%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU193+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 : n022.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 17:43:10 EDT 2023 % Result : Theorem 9.12s 1.99s % Output : Proof 11.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU193+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n022.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 20:45:26 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.48/1.06 Prover 1: Preprocessing ... % 2.48/1.07 Prover 4: Preprocessing ... % 2.48/1.11 Prover 6: Preprocessing ... % 2.48/1.11 Prover 5: Preprocessing ... % 2.48/1.11 Prover 0: Preprocessing ... % 2.48/1.11 Prover 3: Preprocessing ... % 2.48/1.12 Prover 2: Preprocessing ... % 6.01/1.58 Prover 4: Warning: ignoring some quantifiers % 6.01/1.59 Prover 1: Warning: ignoring some quantifiers % 6.01/1.60 Prover 2: Proving ... % 6.01/1.60 Prover 5: Proving ... % 6.01/1.60 Prover 6: Proving ... % 6.01/1.60 Prover 3: Warning: ignoring some quantifiers % 6.52/1.61 Prover 1: Constructing countermodel ... % 6.52/1.62 Prover 0: Proving ... % 6.52/1.62 Prover 3: Constructing countermodel ... % 6.52/1.63 Prover 4: Constructing countermodel ... % 9.12/1.99 Prover 3: proved (1366ms) % 9.12/1.99 % 9.12/1.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.12/1.99 % 9.12/1.99 Prover 0: stopped % 9.12/1.99 Prover 6: stopped % 9.12/1.99 Prover 5: stopped % 9.12/2.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.12/2.00 Prover 2: stopped % 9.12/2.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.12/2.00 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.12/2.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.12/2.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.12/2.03 Prover 13: Preprocessing ... % 9.12/2.05 Prover 10: Preprocessing ... % 9.78/2.07 Prover 11: Preprocessing ... % 9.78/2.07 Prover 7: Preprocessing ... % 9.78/2.08 Prover 8: Preprocessing ... % 9.78/2.12 Prover 1: Found proof (size 39) % 9.78/2.12 Prover 1: proved (1505ms) % 9.78/2.13 Prover 11: stopped % 9.78/2.13 Prover 4: stopped % 9.78/2.14 Prover 10: Warning: ignoring some quantifiers % 9.78/2.15 Prover 10: Constructing countermodel ... % 9.78/2.15 Prover 10: stopped % 9.78/2.16 Prover 13: Warning: ignoring some quantifiers % 9.78/2.16 Prover 7: Warning: ignoring some quantifiers % 9.78/2.17 Prover 7: Constructing countermodel ... % 9.78/2.17 Prover 7: stopped % 9.78/2.18 Prover 13: Constructing countermodel ... % 9.78/2.18 Prover 13: stopped % 9.78/2.21 Prover 8: Warning: ignoring some quantifiers % 9.78/2.21 Prover 8: Constructing countermodel ... % 9.78/2.22 Prover 8: stopped % 9.78/2.22 % 9.78/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.78/2.22 % 10.10/2.23 % SZS output start Proof for theBenchmark % 10.10/2.23 Assumptions after simplification: % 10.10/2.23 --------------------------------- % 10.10/2.23 % 10.10/2.23 (d11_relat_1) % 10.10/2.26 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : % 10.10/2.26 ! [v3: $i] : ( ~ (relation_dom_restriction(v0, v1) = v3) | ~ (relation(v2) % 10.10/2.26 = 0) | ~ $i(v2) | ~ $i(v1) | (( ~ (v3 = v2) | ( ! [v4: $i] : ! [v5: % 10.10/2.26 $i] : ! [v6: $i] : ! [v7: any] : ( ~ (ordered_pair(v4, v5) = v6) % 10.10/2.26 | ~ (in(v6, v0) = v7) | ~ $i(v5) | ~ $i(v4) | ? [v8: any] : ? % 10.10/2.26 [v9: any] : (in(v6, v2) = v8 & in(v4, v1) = v9 & ( ~ (v8 = 0) | % 10.10/2.26 (v9 = 0 & v7 = 0)))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 10.10/2.26 : ( ~ (ordered_pair(v4, v5) = v6) | ~ (in(v6, v0) = 0) | ~ $i(v5) % 10.10/2.27 | ~ $i(v4) | ? [v7: any] : ? [v8: any] : (in(v6, v2) = v8 & % 10.10/2.27 in(v4, v1) = v7 & ( ~ (v7 = 0) | v8 = 0))))) & (v3 = v2 | ? % 10.10/2.27 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : % 10.10/2.27 ? [v9: any] : (ordered_pair(v4, v5) = v6 & in(v6, v2) = v7 & in(v6, % 10.10/2.27 v0) = v9 & in(v4, v1) = v8 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v9 = % 10.10/2.27 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v9 = 0 & v8 = % 10.10/2.27 0))))))) % 10.10/2.27 % 10.10/2.27 (d3_relat_1) % 11.01/2.27 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] % 11.01/2.27 : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 11.01/2.27 relation(v1) = v3) | (( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : ! [v5: % 11.01/2.27 $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = 0) | ~ % 11.01/2.27 $i(v4) | ~ $i(v3) | in(v5, v1) = 0)) & (v2 = 0 | ? [v3: $i] : ? % 11.01/2.27 [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 11.01/2.27 ordered_pair(v3, v4) = v5 & in(v5, v1) = v6 & in(v5, v0) = 0 & % 11.01/2.27 $i(v5) & $i(v4) & $i(v3)))))) % 11.01/2.27 % 11.01/2.27 (dt_k7_relat_1) % 11.01/2.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 11.01/2.27 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 11.01/2.27 (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 11.01/2.27 % 11.01/2.27 (t88_relat_1) % 11.01/2.27 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 11.01/2.27 subset(v2, v1) = v3 & relation_dom_restriction(v1, v0) = v2 & relation(v1) = % 11.01/2.27 0 & $i(v2) & $i(v1) & $i(v0)) % 11.01/2.27 % 11.01/2.27 (function-axioms) % 11.06/2.28 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.06/2.28 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 11.06/2.28 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.06/2.28 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 11.06/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.06/2.28 (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, % 11.06/2.28 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 11.06/2.28 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! % 11.06/2.28 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.06/2.28 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 11.06/2.28 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.06/2.28 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 11.06/2.28 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 11.06/2.28 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 11.06/2.28 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: MultipleValueBool] % 11.06/2.28 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) % 11.06/2.28 | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.06/2.28 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 11.06/2.28 (empty(v2) = v0)) % 11.06/2.28 % 11.06/2.28 Further assumptions not needed in the proof: % 11.06/2.28 -------------------------------------------- % 11.06/2.28 antisymmetry_r2_hidden, cc1_relat_1, commutativity_k2_tarski, d5_tarski, % 11.06/2.28 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k4_tarski, % 11.06/2.28 dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, % 11.06/2.28 fc2_subset_1, fc3_subset_1, fc4_relat_1, rc1_relat_1, rc1_subset_1, % 11.06/2.28 rc1_xboole_0, rc2_relat_1, rc2_subset_1, rc2_xboole_0, reflexivity_r1_tarski, % 11.06/2.28 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, % 11.06/2.28 t8_boole % 11.06/2.28 % 11.06/2.28 Those formulas are unsatisfiable: % 11.06/2.28 --------------------------------- % 11.06/2.28 % 11.06/2.28 Begin of proof % 11.06/2.28 | % 11.06/2.28 | ALPHA: (function-axioms) implies: % 11.06/2.28 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.06/2.28 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 11.06/2.28 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.06/2.28 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 11.06/2.28 | % 11.06/2.28 | DELTA: instantiating (t88_relat_1) with fresh symbols all_36_0, all_36_1, % 11.06/2.28 | all_36_2, all_36_3 gives: % 11.06/2.28 | (3) ~ (all_36_0 = 0) & subset(all_36_1, all_36_2) = all_36_0 & % 11.06/2.28 | relation_dom_restriction(all_36_2, all_36_3) = all_36_1 & % 11.06/2.28 | relation(all_36_2) = 0 & $i(all_36_1) & $i(all_36_2) & $i(all_36_3) % 11.06/2.28 | % 11.06/2.28 | ALPHA: (3) implies: % 11.06/2.28 | (4) ~ (all_36_0 = 0) % 11.06/2.28 | (5) $i(all_36_3) % 11.06/2.29 | (6) $i(all_36_2) % 11.06/2.29 | (7) $i(all_36_1) % 11.06/2.29 | (8) relation(all_36_2) = 0 % 11.06/2.29 | (9) relation_dom_restriction(all_36_2, all_36_3) = all_36_1 % 11.06/2.29 | (10) subset(all_36_1, all_36_2) = all_36_0 % 11.06/2.29 | % 11.06/2.29 | GROUND_INST: instantiating (d11_relat_1) with all_36_2, simplifying with (6), % 11.06/2.29 | (8) gives: % 11.06/2.29 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.06/2.29 | (relation_dom_restriction(all_36_2, v0) = v2) | ~ (relation(v1) = % 11.06/2.29 | 0) | ~ $i(v1) | ~ $i(v0) | (( ~ (v2 = v1) | ( ! [v3: $i] : ! % 11.06/2.29 | [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ (ordered_pair(v3, % 11.06/2.29 | v4) = v5) | ~ (in(v5, all_36_2) = v6) | ~ $i(v4) | ~ % 11.06/2.29 | $i(v3) | ? [v7: any] : ? [v8: any] : (in(v5, v1) = v7 & % 11.06/2.29 | in(v3, v0) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) & ! % 11.06/2.29 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v3, % 11.06/2.29 | v4) = v5) | ~ (in(v5, all_36_2) = 0) | ~ $i(v4) | ~ % 11.06/2.29 | $i(v3) | ? [v6: any] : ? [v7: any] : (in(v5, v1) = v7 & % 11.06/2.29 | in(v3, v0) = v6 & ( ~ (v6 = 0) | v7 = 0))))) & (v2 = v1 | % 11.06/2.29 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: % 11.06/2.29 | any] : ? [v8: any] : (ordered_pair(v3, v4) = v5 & in(v5, v1) % 11.06/2.29 | = v6 & in(v5, all_36_2) = v8 & in(v3, v0) = v7 & $i(v5) & % 11.06/2.29 | $i(v4) & $i(v3) & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & % 11.06/2.29 | (v6 = 0 | (v8 = 0 & v7 = 0)))))) % 11.06/2.29 | % 11.06/2.29 | GROUND_INST: instantiating (dt_k7_relat_1) with all_36_2, all_36_3, all_36_1, % 11.06/2.29 | simplifying with (5), (6), (9) gives: % 11.06/2.29 | (12) ? [v0: any] : ? [v1: any] : (relation(all_36_1) = v1 & % 11.06/2.29 | relation(all_36_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 11.06/2.29 | % 11.06/2.29 | DELTA: instantiating (12) with fresh symbols all_52_0, all_52_1 gives: % 11.06/2.29 | (13) relation(all_36_1) = all_52_0 & relation(all_36_2) = all_52_1 & ( ~ % 11.06/2.29 | (all_52_1 = 0) | all_52_0 = 0) % 11.06/2.29 | % 11.06/2.29 | ALPHA: (13) implies: % 11.06/2.29 | (14) relation(all_36_2) = all_52_1 % 11.06/2.29 | (15) relation(all_36_1) = all_52_0 % 11.06/2.29 | (16) ~ (all_52_1 = 0) | all_52_0 = 0 % 11.06/2.29 | % 11.06/2.29 | GROUND_INST: instantiating (1) with 0, all_52_1, all_36_2, simplifying with % 11.06/2.29 | (8), (14) gives: % 11.06/2.29 | (17) all_52_1 = 0 % 11.06/2.29 | % 11.06/2.29 | BETA: splitting (16) gives: % 11.06/2.29 | % 11.06/2.29 | Case 1: % 11.06/2.29 | | % 11.06/2.29 | | (18) ~ (all_52_1 = 0) % 11.06/2.29 | | % 11.06/2.29 | | REDUCE: (17), (18) imply: % 11.06/2.29 | | (19) $false % 11.06/2.29 | | % 11.06/2.30 | | CLOSE: (19) is inconsistent. % 11.06/2.30 | | % 11.06/2.30 | Case 2: % 11.06/2.30 | | % 11.06/2.30 | | (20) all_52_0 = 0 % 11.06/2.30 | | % 11.06/2.30 | | REDUCE: (15), (20) imply: % 11.06/2.30 | | (21) relation(all_36_1) = 0 % 11.06/2.30 | | % 11.06/2.30 | | GROUND_INST: instantiating (11) with all_36_3, all_36_1, all_36_1, % 11.06/2.30 | | simplifying with (5), (7), (9), (21) gives: % 11.06/2.30 | | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 11.06/2.30 | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_2) = v3) | ~ % 11.06/2.30 | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v2, % 11.06/2.30 | | all_36_1) = v4 & in(v0, all_36_3) = v5 & ( ~ (v4 = 0) | (v5 = % 11.06/2.30 | | 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 11.06/2.30 | | ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_2) = 0) | ~ % 11.06/2.30 | | $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (in(v2, % 11.06/2.30 | | all_36_1) = v4 & in(v0, all_36_3) = v3 & ( ~ (v3 = 0) | v4 = % 11.06/2.30 | | 0))) % 11.06/2.30 | | % 11.06/2.30 | | ALPHA: (22) implies: % 11.06/2.30 | | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 11.06/2.30 | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_2) = v3) | ~ % 11.06/2.30 | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v2, % 11.06/2.30 | | all_36_1) = v4 & in(v0, all_36_3) = v5 & ( ~ (v4 = 0) | (v5 = % 11.06/2.30 | | 0 & v3 = 0)))) % 11.06/2.30 | | % 11.06/2.30 | | GROUND_INST: instantiating (d3_relat_1) with all_36_1, simplifying with (7), % 11.06/2.30 | | (21) gives: % 11.06/2.30 | | (24) ! [v0: $i] : ! [v1: any] : ( ~ (subset(all_36_1, v0) = v1) | ~ % 11.06/2.30 | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & relation(v0) = v2) | (( ~ % 11.06/2.30 | | (v1 = 0) | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 11.06/2.30 | | (ordered_pair(v2, v3) = v4) | ~ (in(v4, all_36_1) = 0) | ~ % 11.06/2.30 | | $i(v3) | ~ $i(v2) | in(v4, v0) = 0)) & (v1 = 0 | ? [v2: % 11.06/2.30 | | $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = % 11.06/2.30 | | 0) & ordered_pair(v2, v3) = v4 & in(v4, v0) = v5 & in(v4, % 11.06/2.30 | | all_36_1) = 0 & $i(v4) & $i(v3) & $i(v2))))) % 11.06/2.30 | | % 11.06/2.30 | | GROUND_INST: instantiating (24) with all_36_2, all_36_0, simplifying with % 11.06/2.30 | | (6), (10) gives: % 11.06/2.30 | | (25) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_2) = v0) | (( ~ % 11.06/2.30 | | (all_36_0 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.06/2.30 | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_1) = 0) | ~ % 11.06/2.30 | | $i(v1) | ~ $i(v0) | in(v2, all_36_2) = 0)) & (all_36_0 = 0 | % 11.06/2.30 | | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 % 11.06/2.30 | | = 0) & ordered_pair(v0, v1) = v2 & in(v2, all_36_1) = 0 & % 11.06/2.30 | | in(v2, all_36_2) = v3 & $i(v2) & $i(v1) & $i(v0)))) % 11.06/2.30 | | % 11.06/2.30 | | BETA: splitting (25) gives: % 11.06/2.30 | | % 11.06/2.30 | | Case 1: % 11.06/2.30 | | | % 11.06/2.30 | | | (26) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_2) = v0) % 11.06/2.30 | | | % 11.06/2.30 | | | DELTA: instantiating (26) with fresh symbol all_72_0 gives: % 11.06/2.30 | | | (27) ~ (all_72_0 = 0) & relation(all_36_2) = all_72_0 % 11.06/2.31 | | | % 11.06/2.31 | | | ALPHA: (27) implies: % 11.06/2.31 | | | (28) ~ (all_72_0 = 0) % 11.06/2.31 | | | (29) relation(all_36_2) = all_72_0 % 11.06/2.31 | | | % 11.06/2.31 | | | GROUND_INST: instantiating (1) with 0, all_72_0, all_36_2, simplifying % 11.06/2.31 | | | with (8), (29) gives: % 11.06/2.31 | | | (30) all_72_0 = 0 % 11.06/2.31 | | | % 11.06/2.31 | | | REDUCE: (28), (30) imply: % 11.06/2.31 | | | (31) $false % 11.06/2.31 | | | % 11.06/2.31 | | | CLOSE: (31) is inconsistent. % 11.06/2.31 | | | % 11.06/2.31 | | Case 2: % 11.06/2.31 | | | % 11.21/2.31 | | | (32) ( ~ (all_36_0 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.21/2.31 | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_1) = 0) | ~ % 11.21/2.31 | | | $i(v1) | ~ $i(v0) | in(v2, all_36_2) = 0)) & (all_36_0 = 0 | % 11.21/2.31 | | | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 % 11.21/2.31 | | | = 0) & ordered_pair(v0, v1) = v2 & in(v2, all_36_1) = 0 & % 11.21/2.31 | | | in(v2, all_36_2) = v3 & $i(v2) & $i(v1) & $i(v0))) % 11.21/2.31 | | | % 11.21/2.31 | | | ALPHA: (32) implies: % 11.21/2.31 | | | (33) all_36_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 11.21/2.31 | | | int] : ( ~ (v3 = 0) & ordered_pair(v0, v1) = v2 & in(v2, % 11.21/2.31 | | | all_36_1) = 0 & in(v2, all_36_2) = v3 & $i(v2) & $i(v1) & % 11.21/2.31 | | | $i(v0)) % 11.21/2.31 | | | % 11.21/2.31 | | | BETA: splitting (33) gives: % 11.21/2.31 | | | % 11.21/2.31 | | | Case 1: % 11.21/2.31 | | | | % 11.21/2.31 | | | | (34) all_36_0 = 0 % 11.21/2.31 | | | | % 11.21/2.31 | | | | REDUCE: (4), (34) imply: % 11.21/2.31 | | | | (35) $false % 11.21/2.31 | | | | % 11.21/2.31 | | | | CLOSE: (35) is inconsistent. % 11.21/2.31 | | | | % 11.21/2.31 | | | Case 2: % 11.21/2.31 | | | | % 11.21/2.31 | | | | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 % 11.21/2.31 | | | | = 0) & ordered_pair(v0, v1) = v2 & in(v2, all_36_1) = 0 & % 11.21/2.31 | | | | in(v2, all_36_2) = v3 & $i(v2) & $i(v1) & $i(v0)) % 11.21/2.31 | | | | % 11.21/2.31 | | | | DELTA: instantiating (36) with fresh symbols all_75_0, all_75_1, % 11.21/2.31 | | | | all_75_2, all_75_3 gives: % 11.21/2.31 | | | | (37) ~ (all_75_0 = 0) & ordered_pair(all_75_3, all_75_2) = all_75_1 % 11.21/2.31 | | | | & in(all_75_1, all_36_1) = 0 & in(all_75_1, all_36_2) = all_75_0 % 11.21/2.31 | | | | & $i(all_75_1) & $i(all_75_2) & $i(all_75_3) % 11.21/2.31 | | | | % 11.21/2.31 | | | | ALPHA: (37) implies: % 11.21/2.31 | | | | (38) ~ (all_75_0 = 0) % 11.21/2.31 | | | | (39) $i(all_75_3) % 11.21/2.31 | | | | (40) $i(all_75_2) % 11.21/2.31 | | | | (41) in(all_75_1, all_36_2) = all_75_0 % 11.21/2.31 | | | | (42) in(all_75_1, all_36_1) = 0 % 11.21/2.31 | | | | (43) ordered_pair(all_75_3, all_75_2) = all_75_1 % 11.21/2.31 | | | | % 11.21/2.31 | | | | GROUND_INST: instantiating (23) with all_75_3, all_75_2, all_75_1, % 11.21/2.31 | | | | all_75_0, simplifying with (39), (40), (41), (43) gives: % 11.21/2.31 | | | | (44) ? [v0: any] : ? [v1: any] : (in(all_75_1, all_36_1) = v0 & % 11.21/2.31 | | | | in(all_75_3, all_36_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 11.21/2.31 | | | | all_75_0 = 0))) % 11.21/2.31 | | | | % 11.21/2.31 | | | | DELTA: instantiating (44) with fresh symbols all_88_0, all_88_1 gives: % 11.21/2.31 | | | | (45) in(all_75_1, all_36_1) = all_88_1 & in(all_75_3, all_36_3) = % 11.21/2.31 | | | | all_88_0 & ( ~ (all_88_1 = 0) | (all_88_0 = 0 & all_75_0 = 0)) % 11.21/2.31 | | | | % 11.21/2.31 | | | | ALPHA: (45) implies: % 11.21/2.31 | | | | (46) in(all_75_1, all_36_1) = all_88_1 % 11.21/2.31 | | | | (47) ~ (all_88_1 = 0) | (all_88_0 = 0 & all_75_0 = 0) % 11.21/2.31 | | | | % 11.21/2.31 | | | | BETA: splitting (47) gives: % 11.21/2.31 | | | | % 11.21/2.31 | | | | Case 1: % 11.21/2.31 | | | | | % 11.21/2.32 | | | | | (48) ~ (all_88_1 = 0) % 11.21/2.32 | | | | | % 11.21/2.32 | | | | | GROUND_INST: instantiating (2) with 0, all_88_1, all_36_1, all_75_1, % 11.21/2.32 | | | | | simplifying with (42), (46) gives: % 11.21/2.32 | | | | | (49) all_88_1 = 0 % 11.21/2.32 | | | | | % 11.21/2.32 | | | | | REDUCE: (48), (49) imply: % 11.21/2.32 | | | | | (50) $false % 11.21/2.32 | | | | | % 11.21/2.32 | | | | | CLOSE: (50) is inconsistent. % 11.21/2.32 | | | | | % 11.21/2.32 | | | | Case 2: % 11.21/2.32 | | | | | % 11.21/2.32 | | | | | (51) all_88_0 = 0 & all_75_0 = 0 % 11.21/2.32 | | | | | % 11.21/2.32 | | | | | ALPHA: (51) implies: % 11.21/2.32 | | | | | (52) all_75_0 = 0 % 11.21/2.32 | | | | | % 11.21/2.32 | | | | | REDUCE: (38), (52) imply: % 11.21/2.32 | | | | | (53) $false % 11.21/2.32 | | | | | % 11.21/2.32 | | | | | CLOSE: (53) is inconsistent. % 11.21/2.32 | | | | | % 11.21/2.32 | | | | End of split % 11.21/2.32 | | | | % 11.21/2.32 | | | End of split % 11.21/2.32 | | | % 11.21/2.32 | | End of split % 11.21/2.32 | | % 11.21/2.32 | End of split % 11.21/2.32 | % 11.21/2.32 End of proof % 11.21/2.32 % SZS output end Proof for theBenchmark % 11.21/2.32 % 11.21/2.32 1716ms %------------------------------------------------------------------------------