%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU153+1 : 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 17:42:49 EDT 2023 % Result : Theorem 6.36s 1.62s % Output : Proof 7.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU153+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n004.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % 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 12:36:38 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. % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.11/1.02 Prover 1: Preprocessing ... % 2.11/1.02 Prover 4: Preprocessing ... % 2.11/1.06 Prover 2: Preprocessing ... % 2.11/1.06 Prover 0: Preprocessing ... % 2.11/1.06 Prover 3: Preprocessing ... % 2.11/1.06 Prover 6: Preprocessing ... % 2.11/1.06 Prover 5: Preprocessing ... % 4.20/1.36 Prover 1: Warning: ignoring some quantifiers % 4.20/1.38 Prover 3: Warning: ignoring some quantifiers % 4.20/1.39 Prover 4: Warning: ignoring some quantifiers % 4.20/1.40 Prover 6: Proving ... % 4.20/1.40 Prover 3: Constructing countermodel ... % 4.20/1.40 Prover 5: Proving ... % 4.20/1.40 Prover 2: Proving ... % 4.20/1.40 Prover 4: Constructing countermodel ... % 4.20/1.41 Prover 1: Constructing countermodel ... % 4.20/1.42 Prover 0: Proving ... % 6.36/1.62 Prover 3: proved (1001ms) % 6.36/1.62 % 6.36/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.36/1.62 % 6.36/1.62 Prover 5: stopped % 6.36/1.62 Prover 6: stopped % 6.36/1.63 Prover 0: stopped % 6.36/1.63 Prover 2: stopped % 6.36/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.36/1.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.36/1.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.36/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.36/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.36/1.66 Prover 7: Preprocessing ... % 6.36/1.66 Prover 8: Preprocessing ... % 6.36/1.66 Prover 11: Preprocessing ... % 6.36/1.66 Prover 13: Preprocessing ... % 6.36/1.67 Prover 10: Preprocessing ... % 6.90/1.70 Prover 1: Found proof (size 35) % 6.90/1.70 Prover 1: proved (1085ms) % 6.90/1.70 Prover 4: stopped % 6.90/1.71 Prover 13: stopped % 6.90/1.71 Prover 11: stopped % 6.90/1.71 Prover 10: stopped % 6.90/1.72 Prover 7: Warning: ignoring some quantifiers % 6.90/1.73 Prover 7: Constructing countermodel ... % 6.90/1.73 Prover 7: stopped % 6.90/1.75 Prover 8: Warning: ignoring some quantifiers % 6.90/1.76 Prover 8: Constructing countermodel ... % 6.90/1.76 Prover 8: stopped % 6.90/1.77 % 6.90/1.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.90/1.77 % 6.90/1.77 % SZS output start Proof for theBenchmark % 7.48/1.78 Assumptions after simplification: % 7.48/1.78 --------------------------------- % 7.48/1.78 % 7.48/1.78 (commutativity_k3_xboole_0) % 7.56/1.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 7.56/1.80 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 7.56/1.80 % 7.56/1.80 (d1_tarski) % 7.56/1.81 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | % 7.56/1.81 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & % 7.56/1.81 $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0: $i] % 7.56/1.81 : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: % 7.56/1.81 $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 = % 7.56/1.81 0 | ~ (in(v0, v1) = v2)))) % 7.56/1.81 % 7.56/1.81 (d1_xboole_0) % 7.56/1.81 $i(empty_set) & ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0)) & ? % 7.56/1.81 [v0: $i] : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : (in(v1, v0) = 0 & % 7.56/1.81 $i(v1))) % 7.56/1.81 % 7.56/1.81 (d3_xboole_0) % 7.56/1.81 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 7.56/1.81 (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 7.56/1.81 [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 & % 7.56/1.81 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) | % 7.56/1.81 ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] % 7.56/1.81 : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 7.56/1.81 ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) % 7.56/1.81 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ % 7.56/1.81 (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) % 7.56/1.81 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, % 7.56/1.81 v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 7.56/1.81 % 7.56/1.81 (d7_xboole_0) % 7.67/1.82 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 7.67/1.82 (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = % 7.67/1.82 empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : % 7.67/1.82 ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 7.67/1.82 set_intersection2(v0, v1) = empty_set) % 7.67/1.82 % 7.67/1.82 (l25_zfmisc_1) % 7.67/1.82 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (disjoint(v2, v1) = 0 & % 7.67/1.82 singleton(v0) = v2 & in(v0, v1) = 0 & $i(v2) & $i(v1) & $i(v0)) % 7.67/1.82 % 7.67/1.82 (symmetry_r1_xboole_0) % 7.67/1.82 ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) % 7.69/1.82 | disjoint(v1, v0) = 0) % 7.69/1.82 % 7.69/1.82 (function-axioms) % 7.69/1.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.69/1.82 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 7.69/1.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.69/1.82 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 7.69/1.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 7.69/1.82 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 7.69/1.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.69/1.82 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 7.69/1.82 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 7.69/1.82 % 7.69/1.82 Further assumptions not needed in the proof: % 7.69/1.82 -------------------------------------------- % 7.69/1.82 antisymmetry_r2_hidden, dt_k1_tarski, dt_k1_xboole_0, dt_k3_xboole_0, % 7.69/1.82 fc1_xboole_0, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0 % 7.69/1.82 % 7.69/1.82 Those formulas are unsatisfiable: % 7.69/1.82 --------------------------------- % 7.69/1.82 % 7.69/1.82 Begin of proof % 7.69/1.82 | % 7.69/1.82 | ALPHA: (d1_tarski) implies: % 7.69/1.82 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 7.69/1.82 | $i(v0) | ( ! [v2: $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & % 7.69/1.82 | ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2)))) % 7.69/1.82 | % 7.69/1.82 | ALPHA: (d1_xboole_0) implies: % 7.69/1.83 | (2) ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0)) % 7.69/1.83 | % 7.69/1.83 | ALPHA: (d3_xboole_0) implies: % 7.69/1.83 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, % 7.69/1.83 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! % 7.69/1.83 | [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? % 7.69/1.83 | [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | % 7.69/1.83 | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) | % 7.69/1.83 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & % 7.69/1.83 | in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 7.69/1.83 | % 7.69/1.83 | ALPHA: (d7_xboole_0) implies: % 7.69/1.83 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ % 7.69/1.83 | $i(v0) | set_intersection2(v0, v1) = empty_set) % 7.69/1.83 | % 7.69/1.83 | ALPHA: (function-axioms) implies: % 7.69/1.83 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.69/1.83 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 7.69/1.83 | % 7.69/1.83 | DELTA: instantiating (l25_zfmisc_1) with fresh symbols all_18_0, all_18_1, % 7.69/1.83 | all_18_2 gives: % 7.69/1.83 | (6) disjoint(all_18_0, all_18_1) = 0 & singleton(all_18_2) = all_18_0 & % 7.69/1.83 | in(all_18_2, all_18_1) = 0 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) % 7.69/1.83 | % 7.69/1.83 | ALPHA: (6) implies: % 7.69/1.83 | (7) $i(all_18_2) % 7.69/1.83 | (8) $i(all_18_1) % 7.69/1.83 | (9) $i(all_18_0) % 7.69/1.83 | (10) in(all_18_2, all_18_1) = 0 % 7.69/1.83 | (11) singleton(all_18_2) = all_18_0 % 7.69/1.83 | (12) disjoint(all_18_0, all_18_1) = 0 % 7.69/1.83 | % 7.69/1.83 | GROUND_INST: instantiating (1) with all_18_2, all_18_0, simplifying with (7), % 7.69/1.83 | (9), (11) gives: % 7.69/1.83 | (13) ! [v0: any] : (v0 = all_18_2 | ~ (in(v0, all_18_0) = 0) | ~ $i(v0)) % 7.69/1.83 | & ! [v0: int] : (v0 = 0 | ~ (in(all_18_2, all_18_0) = v0)) % 7.69/1.83 | % 7.69/1.83 | ALPHA: (13) implies: % 7.69/1.84 | (14) ! [v0: int] : (v0 = 0 | ~ (in(all_18_2, all_18_0) = v0)) % 7.69/1.84 | % 7.69/1.84 | GROUND_INST: instantiating (symmetry_r1_xboole_0) with all_18_0, all_18_1, % 7.69/1.84 | simplifying with (8), (9), (12) gives: % 7.69/1.84 | (15) disjoint(all_18_1, all_18_0) = 0 % 7.69/1.84 | % 7.69/1.84 | GROUND_INST: instantiating (4) with all_18_0, all_18_1, simplifying with (8), % 7.69/1.84 | (9), (12) gives: % 7.69/1.84 | (16) set_intersection2(all_18_0, all_18_1) = empty_set % 7.69/1.84 | % 7.69/1.84 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_18_0, % 7.69/1.84 | all_18_1, empty_set, simplifying with (8), (9), (16) gives: % 7.69/1.84 | (17) set_intersection2(all_18_1, all_18_0) = empty_set & $i(empty_set) % 7.69/1.84 | % 7.69/1.84 | ALPHA: (17) implies: % 7.69/1.84 | (18) $i(empty_set) % 7.69/1.84 | % 7.69/1.84 | GROUND_INST: instantiating (4) with all_18_1, all_18_0, simplifying with (8), % 7.69/1.84 | (9), (15) gives: % 7.69/1.84 | (19) set_intersection2(all_18_1, all_18_0) = empty_set % 7.69/1.84 | % 7.69/1.84 | GROUND_INST: instantiating (3) with all_18_1, all_18_0, empty_set, simplifying % 7.69/1.84 | with (8), (9), (18), (19) gives: % 7.69/1.84 | (20) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_1) = v1) | ~ $i(v0) | % 7.69/1.84 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v3 & in(v0, % 7.69/1.84 | empty_set) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0: % 7.69/1.84 | $i] : ( ~ (in(v0, all_18_1) = 0) | ~ $i(v0) | ? [v1: any] : ? % 7.69/1.84 | [v2: any] : (in(v0, all_18_0) = v1 & in(v0, empty_set) = v2 & ( ~ % 7.69/1.84 | (v1 = 0) | v2 = 0))) % 7.69/1.84 | % 7.69/1.84 | ALPHA: (20) implies: % 7.69/1.84 | (21) ! [v0: $i] : ( ~ (in(v0, all_18_1) = 0) | ~ $i(v0) | ? [v1: any] : % 7.69/1.84 | ? [v2: any] : (in(v0, all_18_0) = v1 & in(v0, empty_set) = v2 & ( ~ % 7.69/1.84 | (v1 = 0) | v2 = 0))) % 7.69/1.84 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_1) = v1) | ~ $i(v0) | % 7.69/1.84 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v3 & in(v0, % 7.69/1.84 | empty_set) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) % 7.69/1.84 | % 7.69/1.84 | GROUND_INST: instantiating (21) with all_18_2, simplifying with (7), (10) % 7.69/1.84 | gives: % 7.69/1.84 | (23) ? [v0: any] : ? [v1: any] : (in(all_18_2, all_18_0) = v0 & % 7.69/1.84 | in(all_18_2, empty_set) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 7.69/1.84 | % 7.69/1.84 | GROUND_INST: instantiating (22) with all_18_2, 0, simplifying with (7), (10) % 7.69/1.84 | gives: % 7.69/1.84 | (24) ? [v0: any] : ? [v1: any] : (in(all_18_2, all_18_0) = v1 & % 7.69/1.84 | in(all_18_2, empty_set) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 7.69/1.84 | % 7.69/1.84 | DELTA: instantiating (24) with fresh symbols all_46_0, all_46_1 gives: % 7.69/1.84 | (25) in(all_18_2, all_18_0) = all_46_0 & in(all_18_2, empty_set) = all_46_1 % 7.69/1.84 | & ( ~ (all_46_1 = 0) | all_46_0 = 0) % 7.69/1.84 | % 7.69/1.84 | ALPHA: (25) implies: % 7.69/1.84 | (26) in(all_18_2, empty_set) = all_46_1 % 7.69/1.85 | (27) in(all_18_2, all_18_0) = all_46_0 % 7.69/1.85 | % 7.69/1.85 | DELTA: instantiating (23) with fresh symbols all_48_0, all_48_1 gives: % 7.69/1.85 | (28) in(all_18_2, all_18_0) = all_48_1 & in(all_18_2, empty_set) = all_48_0 % 7.69/1.85 | & ( ~ (all_48_1 = 0) | all_48_0 = 0) % 7.69/1.85 | % 7.69/1.85 | ALPHA: (28) implies: % 7.69/1.85 | (29) in(all_18_2, empty_set) = all_48_0 % 7.69/1.85 | (30) in(all_18_2, all_18_0) = all_48_1 % 7.69/1.85 | (31) ~ (all_48_1 = 0) | all_48_0 = 0 % 7.69/1.85 | % 7.69/1.85 | GROUND_INST: instantiating (5) with all_46_1, all_48_0, empty_set, all_18_2, % 7.69/1.85 | simplifying with (26), (29) gives: % 7.69/1.85 | (32) all_48_0 = all_46_1 % 7.69/1.85 | % 7.69/1.85 | GROUND_INST: instantiating (5) with all_46_0, all_48_1, all_18_0, all_18_2, % 7.69/1.85 | simplifying with (27), (30) gives: % 7.69/1.85 | (33) all_48_1 = all_46_0 % 7.69/1.85 | % 7.69/1.85 | GROUND_INST: instantiating (14) with all_48_1, simplifying with (30) gives: % 7.69/1.85 | (34) all_48_1 = 0 % 7.69/1.85 | % 7.69/1.85 | COMBINE_EQS: (33), (34) imply: % 7.69/1.85 | (35) all_46_0 = 0 % 7.69/1.85 | % 7.69/1.85 | BETA: splitting (31) gives: % 7.69/1.85 | % 7.69/1.85 | Case 1: % 7.69/1.85 | | % 7.69/1.85 | | (36) ~ (all_48_1 = 0) % 7.69/1.85 | | % 7.69/1.85 | | REDUCE: (34), (36) imply: % 7.69/1.85 | | (37) $false % 7.69/1.85 | | % 7.69/1.85 | | CLOSE: (37) is inconsistent. % 7.69/1.85 | | % 7.69/1.85 | Case 2: % 7.69/1.85 | | % 7.69/1.85 | | (38) all_48_0 = 0 % 7.69/1.85 | | % 7.69/1.85 | | COMBINE_EQS: (32), (38) imply: % 7.69/1.85 | | (39) all_46_1 = 0 % 7.69/1.85 | | % 7.69/1.85 | | REDUCE: (26), (39) imply: % 7.69/1.85 | | (40) in(all_18_2, empty_set) = 0 % 7.69/1.85 | | % 7.69/1.85 | | GROUND_INST: instantiating (2) with all_18_2, simplifying with (7), (40) % 7.69/1.85 | | gives: % 7.69/1.85 | | (41) $false % 7.69/1.85 | | % 7.69/1.85 | | CLOSE: (41) is inconsistent. % 7.69/1.85 | | % 7.69/1.85 | End of split % 7.69/1.85 | % 7.69/1.85 End of proof % 7.69/1.85 % SZS output end Proof for theBenchmark % 7.69/1.85 % 7.69/1.85 1254ms %------------------------------------------------------------------------------