%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU120+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 : n028.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 17:42:35 EDT 2023 % Result : Theorem 7.32s 1.78s % Output : Proof 9.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU120+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n028.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Aug 23 17:00:48 EDT 2023 % 0.12/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 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 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 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 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 % 2.40/1.00 Prover 1: Preprocessing ... % 2.40/1.00 Prover 4: Preprocessing ... % 2.40/1.04 Prover 6: Preprocessing ... % 2.40/1.04 Prover 0: Preprocessing ... % 2.40/1.04 Prover 5: Preprocessing ... % 2.40/1.04 Prover 3: Preprocessing ... % 2.40/1.05 Prover 2: Preprocessing ... % 4.38/1.33 Prover 5: Proving ... % 4.38/1.36 Prover 1: Warning: ignoring some quantifiers % 4.38/1.36 Prover 6: Proving ... % 4.38/1.37 Prover 2: Proving ... % 4.38/1.38 Prover 3: Warning: ignoring some quantifiers % 4.38/1.38 Prover 1: Constructing countermodel ... % 4.38/1.39 Prover 3: Constructing countermodel ... % 4.98/1.39 Prover 4: Warning: ignoring some quantifiers % 4.98/1.41 Prover 0: Proving ... % 4.98/1.42 Prover 4: Constructing countermodel ... % 7.32/1.78 Prover 0: proved (1136ms) % 7.32/1.78 % 7.32/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.32/1.79 % 7.32/1.79 Prover 3: stopped % 7.32/1.79 Prover 5: stopped % 7.94/1.80 Prover 2: stopped % 7.94/1.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.94/1.80 Prover 6: stopped % 7.94/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.94/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.94/1.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.94/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.94/1.81 Prover 7: Preprocessing ... % 7.94/1.82 Prover 8: Preprocessing ... % 7.94/1.82 Prover 1: Found proof (size 61) % 7.94/1.82 Prover 1: proved (1178ms) % 7.94/1.83 Prover 4: stopped % 7.94/1.83 Prover 11: Preprocessing ... % 7.94/1.83 Prover 10: Preprocessing ... % 7.94/1.84 Prover 13: Preprocessing ... % 7.94/1.84 Prover 7: stopped % 7.94/1.85 Prover 10: stopped % 7.94/1.86 Prover 13: stopped % 7.94/1.87 Prover 11: stopped % 8.56/1.90 Prover 8: Warning: ignoring some quantifiers % 8.66/1.91 Prover 8: Constructing countermodel ... % 8.66/1.91 Prover 8: stopped % 8.66/1.91 % 8.66/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.66/1.92 % 8.73/1.92 % SZS output start Proof for theBenchmark % 8.73/1.93 Assumptions after simplification: % 8.73/1.93 --------------------------------- % 8.73/1.93 % 8.73/1.93 (commutativity_k3_xboole_0) % 8.73/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 8.73/1.95 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 8.73/1.95 % 8.73/1.95 (d1_xboole_0) % 8.73/1.96 $i(empty_set) & ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0)) & ? % 8.73/1.96 [v0: $i] : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : (in(v1, v0) = 0 & % 8.73/1.96 $i(v1))) % 8.73/1.96 % 8.73/1.96 (d3_xboole_0) % 8.73/1.96 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 8.73/1.96 (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 8.73/1.96 [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 & % 8.73/1.96 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) | % 8.73/1.96 ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] % 8.73/1.96 : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 8.73/1.96 ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) % 8.73/1.96 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ % 8.73/1.96 (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) % 8.73/1.96 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, % 8.73/1.97 v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 8.73/1.97 % 8.73/1.97 (d7_xboole_0) % 8.73/1.97 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 8.73/1.97 (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = % 8.73/1.97 empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : % 8.73/1.97 ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 8.73/1.97 set_intersection2(v0, v1) = empty_set) % 8.73/1.97 % 8.73/1.97 (t3_xboole_0) % 8.73/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 8.73/1.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (in(v3, v1) = 0 & in(v3, v0) = % 8.73/1.97 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ % 8.73/1.97 $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | ? % 8.73/1.97 [v3: int] : ( ~ (v3 = 0) & in(v2, v1) = v3))) % 8.73/1.97 % 8.73/1.97 (t4_xboole_0) % 8.73/1.97 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : (disjoint(v0, v1) = % 8.73/1.97 v2 & set_intersection2(v0, v1) = v3 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & % 8.73/1.97 ? [v4: $i] : (in(v4, v3) = 0 & $i(v4))) | ( ~ (v2 = 0) & ! [v4: $i] : ( % 8.73/1.97 ~ (in(v4, v3) = 0) | ~ $i(v4))))) % 8.73/1.97 % 8.73/1.97 (function-axioms) % 8.73/1.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.73/1.98 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 8.73/1.98 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.73/1.98 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 8.73/1.98 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.73/1.98 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 8.73/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.73/1.98 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 8.73/1.98 % 8.73/1.98 Further assumptions not needed in the proof: % 8.73/1.98 -------------------------------------------- % 8.73/1.98 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k3_xboole_0, fc1_xboole_0, % 8.73/1.98 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, symmetry_r1_xboole_0 % 8.73/1.98 % 8.73/1.98 Those formulas are unsatisfiable: % 8.73/1.98 --------------------------------- % 8.73/1.98 % 8.73/1.98 Begin of proof % 8.73/1.98 | % 8.73/1.98 | ALPHA: (d1_xboole_0) implies: % 8.73/1.98 | (1) ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0)) % 8.73/1.98 | % 8.73/1.98 | ALPHA: (d3_xboole_0) implies: % 8.73/1.98 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, % 8.73/1.98 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! % 8.73/1.98 | [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? % 8.73/1.98 | [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | % 8.73/1.98 | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) | % 8.73/1.98 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & % 8.73/1.98 | in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 8.73/1.98 | % 8.73/1.98 | ALPHA: (d7_xboole_0) implies: % 8.73/1.98 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ % 8.73/1.98 | $i(v0) | set_intersection2(v0, v1) = empty_set) % 8.73/1.98 | % 8.73/1.98 | ALPHA: (t3_xboole_0) implies: % 8.73/1.99 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 8.73/1.99 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (in(v3, v1) = 0 % 8.73/1.99 | & in(v3, v0) = 0 & $i(v3))) % 8.73/1.99 | % 8.73/1.99 | ALPHA: (function-axioms) implies: % 8.73/1.99 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.73/1.99 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 8.73/1.99 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.73/1.99 | (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = % 8.73/1.99 | v0)) % 8.73/1.99 | % 8.73/1.99 | DELTA: instantiating (t4_xboole_0) with fresh symbols all_18_0, all_18_1, % 8.73/1.99 | all_18_2, all_18_3 gives: % 8.73/1.99 | (7) disjoint(all_18_3, all_18_2) = all_18_1 & set_intersection2(all_18_3, % 8.73/1.99 | all_18_2) = all_18_0 & $i(all_18_0) & $i(all_18_2) & $i(all_18_3) & % 8.73/1.99 | ((all_18_1 = 0 & ? [v0: $i] : (in(v0, all_18_0) = 0 & $i(v0))) | ( ~ % 8.73/1.99 | (all_18_1 = 0) & ! [v0: $i] : ( ~ (in(v0, all_18_0) = 0) | ~ % 8.73/1.99 | $i(v0)))) % 8.73/1.99 | % 8.73/1.99 | ALPHA: (7) implies: % 8.73/1.99 | (8) $i(all_18_3) % 8.73/1.99 | (9) $i(all_18_2) % 8.73/1.99 | (10) $i(all_18_0) % 8.73/1.99 | (11) set_intersection2(all_18_3, all_18_2) = all_18_0 % 8.73/1.99 | (12) disjoint(all_18_3, all_18_2) = all_18_1 % 8.73/1.99 | (13) (all_18_1 = 0 & ? [v0: $i] : (in(v0, all_18_0) = 0 & $i(v0))) | ( ~ % 8.73/1.99 | (all_18_1 = 0) & ! [v0: $i] : ( ~ (in(v0, all_18_0) = 0) | ~ % 8.73/1.99 | $i(v0))) % 8.73/1.99 | % 8.73/1.99 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_0, simplifying % 8.73/1.99 | with (8), (9), (10), (11) gives: % 8.73/2.00 | (14) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_3) = v1) | ~ $i(v0) | % 8.73/2.00 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v2 & in(v0, % 8.73/2.00 | all_18_2) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 8.73/2.00 | $i] : ( ~ (in(v0, all_18_3) = 0) | ~ $i(v0) | ? [v1: any] : ? % 8.73/2.00 | [v2: any] : (in(v0, all_18_0) = v2 & in(v0, all_18_2) = v1 & ( ~ (v1 % 8.73/2.00 | = 0) | v2 = 0))) % 8.73/2.00 | % 8.73/2.00 | ALPHA: (14) implies: % 8.73/2.00 | (15) ! [v0: $i] : ( ~ (in(v0, all_18_3) = 0) | ~ $i(v0) | ? [v1: any] : % 8.73/2.00 | ? [v2: any] : (in(v0, all_18_0) = v2 & in(v0, all_18_2) = v1 & ( ~ % 8.73/2.00 | (v1 = 0) | v2 = 0))) % 8.73/2.00 | (16) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_3) = v1) | ~ $i(v0) | % 8.73/2.00 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v2 & in(v0, % 8.73/2.00 | all_18_2) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 8.73/2.00 | % 8.73/2.00 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_18_3, % 8.73/2.00 | all_18_2, all_18_0, simplifying with (8), (9), (11) gives: % 8.73/2.00 | (17) set_intersection2(all_18_2, all_18_3) = all_18_0 & $i(all_18_0) % 8.73/2.00 | % 8.73/2.00 | ALPHA: (17) implies: % 8.73/2.00 | (18) set_intersection2(all_18_2, all_18_3) = all_18_0 % 8.73/2.00 | % 8.73/2.00 | GROUND_INST: instantiating (4) with all_18_3, all_18_2, all_18_1, simplifying % 8.73/2.00 | with (8), (9), (12) gives: % 8.73/2.00 | (19) all_18_1 = 0 | ? [v0: $i] : (in(v0, all_18_2) = 0 & in(v0, all_18_3) % 8.73/2.00 | = 0 & $i(v0)) % 8.73/2.00 | % 8.73/2.00 | GROUND_INST: instantiating (2) with all_18_2, all_18_3, all_18_0, simplifying % 8.73/2.00 | with (8), (9), (10), (18) gives: % 8.73/2.00 | (20) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_2) = v1) | ~ $i(v0) | % 8.73/2.00 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v2 & in(v0, % 8.73/2.00 | all_18_3) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 8.73/2.00 | $i] : ( ~ (in(v0, all_18_2) = 0) | ~ $i(v0) | ? [v1: any] : ? % 8.73/2.00 | [v2: any] : (in(v0, all_18_0) = v2 & in(v0, all_18_3) = v1 & ( ~ (v1 % 8.73/2.00 | = 0) | v2 = 0))) % 8.73/2.00 | % 8.73/2.00 | ALPHA: (20) implies: % 8.73/2.00 | (21) ! [v0: $i] : ( ~ (in(v0, all_18_2) = 0) | ~ $i(v0) | ? [v1: any] : % 8.73/2.00 | ? [v2: any] : (in(v0, all_18_0) = v2 & in(v0, all_18_3) = v1 & ( ~ % 8.73/2.00 | (v1 = 0) | v2 = 0))) % 8.73/2.01 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_2) = v1) | ~ $i(v0) | % 8.73/2.01 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v2 & in(v0, % 8.73/2.01 | all_18_3) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 8.73/2.01 | % 8.73/2.01 | BETA: splitting (13) gives: % 8.73/2.01 | % 8.73/2.01 | Case 1: % 8.73/2.01 | | % 8.73/2.01 | | (23) all_18_1 = 0 & ? [v0: $i] : (in(v0, all_18_0) = 0 & $i(v0)) % 8.73/2.01 | | % 8.73/2.01 | | ALPHA: (23) implies: % 8.73/2.01 | | (24) all_18_1 = 0 % 8.73/2.01 | | (25) ? [v0: $i] : (in(v0, all_18_0) = 0 & $i(v0)) % 8.73/2.01 | | % 8.73/2.01 | | DELTA: instantiating (25) with fresh symbol all_46_0 gives: % 8.73/2.01 | | (26) in(all_46_0, all_18_0) = 0 & $i(all_46_0) % 8.73/2.01 | | % 8.73/2.01 | | ALPHA: (26) implies: % 8.73/2.01 | | (27) $i(all_46_0) % 8.73/2.01 | | (28) in(all_46_0, all_18_0) = 0 % 8.73/2.01 | | % 8.73/2.01 | | REDUCE: (12), (24) imply: % 8.73/2.01 | | (29) disjoint(all_18_3, all_18_2) = 0 % 8.73/2.01 | | % 8.73/2.01 | | GROUND_INST: instantiating (3) with all_18_3, all_18_2, simplifying with % 8.73/2.01 | | (8), (9), (29) gives: % 8.73/2.01 | | (30) set_intersection2(all_18_3, all_18_2) = empty_set % 8.73/2.01 | | % 9.18/2.01 | | GROUND_INST: instantiating (6) with all_18_0, empty_set, all_18_2, all_18_3, % 9.18/2.01 | | simplifying with (11), (30) gives: % 9.18/2.01 | | (31) all_18_0 = empty_set % 9.18/2.01 | | % 9.18/2.01 | | REDUCE: (28), (31) imply: % 9.18/2.01 | | (32) in(all_46_0, empty_set) = 0 % 9.18/2.01 | | % 9.18/2.01 | | GROUND_INST: instantiating (1) with all_46_0, simplifying with (27), (32) % 9.18/2.01 | | gives: % 9.18/2.01 | | (33) $false % 9.18/2.01 | | % 9.18/2.01 | | CLOSE: (33) is inconsistent. % 9.18/2.01 | | % 9.18/2.01 | Case 2: % 9.18/2.01 | | % 9.18/2.01 | | (34) ~ (all_18_1 = 0) & ! [v0: $i] : ( ~ (in(v0, all_18_0) = 0) | ~ % 9.18/2.01 | | $i(v0)) % 9.18/2.01 | | % 9.18/2.01 | | ALPHA: (34) implies: % 9.18/2.01 | | (35) ~ (all_18_1 = 0) % 9.18/2.01 | | (36) ! [v0: $i] : ( ~ (in(v0, all_18_0) = 0) | ~ $i(v0)) % 9.18/2.01 | | % 9.18/2.01 | | BETA: splitting (19) gives: % 9.18/2.01 | | % 9.18/2.01 | | Case 1: % 9.18/2.01 | | | % 9.18/2.01 | | | (37) all_18_1 = 0 % 9.18/2.01 | | | % 9.18/2.01 | | | REDUCE: (35), (37) imply: % 9.18/2.01 | | | (38) $false % 9.18/2.01 | | | % 9.18/2.01 | | | CLOSE: (38) is inconsistent. % 9.18/2.01 | | | % 9.18/2.01 | | Case 2: % 9.18/2.01 | | | % 9.18/2.01 | | | (39) ? [v0: $i] : (in(v0, all_18_2) = 0 & in(v0, all_18_3) = 0 & % 9.18/2.01 | | | $i(v0)) % 9.18/2.01 | | | % 9.18/2.01 | | | DELTA: instantiating (39) with fresh symbol all_57_0 gives: % 9.18/2.01 | | | (40) in(all_57_0, all_18_2) = 0 & in(all_57_0, all_18_3) = 0 & % 9.18/2.01 | | | $i(all_57_0) % 9.18/2.01 | | | % 9.18/2.01 | | | ALPHA: (40) implies: % 9.18/2.02 | | | (41) $i(all_57_0) % 9.18/2.02 | | | (42) in(all_57_0, all_18_3) = 0 % 9.18/2.02 | | | (43) in(all_57_0, all_18_2) = 0 % 9.18/2.02 | | | % 9.18/2.02 | | | GROUND_INST: instantiating (15) with all_57_0, simplifying with (41), (42) % 9.18/2.02 | | | gives: % 9.18/2.02 | | | (44) ? [v0: any] : ? [v1: any] : (in(all_57_0, all_18_0) = v1 & % 9.18/2.02 | | | in(all_57_0, all_18_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 9.18/2.02 | | | % 9.18/2.02 | | | GROUND_INST: instantiating (16) with all_57_0, 0, simplifying with (41), % 9.18/2.02 | | | (42) gives: % 9.18/2.02 | | | (45) ? [v0: any] : ? [v1: any] : (in(all_57_0, all_18_0) = v0 & % 9.18/2.02 | | | in(all_57_0, all_18_2) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 9.18/2.02 | | | % 9.18/2.02 | | | GROUND_INST: instantiating (21) with all_57_0, simplifying with (41), (43) % 9.18/2.02 | | | gives: % 9.18/2.02 | | | (46) ? [v0: any] : ? [v1: any] : (in(all_57_0, all_18_0) = v1 & % 9.18/2.02 | | | in(all_57_0, all_18_3) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 9.18/2.02 | | | % 9.18/2.02 | | | GROUND_INST: instantiating (22) with all_57_0, 0, simplifying with (41), % 9.18/2.02 | | | (43) gives: % 9.18/2.02 | | | (47) ? [v0: any] : ? [v1: any] : (in(all_57_0, all_18_0) = v0 & % 9.18/2.02 | | | in(all_57_0, all_18_3) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 9.18/2.02 | | | % 9.18/2.02 | | | DELTA: instantiating (44) with fresh symbols all_72_0, all_72_1 gives: % 9.18/2.02 | | | (48) in(all_57_0, all_18_0) = all_72_0 & in(all_57_0, all_18_2) = % 9.18/2.02 | | | all_72_1 & ( ~ (all_72_1 = 0) | all_72_0 = 0) % 9.18/2.02 | | | % 9.18/2.02 | | | ALPHA: (48) implies: % 9.18/2.02 | | | (49) in(all_57_0, all_18_2) = all_72_1 % 9.18/2.02 | | | (50) in(all_57_0, all_18_0) = all_72_0 % 9.18/2.02 | | | (51) ~ (all_72_1 = 0) | all_72_0 = 0 % 9.18/2.02 | | | % 9.18/2.02 | | | DELTA: instantiating (46) with fresh symbols all_74_0, all_74_1 gives: % 9.18/2.02 | | | (52) in(all_57_0, all_18_0) = all_74_0 & in(all_57_0, all_18_3) = % 9.18/2.02 | | | all_74_1 & ( ~ (all_74_1 = 0) | all_74_0 = 0) % 9.18/2.02 | | | % 9.18/2.02 | | | ALPHA: (52) implies: % 9.18/2.02 | | | (53) in(all_57_0, all_18_0) = all_74_0 % 9.18/2.02 | | | % 9.18/2.02 | | | DELTA: instantiating (45) with fresh symbols all_76_0, all_76_1 gives: % 9.18/2.02 | | | (54) in(all_57_0, all_18_0) = all_76_1 & in(all_57_0, all_18_2) = % 9.18/2.02 | | | all_76_0 & ( ~ (all_76_1 = 0) | all_76_0 = 0) % 9.18/2.02 | | | % 9.18/2.02 | | | ALPHA: (54) implies: % 9.18/2.02 | | | (55) in(all_57_0, all_18_2) = all_76_0 % 9.18/2.02 | | | (56) in(all_57_0, all_18_0) = all_76_1 % 9.18/2.02 | | | % 9.18/2.02 | | | DELTA: instantiating (47) with fresh symbols all_78_0, all_78_1 gives: % 9.18/2.02 | | | (57) in(all_57_0, all_18_0) = all_78_1 & in(all_57_0, all_18_3) = % 9.18/2.02 | | | all_78_0 & ( ~ (all_78_1 = 0) | all_78_0 = 0) % 9.18/2.02 | | | % 9.18/2.02 | | | ALPHA: (57) implies: % 9.18/2.02 | | | (58) in(all_57_0, all_18_0) = all_78_1 % 9.18/2.02 | | | % 9.18/2.02 | | | GROUND_INST: instantiating (5) with 0, all_76_0, all_18_2, all_57_0, % 9.18/2.02 | | | simplifying with (43), (55) gives: % 9.18/2.02 | | | (59) all_76_0 = 0 % 9.18/2.02 | | | % 9.18/2.03 | | | GROUND_INST: instantiating (5) with all_72_1, all_76_0, all_18_2, % 9.18/2.03 | | | all_57_0, simplifying with (49), (55) gives: % 9.18/2.03 | | | (60) all_76_0 = all_72_1 % 9.18/2.03 | | | % 9.18/2.03 | | | GROUND_INST: instantiating (5) with all_72_0, all_76_1, all_18_0, % 9.18/2.03 | | | all_57_0, simplifying with (50), (56) gives: % 9.18/2.03 | | | (61) all_76_1 = all_72_0 % 9.18/2.03 | | | % 9.18/2.03 | | | GROUND_INST: instantiating (5) with all_76_1, all_78_1, all_18_0, % 9.18/2.03 | | | all_57_0, simplifying with (56), (58) gives: % 9.18/2.03 | | | (62) all_78_1 = all_76_1 % 9.18/2.03 | | | % 9.18/2.03 | | | GROUND_INST: instantiating (5) with all_74_0, all_78_1, all_18_0, % 9.18/2.03 | | | all_57_0, simplifying with (53), (58) gives: % 9.18/2.03 | | | (63) all_78_1 = all_74_0 % 9.18/2.03 | | | % 9.18/2.03 | | | COMBINE_EQS: (62), (63) imply: % 9.18/2.03 | | | (64) all_76_1 = all_74_0 % 9.18/2.03 | | | % 9.18/2.03 | | | SIMP: (64) implies: % 9.18/2.03 | | | (65) all_76_1 = all_74_0 % 9.18/2.03 | | | % 9.18/2.03 | | | COMBINE_EQS: (59), (60) imply: % 9.18/2.03 | | | (66) all_72_1 = 0 % 9.18/2.03 | | | % 9.18/2.03 | | | COMBINE_EQS: (61), (65) imply: % 9.18/2.03 | | | (67) all_74_0 = all_72_0 % 9.18/2.03 | | | % 9.18/2.03 | | | SIMP: (67) implies: % 9.18/2.03 | | | (68) all_74_0 = all_72_0 % 9.18/2.03 | | | % 9.18/2.03 | | | BETA: splitting (51) gives: % 9.18/2.03 | | | % 9.18/2.03 | | | Case 1: % 9.18/2.03 | | | | % 9.18/2.03 | | | | (69) ~ (all_72_1 = 0) % 9.18/2.03 | | | | % 9.18/2.03 | | | | REDUCE: (66), (69) imply: % 9.18/2.03 | | | | (70) $false % 9.18/2.03 | | | | % 9.18/2.03 | | | | CLOSE: (70) is inconsistent. % 9.18/2.03 | | | | % 9.18/2.03 | | | Case 2: % 9.18/2.03 | | | | % 9.18/2.03 | | | | (71) all_72_0 = 0 % 9.18/2.03 | | | | % 9.18/2.03 | | | | REDUCE: (50), (71) imply: % 9.18/2.03 | | | | (72) in(all_57_0, all_18_0) = 0 % 9.18/2.03 | | | | % 9.18/2.03 | | | | GROUND_INST: instantiating (36) with all_57_0, simplifying with (41), % 9.18/2.03 | | | | (72) gives: % 9.18/2.03 | | | | (73) $false % 9.18/2.03 | | | | % 9.18/2.03 | | | | CLOSE: (73) is inconsistent. % 9.18/2.03 | | | | % 9.18/2.03 | | | End of split % 9.18/2.03 | | | % 9.18/2.03 | | End of split % 9.18/2.03 | | % 9.18/2.03 | End of split % 9.18/2.03 | % 9.18/2.03 End of proof % 9.18/2.03 % SZS output end Proof for theBenchmark % 9.18/2.03 % 9.18/2.03 1401ms %------------------------------------------------------------------------------