, all_17_4) = all_17_1 % 7.41/2.37 | % 7.41/2.37 | GROUND_INST: instantiating (3) with all_17_1, all_17_2, all_17_0, simplifying % 7.41/2.37 | with (9), (10), (13), (16) gives: % 7.41/2.37 | (18) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_17_1) = v1) | ~ $i(v0) | % 7.41/2.37 | ? [v2: any] : ? [v3: any] : (in(v0, all_17_0) = v2 & in(v0, % 7.41/2.37 | all_17_2) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 7.41/2.37 | $i] : ( ~ (in(v0, all_17_1) = 0) | ~ $i(v0) | ? [v1: any] : ? % 7.41/2.37 | [v2: any] : (in(v0, all_17_0) = v2 & in(v0, all_17_2) = v1 & ( ~ (v1 % 7.41/2.37 | = 0) | v2 = 0))) % 7.41/2.38 | % 7.41/2.38 | ALPHA: (18) implies: % 7.41/2.38 | (19) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_17_1) = v1) | ~ $i(v0) | % 7.41/2.38 | ? [v2: any] : ? [v3: any] : (in(v0, all_17_0) = v2 & in(v0, % 7.41/2.38 | all_17_2) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 7.41/2.38 | % 7.41/2.38 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_17_1, % 7.41/2.38 | all_17_2, all_17_0, simplifying with (9), (13), (16) gives: % 7.41/2.38 | (20) set_intersection2(all_17_2, all_17_1) = all_17_0 & $i(all_17_0) % 7.41/2.38 | % 7.41/2.38 | ALPHA: (20) implies: % 7.41/2.39 | (21) set_intersection2(all_17_2, all_17_1) = all_17_0 % 7.41/2.39 | % 7.41/2.39 | GROUND_INST: instantiating (1) with all_17_4, all_17_0, simplifying with (7), % 7.41/2.39 | (10), (14) gives: % 7.41/2.39 | (22) ! [v0: any] : (v0 = all_17_4 | ~ (in(v0, all_17_0) = 0) | ~ $i(v0)) % 7.41/2.39 | & ! [v0: int] : (v0 = 0 | ~ (in(all_17_4, all_17_0) = v0)) % 7.41/2.39 | % 7.41/2.39 | ALPHA: (22) implies: % 7.41/2.39 | (23) ! [v0: any] : (v0 = all_17_4 | ~ (in(v0, all_17_0) = 0) | ~ $i(v0)) % 7.41/2.39 | % 7.41/2.39 | GROUND_INST: instantiating (2) with all_17_3, all_17_4, all_17_1, simplifying % 7.41/2.39 | with (7), (8), (16), (17) gives: % 7.41/2.39 | (24) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_17_1) = v1) | ~ % 7.41/2.39 | $i(v0) | ( ~ (v0 = all_17_3) & ~ (v0 = all_17_4))) & ! [v0: any] : % 7.41/2.39 | (v0 = all_17_3 | v0 = all_17_4 | ~ (in(v0, all_17_1) = 0) | ~ % 7.41/2.39 | $i(v0)) % 7.41/2.39 | % 7.41/2.39 | ALPHA: (24) implies: % 7.41/2.39 | (25) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_17_1) = v1) | ~ % 7.41/2.39 | $i(v0) | ( ~ (v0 = all_17_3) & ~ (v0 = all_17_4))) % 7.41/2.39 | % 7.41/2.39 | GROUND_INST: instantiating (3) with all_17_2, all_17_1, all_17_0, simplifying % 7.41/2.39 | with (9), (10), (16), (21) gives: % 7.41/2.39 | (26) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_17_2) = v1) | ~ $i(v0) | % 7.41/2.39 | ? [v2: any] : ? [v3: any] : (in(v0, all_17_0) = v2 & in(v0, % 7.41/2.39 | all_17_1) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 7.41/2.39 | $i] : ( ~ (in(v0, all_17_2) = 0) | ~ $i(v0) | ? [v1: any] : ? % 7.41/2.39 | [v2: any] : (in(v0, all_17_0) = v2 & in(v0, all_17_1) = v1 & ( ~ (v1 % 7.41/2.39 | = 0) | v2 = 0))) % 7.41/2.39 | % 7.41/2.39 | ALPHA: (26) implies: % 7.41/2.40 | (27) ! [v0: $i] : ( ~ (in(v0, all_17_2) = 0) | ~ $i(v0) | ? [v1: any] : % 7.41/2.40 | ? [v2: any] : (in(v0, all_17_0) = v2 & in(v0, all_17_1) = v1 & ( ~ % 7.41/2.40 | (v1 = 0) | v2 = 0))) % 7.57/2.40 | (28) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_17_2) = v1) | ~ $i(v0) | % 7.57/2.40 | ? [v2: any] : ? [v3: any] : (in(v0, all_17_0) = v2 & in(v0, % 7.57/2.40 | all_17_1) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 7.57/2.40 | % 7.57/2.40 | GROUND_INST: instantiating (27) with all_17_3, simplifying with (8), (11) % 7.57/2.40 | gives: % 7.57/2.40 | (29) ? [v0: any] : ? [v1: any] : (in(all_17_3, all_17_0) = v1 & % 7.57/2.40 | in(all_17_3, all_17_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 7.57/2.40 | % 7.57/2.40 | GROUND_INST: instantiating (28) with all_17_3, 0, simplifying with (8), (11) % 7.57/2.40 | gives: % 7.57/2.40 | (30) ? [v0: any] : ? [v1: any] : (in(all_17_3, all_17_0) = v0 & % 7.57/2.40 | in(all_17_3, all_17_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 7.57/2.40 | % 7.57/2.40 | DELTA: instantiating (30) with fresh symbols all_41_0, all_41_1 gives: % 7.57/2.40 | (31) in(all_17_3, all_17_0) = all_41_1 & in(all_17_3, all_17_1) = all_41_0 % 7.57/2.40 | & ( ~ (all_41_1 = 0) | all_41_0 = 0) % 7.57/2.40 | % 7.57/2.40 | ALPHA: (31) implies: % 7.57/2.40 | (32) in(all_17_3, all_17_1) = all_41_0 % 7.57/2.40 | (33) in(all_17_3, all_17_0) = all_41_1 % 7.57/2.40 | % 7.57/2.40 | DELTA: instantiating (29) with fresh symbols all_43_0, all_43_1 gives: % 7.57/2.40 | (34) in(all_17_3, all_17_0) = all_43_0 & in(all_17_3, all_17_1) = all_43_1 % 7.57/2.40 | & ( ~ (all_43_1 = 0) | all_43_0 = 0) % 7.57/2.40 | % 7.57/2.40 | ALPHA: (34) implies: % 7.57/2.40 | (35) in(all_17_3, all_17_1) = all_43_1 % 7.57/2.40 | (36) in(all_17_3, all_17_0) = all_43_0 % 7.57/2.40 | (37) ~ (all_43_1 = 0) | all_43_0 = 0 % 7.57/2.40 | % 7.57/2.40 | GROUND_INST: instantiating (4) with all_41_0, all_43_1, all_17_1, all_17_3, % 7.57/2.40 | simplifying with (32), (35) gives: % 7.57/2.40 | (38) all_43_1 = all_41_0 % 7.57/2.40 | % 7.57/2.40 | GROUND_INST: instantiating (4) with all_41_1, all_43_0, all_17_0, all_17_3, % 7.57/2.40 | simplifying with (33), (36) gives: % 7.57/2.40 | (39) all_43_0 = all_41_1 % 7.57/2.40 | % 7.57/2.40 | GROUND_INST: instantiating (25) with all_17_3, all_41_0, simplifying with (8), % 7.57/2.40 | (32) gives: % 7.57/2.40 | (40) all_41_0 = 0 % 7.57/2.40 | % 7.57/2.40 | GROUND_INST: instantiating (19) with all_17_3, all_41_0, simplifying with (8), % 7.57/2.40 | (32) gives: % 7.57/2.41 | (41) ? [v0: any] : ? [v1: any] : (in(all_17_3, all_17_0) = v0 & % 7.57/2.41 | in(all_17_3, all_17_2) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_41_0 = % 7.57/2.41 | 0))) % 7.57/2.41 | % 7.57/2.41 | COMBINE_EQS: (38), (40) imply: % 7.57/2.41 | (42) all_43_1 = 0 % 7.57/2.41 | % 7.57/2.41 | DELTA: instantiating (41) with fresh symbols all_55_0, all_55_1 gives: % 7.57/2.41 | (43) in(all_17_3, all_17_0) = all_55_1 & in(all_17_3, all_17_2) = all_55_0 % 7.57/2.41 | & ( ~ (all_55_1 = 0) | (all_55_0 = 0 & all_41_0 = 0)) % 7.57/2.41 | % 7.57/2.41 | ALPHA: (43) implies: % 7.57/2.41 | (44) in(all_17_3, all_17_0) = all_55_1 % 7.57/2.41 | % 7.57/2.41 | BETA: splitting (37) gives: % 7.57/2.41 | % 7.57/2.41 | Case 1: % 7.57/2.41 | | % 7.57/2.41 | | (45) ~ (all_43_1 = 0) % 7.57/2.41 | | % 7.57/2.41 | | REDUCE: (42), (45) imply: % 7.57/2.41 | | (46) $false % 7.57/2.42 | | % 7.57/2.42 | | CLOSE: (46) is inconsistent. % 7.57/2.42 | | % 7.57/2.42 | Case 2: % 7.57/2.42 | | % 7.57/2.43 | | (47) all_43_0 = 0 % 7.57/2.43 | | % 7.57/2.43 | | COMBINE_EQS: (39), (47) imply: % 7.57/2.43 | | (48) all_41_1 = 0 % 7.57/2.43 | | % 7.57/2.43 | | REDUCE: (33), (48) imply: % 7.57/2.43 | | (49) in(all_17_3, all_17_0) = 0 % 7.57/2.43 | | % 7.57/2.43 | | GROUND_INST: instantiating (4) with 0, all_55_1, all_17_0, all_17_3, % 7.57/2.43 | | simplifying with (44), (49) gives: % 7.57/2.43 | | (50) all_55_1 = 0 % 7.57/2.43 | | % 7.57/2.43 | | GROUND_INST: instantiating (23) with all_17_3, simplifying with (8), (49) % 7.57/2.43 | | gives: % 7.57/2.43 | | (51) all_17_3 = all_17_4 % 7.57/2.43 | | % 7.57/2.43 | | REDUCE: (6), (51) imply: % 7.57/2.43 | | (52) $false % 7.57/2.43 | | % 7.57/2.43 | | CLOSE: (52) is inconsistent. % 7.57/2.43 | | % 7.57/2.43 | End of split % 7.57/2.43 | % 7.57/2.43 End of proof % 7.57/2.43 % SZS output end Proof for theBenchmark % 7.57/2.43 % 7.57/2.43 1741ms %------------------------------------------------------------------------------