%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU128+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 17:42:39 EDT 2023 % Result : Theorem 8.43s 1.93s % Output : Proof 11.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU128+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n004.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 19:00:23 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.68/1.11 Prover 4: Preprocessing ... % 2.68/1.11 Prover 1: Preprocessing ... % 3.25/1.15 Prover 6: Preprocessing ... % 3.25/1.15 Prover 0: Preprocessing ... % 3.25/1.15 Prover 5: Preprocessing ... % 3.25/1.15 Prover 2: Preprocessing ... % 3.25/1.15 Prover 3: Preprocessing ... % 6.24/1.59 Prover 1: Warning: ignoring some quantifiers % 6.60/1.62 Prover 5: Proving ... % 6.60/1.64 Prover 1: Constructing countermodel ... % 6.80/1.65 Prover 6: Proving ... % 6.80/1.69 Prover 3: Warning: ignoring some quantifiers % 6.80/1.71 Prover 3: Constructing countermodel ... % 7.35/1.73 Prover 2: Proving ... % 7.35/1.74 Prover 4: Warning: ignoring some quantifiers % 7.73/1.78 Prover 4: Constructing countermodel ... % 8.25/1.86 Prover 0: Proving ... % 8.43/1.93 Prover 3: proved (1302ms) % 8.43/1.93 % 8.43/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.43/1.93 % 8.43/1.93 Prover 2: stopped % 8.43/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.43/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.43/1.94 Prover 6: stopped % 8.43/1.95 Prover 5: stopped % 8.43/1.95 Prover 0: stopped % 8.43/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.43/1.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.43/1.97 Prover 7: Preprocessing ... % 8.43/1.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.43/1.99 Prover 8: Preprocessing ... % 9.38/2.04 Prover 10: Preprocessing ... % 9.38/2.04 Prover 11: Preprocessing ... % 9.62/2.05 Prover 13: Preprocessing ... % 9.62/2.12 Prover 7: Warning: ignoring some quantifiers % 10.22/2.14 Prover 7: Constructing countermodel ... % 10.22/2.17 Prover 13: Warning: ignoring some quantifiers % 10.22/2.17 Prover 10: Warning: ignoring some quantifiers % 10.56/2.18 Prover 1: Found proof (size 43) % 10.56/2.18 Prover 1: proved (1565ms) % 10.56/2.19 Prover 4: stopped % 10.56/2.19 Prover 13: Constructing countermodel ... % 10.56/2.19 Prover 7: stopped % 10.56/2.19 Prover 10: Constructing countermodel ... % 10.56/2.19 Prover 13: stopped % 10.56/2.19 Prover 8: Warning: ignoring some quantifiers % 10.56/2.20 Prover 10: stopped % 10.56/2.21 Prover 8: Constructing countermodel ... % 10.56/2.21 Prover 8: stopped % 10.56/2.23 Prover 11: Warning: ignoring some quantifiers % 10.56/2.24 Prover 11: Constructing countermodel ... % 10.97/2.25 Prover 11: stopped % 10.97/2.25 % 10.97/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.97/2.25 % 10.97/2.26 % SZS output start Proof for theBenchmark % 10.97/2.26 Assumptions after simplification: % 10.97/2.26 --------------------------------- % 10.97/2.26 % 10.97/2.26 (commutativity_k3_xboole_0) % 11.07/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 11.07/2.29 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 11.07/2.29 % 11.07/2.29 (d3_tarski) % 11.07/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 11.07/2.29 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 11.07/2.29 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 11.07/2.29 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 11.07/2.29 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 11.07/2.29 % 11.07/2.29 (d3_xboole_0) % 11.07/2.30 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 11.07/2.30 (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.07/2.30 [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 & % 11.07/2.30 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) | % 11.07/2.30 ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] % 11.07/2.30 : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 11.07/2.30 ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) % 11.07/2.30 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ % 11.07/2.30 (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) % 11.07/2.30 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, % 11.07/2.30 v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 11.07/2.30 % 11.07/2.30 (t19_xboole_1) % 11.07/2.30 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 11.07/2.30 = 0) & subset(v0, v3) = v4 & subset(v0, v2) = 0 & subset(v0, v1) = 0 & % 11.07/2.30 set_intersection2(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.07/2.30 % 11.07/2.30 (t1_xboole_1) % 11.07/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.07/2.30 (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 11.07/2.30 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 11.07/2.30 % 11.07/2.30 (function-axioms) % 11.07/2.31 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.07/2.31 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 11.07/2.31 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.07/2.31 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 11.07/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.07/2.31 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 11.07/2.31 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.07/2.31 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 11.07/2.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.07/2.31 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 11.07/2.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 11.07/2.31 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 11.07/2.31 % 11.07/2.31 Further assumptions not needed in the proof: % 11.07/2.31 -------------------------------------------- % 11.07/2.31 antisymmetry_r2_hidden, commutativity_k2_xboole_0, d10_xboole_0, d1_xboole_0, % 11.07/2.31 d2_xboole_0, d7_xboole_0, dt_k1_xboole_0, dt_k2_xboole_0, dt_k3_xboole_0, % 11.07/2.31 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 11.07/2.31 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 11.07/2.31 symmetry_r1_xboole_0, t12_xboole_1, t17_xboole_1, t1_boole, t2_boole, % 11.07/2.31 t2_xboole_1, t3_xboole_0, t3_xboole_1, t4_xboole_0, t6_boole, t7_boole, % 11.07/2.31 t7_xboole_1, t8_boole, t8_xboole_1 % 11.07/2.31 % 11.07/2.31 Those formulas are unsatisfiable: % 11.07/2.31 --------------------------------- % 11.07/2.31 % 11.07/2.31 Begin of proof % 11.07/2.31 | % 11.07/2.31 | ALPHA: (d3_tarski) implies: % 11.07/2.31 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 11.07/2.31 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1) % 11.07/2.31 | = 0)) % 11.07/2.31 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 11.07/2.31 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 11.07/2.31 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 11.07/2.31 | % 11.07/2.31 | ALPHA: (d3_xboole_0) implies: % 11.07/2.31 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, % 11.07/2.31 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! % 11.07/2.31 | [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? % 11.07/2.31 | [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | % 11.07/2.31 | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) | % 11.07/2.31 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & % 11.07/2.31 | in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 11.07/2.31 | % 11.07/2.31 | ALPHA: (function-axioms) implies: % 11.07/2.31 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.07/2.31 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 11.07/2.31 | % 11.07/2.31 | DELTA: instantiating (t19_xboole_1) with fresh symbols all_41_0, all_41_1, % 11.07/2.31 | all_41_2, all_41_3, all_41_4 gives: % 11.07/2.32 | (5) ~ (all_41_0 = 0) & subset(all_41_4, all_41_1) = all_41_0 & % 11.07/2.32 | subset(all_41_4, all_41_2) = 0 & subset(all_41_4, all_41_3) = 0 & % 11.07/2.32 | set_intersection2(all_41_3, all_41_2) = all_41_1 & $i(all_41_1) & % 11.07/2.32 | $i(all_41_2) & $i(all_41_3) & $i(all_41_4) % 11.07/2.32 | % 11.07/2.32 | ALPHA: (5) implies: % 11.07/2.32 | (6) ~ (all_41_0 = 0) % 11.07/2.32 | (7) $i(all_41_4) % 11.07/2.32 | (8) $i(all_41_3) % 11.07/2.32 | (9) $i(all_41_2) % 11.07/2.32 | (10) $i(all_41_1) % 11.33/2.32 | (11) set_intersection2(all_41_3, all_41_2) = all_41_1 % 11.33/2.32 | (12) subset(all_41_4, all_41_3) = 0 % 11.33/2.32 | (13) subset(all_41_4, all_41_2) = 0 % 11.33/2.32 | (14) subset(all_41_4, all_41_1) = all_41_0 % 11.33/2.32 | % 11.33/2.32 | GROUND_INST: instantiating (3) with all_41_3, all_41_2, all_41_1, simplifying % 11.33/2.32 | with (8), (9), (10), (11) gives: % 11.33/2.32 | (15) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_41_3) = v1) | ~ $i(v0) | % 11.33/2.32 | ? [v2: any] : ? [v3: any] : (in(v0, all_41_1) = v2 & in(v0, % 11.33/2.32 | all_41_2) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 11.33/2.32 | $i] : ( ~ (in(v0, all_41_3) = 0) | ~ $i(v0) | ? [v1: any] : ? % 11.33/2.32 | [v2: any] : (in(v0, all_41_1) = v2 & in(v0, all_41_2) = v1 & ( ~ (v1 % 11.33/2.32 | = 0) | v2 = 0))) % 11.33/2.32 | % 11.33/2.32 | ALPHA: (15) implies: % 11.33/2.32 | (16) ! [v0: $i] : ( ~ (in(v0, all_41_3) = 0) | ~ $i(v0) | ? [v1: any] : % 11.33/2.32 | ? [v2: any] : (in(v0, all_41_1) = v2 & in(v0, all_41_2) = v1 & ( ~ % 11.33/2.32 | (v1 = 0) | v2 = 0))) % 11.33/2.32 | % 11.33/2.32 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_41_3, % 11.33/2.32 | all_41_2, all_41_1, simplifying with (8), (9), (11) gives: % 11.33/2.32 | (17) set_intersection2(all_41_2, all_41_3) = all_41_1 & $i(all_41_1) % 11.33/2.32 | % 11.33/2.32 | ALPHA: (17) implies: % 11.33/2.32 | (18) set_intersection2(all_41_2, all_41_3) = all_41_1 % 11.33/2.32 | % 11.33/2.32 | GROUND_INST: instantiating (1) with all_41_4, all_41_3, simplifying with (7), % 11.33/2.32 | (8), (12) gives: % 11.33/2.32 | (19) ! [v0: $i] : ( ~ (in(v0, all_41_4) = 0) | ~ $i(v0) | in(v0, % 11.33/2.32 | all_41_3) = 0) % 11.33/2.32 | % 11.33/2.32 | GROUND_INST: instantiating (1) with all_41_4, all_41_2, simplifying with (7), % 11.33/2.32 | (9), (13) gives: % 11.33/2.32 | (20) ! [v0: $i] : ( ~ (in(v0, all_41_4) = 0) | ~ $i(v0) | in(v0, % 11.33/2.32 | all_41_2) = 0) % 11.33/2.32 | % 11.33/2.32 | GROUND_INST: instantiating (t1_xboole_1) with all_41_4, all_41_3, all_41_1, % 11.33/2.32 | all_41_0, simplifying with (7), (8), (10), (12), (14) gives: % 11.33/2.32 | (21) all_41_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_41_3, % 11.33/2.32 | all_41_1) = v0) % 11.33/2.32 | % 11.33/2.32 | GROUND_INST: instantiating (2) with all_41_4, all_41_1, all_41_0, simplifying % 11.33/2.32 | with (7), (10), (14) gives: % 11.33/2.33 | (22) all_41_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 11.33/2.33 | all_41_1) = v1 & in(v0, all_41_4) = 0 & $i(v0)) % 11.33/2.33 | % 11.33/2.33 | BETA: splitting (22) gives: % 11.33/2.33 | % 11.33/2.33 | Case 1: % 11.33/2.33 | | % 11.33/2.33 | | (23) all_41_0 = 0 % 11.33/2.33 | | % 11.33/2.33 | | REDUCE: (6), (23) imply: % 11.33/2.33 | | (24) $false % 11.33/2.33 | | % 11.33/2.33 | | CLOSE: (24) is inconsistent. % 11.33/2.33 | | % 11.33/2.33 | Case 2: % 11.33/2.33 | | % 11.33/2.33 | | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_41_1) = v1 & % 11.33/2.33 | | in(v0, all_41_4) = 0 & $i(v0)) % 11.33/2.33 | | % 11.33/2.33 | | DELTA: instantiating (25) with fresh symbols all_60_0, all_60_1 gives: % 11.33/2.33 | | (26) ~ (all_60_0 = 0) & in(all_60_1, all_41_1) = all_60_0 & in(all_60_1, % 11.33/2.33 | | all_41_4) = 0 & $i(all_60_1) % 11.33/2.33 | | % 11.33/2.33 | | ALPHA: (26) implies: % 11.33/2.33 | | (27) ~ (all_60_0 = 0) % 11.33/2.33 | | (28) $i(all_60_1) % 11.33/2.33 | | (29) in(all_60_1, all_41_4) = 0 % 11.33/2.33 | | (30) in(all_60_1, all_41_1) = all_60_0 % 11.33/2.33 | | % 11.33/2.33 | | BETA: splitting (21) gives: % 11.33/2.33 | | % 11.33/2.33 | | Case 1: % 11.33/2.33 | | | % 11.33/2.33 | | | (31) all_41_0 = 0 % 11.33/2.33 | | | % 11.33/2.33 | | | REDUCE: (6), (31) imply: % 11.33/2.33 | | | (32) $false % 11.33/2.33 | | | % 11.33/2.33 | | | CLOSE: (32) is inconsistent. % 11.33/2.33 | | | % 11.33/2.33 | | Case 2: % 11.33/2.33 | | | % 11.33/2.33 | | | % 11.33/2.33 | | | GROUND_INST: instantiating (20) with all_60_1, simplifying with (28), (29) % 11.33/2.33 | | | gives: % 11.33/2.33 | | | (33) in(all_60_1, all_41_2) = 0 % 11.33/2.33 | | | % 11.33/2.33 | | | GROUND_INST: instantiating (19) with all_60_1, simplifying with (28), (29) % 11.33/2.33 | | | gives: % 11.33/2.33 | | | (34) in(all_60_1, all_41_3) = 0 % 11.33/2.33 | | | % 11.33/2.33 | | | GROUND_INST: instantiating (3) with all_41_2, all_41_3, all_41_1, % 11.33/2.33 | | | simplifying with (8), (9), (10), (18) gives: % 11.33/2.33 | | | (35) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_41_2) = v1) | ~ % 11.33/2.33 | | | $i(v0) | ? [v2: any] : ? [v3: any] : (in(v0, all_41_1) = v2 & % 11.33/2.33 | | | in(v0, all_41_3) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & % 11.33/2.33 | | | ! [v0: $i] : ( ~ (in(v0, all_41_2) = 0) | ~ $i(v0) | ? [v1: any] % 11.33/2.33 | | | : ? [v2: any] : (in(v0, all_41_1) = v2 & in(v0, all_41_3) = v1 % 11.33/2.33 | | | & ( ~ (v1 = 0) | v2 = 0))) % 11.33/2.33 | | | % 11.33/2.33 | | | ALPHA: (35) implies: % 11.33/2.33 | | | (36) ! [v0: $i] : ( ~ (in(v0, all_41_2) = 0) | ~ $i(v0) | ? [v1: % 11.33/2.33 | | | any] : ? [v2: any] : (in(v0, all_41_1) = v2 & in(v0, % 11.33/2.33 | | | all_41_3) = v1 & ( ~ (v1 = 0) | v2 = 0))) % 11.33/2.33 | | | % 11.33/2.33 | | | GROUND_INST: instantiating (16) with all_60_1, simplifying with (28), (34) % 11.33/2.33 | | | gives: % 11.33/2.33 | | | (37) ? [v0: any] : ? [v1: any] : (in(all_60_1, all_41_1) = v1 & % 11.33/2.33 | | | in(all_60_1, all_41_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 11.33/2.33 | | | % 11.33/2.33 | | | GROUND_INST: instantiating (36) with all_60_1, simplifying with (28), (33) % 11.33/2.33 | | | gives: % 11.33/2.33 | | | (38) ? [v0: any] : ? [v1: any] : (in(all_60_1, all_41_1) = v1 & % 11.33/2.33 | | | in(all_60_1, all_41_3) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 11.33/2.33 | | | % 11.33/2.33 | | | DELTA: instantiating (38) with fresh symbols all_115_0, all_115_1 gives: % 11.33/2.33 | | | (39) in(all_60_1, all_41_1) = all_115_0 & in(all_60_1, all_41_3) = % 11.33/2.33 | | | all_115_1 & ( ~ (all_115_1 = 0) | all_115_0 = 0) % 11.33/2.33 | | | % 11.33/2.33 | | | ALPHA: (39) implies: % 11.33/2.33 | | | (40) in(all_60_1, all_41_3) = all_115_1 % 11.33/2.33 | | | (41) in(all_60_1, all_41_1) = all_115_0 % 11.33/2.34 | | | (42) ~ (all_115_1 = 0) | all_115_0 = 0 % 11.33/2.34 | | | % 11.33/2.34 | | | DELTA: instantiating (37) with fresh symbols all_121_0, all_121_1 gives: % 11.33/2.34 | | | (43) in(all_60_1, all_41_1) = all_121_0 & in(all_60_1, all_41_2) = % 11.33/2.34 | | | all_121_1 & ( ~ (all_121_1 = 0) | all_121_0 = 0) % 11.33/2.34 | | | % 11.33/2.34 | | | ALPHA: (43) implies: % 11.33/2.34 | | | (44) in(all_60_1, all_41_1) = all_121_0 % 11.33/2.34 | | | % 11.33/2.34 | | | GROUND_INST: instantiating (4) with 0, all_115_1, all_41_3, all_60_1, % 11.33/2.34 | | | simplifying with (34), (40) gives: % 11.33/2.34 | | | (45) all_115_1 = 0 % 11.33/2.34 | | | % 11.33/2.34 | | | GROUND_INST: instantiating (4) with all_60_0, all_121_0, all_41_1, % 11.33/2.34 | | | all_60_1, simplifying with (30), (44) gives: % 11.33/2.34 | | | (46) all_121_0 = all_60_0 % 11.33/2.34 | | | % 11.33/2.34 | | | GROUND_INST: instantiating (4) with all_115_0, all_121_0, all_41_1, % 11.33/2.34 | | | all_60_1, simplifying with (41), (44) gives: % 11.33/2.34 | | | (47) all_121_0 = all_115_0 % 11.33/2.34 | | | % 11.33/2.34 | | | COMBINE_EQS: (46), (47) imply: % 11.33/2.34 | | | (48) all_115_0 = all_60_0 % 11.33/2.34 | | | % 11.33/2.34 | | | BETA: splitting (42) gives: % 11.33/2.34 | | | % 11.33/2.34 | | | Case 1: % 11.33/2.34 | | | | % 11.33/2.34 | | | | (49) ~ (all_115_1 = 0) % 11.33/2.34 | | | | % 11.33/2.34 | | | | REDUCE: (45), (49) imply: % 11.33/2.34 | | | | (50) $false % 11.33/2.34 | | | | % 11.33/2.34 | | | | CLOSE: (50) is inconsistent. % 11.33/2.34 | | | | % 11.33/2.34 | | | Case 2: % 11.33/2.34 | | | | % 11.33/2.34 | | | | (51) all_115_0 = 0 % 11.33/2.34 | | | | % 11.33/2.34 | | | | COMBINE_EQS: (48), (51) imply: % 11.33/2.34 | | | | (52) all_60_0 = 0 % 11.33/2.34 | | | | % 11.33/2.34 | | | | SIMP: (52) implies: % 11.33/2.34 | | | | (53) all_60_0 = 0 % 11.33/2.34 | | | | % 11.33/2.34 | | | | REDUCE: (27), (53) imply: % 11.33/2.34 | | | | (54) $false % 11.33/2.34 | | | | % 11.33/2.34 | | | | CLOSE: (54) is inconsistent. % 11.33/2.34 | | | | % 11.33/2.34 | | | End of split % 11.33/2.34 | | | % 11.33/2.34 | | End of split % 11.33/2.34 | | % 11.33/2.34 | End of split % 11.33/2.34 | % 11.33/2.34 End of proof % 11.33/2.34 % SZS output end Proof for theBenchmark % 11.33/2.34 % 11.33/2.34 1739ms %------------------------------------------------------------------------------