%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU209+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 : n019.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 17:43:17 EDT 2023 % Result : Theorem 8.98s 1.97s % Output : Proof 11.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU209+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 : n019.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 18:06:43 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.57 ________ _____ % 0.21/0.57 ___ __ \_________(_)________________________________ % 0.21/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.57 % 0.21/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.57 (2023-06-19) % 0.21/0.57 % 0.21/0.57 (c) Philipp Rümmer, 2009-2023 % 0.21/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.57 Amanda Stjerna. % 0.21/0.57 Free software under BSD-3-Clause. % 0.21/0.57 % 0.21/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.57 % 0.21/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.58 Running up to 7 provers in parallel. % 0.21/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.51/1.06 Prover 4: Preprocessing ... % 2.51/1.06 Prover 1: Preprocessing ... % 2.95/1.10 Prover 2: Preprocessing ... % 2.95/1.10 Prover 3: Preprocessing ... % 2.95/1.10 Prover 6: Preprocessing ... % 2.95/1.10 Prover 5: Preprocessing ... % 2.95/1.11 Prover 0: Preprocessing ... % 5.89/1.55 Prover 1: Warning: ignoring some quantifiers % 5.89/1.56 Prover 5: Proving ... % 5.89/1.58 Prover 1: Constructing countermodel ... % 6.60/1.59 Prover 6: Proving ... % 6.64/1.60 Prover 3: Warning: ignoring some quantifiers % 6.73/1.62 Prover 3: Constructing countermodel ... % 6.73/1.63 Prover 2: Proving ... % 6.73/1.63 Prover 4: Warning: ignoring some quantifiers % 6.73/1.67 Prover 4: Constructing countermodel ... % 7.42/1.71 Prover 0: Proving ... % 8.98/1.96 Prover 3: proved (1362ms) % 8.98/1.97 % 8.98/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.98/1.97 % 8.98/1.99 Prover 2: stopped % 8.98/1.99 Prover 6: stopped % 8.98/1.99 Prover 0: stopped % 8.98/1.99 Prover 5: stopped % 8.98/1.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.98/1.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.98/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.98/1.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.98/2.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.38/2.04 Prover 7: Preprocessing ... % 9.38/2.06 Prover 8: Preprocessing ... % 9.38/2.06 Prover 10: Preprocessing ... % 9.38/2.07 Prover 13: Preprocessing ... % 9.38/2.08 Prover 11: Preprocessing ... % 9.38/2.11 Prover 1: Found proof (size 40) % 9.38/2.11 Prover 1: proved (1515ms) % 9.38/2.11 Prover 4: stopped % 9.38/2.11 Prover 7: stopped % 9.38/2.12 Prover 10: stopped % 10.51/2.16 Prover 11: stopped % 10.51/2.16 Prover 13: stopped % 10.51/2.19 Prover 8: Warning: ignoring some quantifiers % 10.51/2.20 Prover 8: Constructing countermodel ... % 10.51/2.20 Prover 8: stopped % 10.51/2.20 % 10.51/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.51/2.20 % 10.51/2.21 % SZS output start Proof for theBenchmark % 10.99/2.21 Assumptions after simplification: % 10.99/2.21 --------------------------------- % 10.99/2.21 % 10.99/2.21 (d14_relat_1) % 10.99/2.24 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ( ? [v1: $i] : ! [v2: $i] % 10.99/2.24 : ! [v3: $i] : (v3 = v1 | ~ (relation_inverse_image(v0, v2) = v3) | ~ % 10.99/2.24 $i(v2) | ~ $i(v1) | ? [v4: $i] : ? [v5: any] : (in(v4, v1) = v5 & % 10.99/2.24 $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ % 10.99/2.24 (ordered_pair(v4, v6) = v7) | ~ (in(v7, v0) = 0) | ~ $i(v6) | ? % 10.99/2.24 [v8: int] : ( ~ (v8 = 0) & in(v6, v2) = v8))) & (v5 = 0 | ? [v6: % 10.99/2.24 $i] : ? [v7: $i] : (ordered_pair(v4, v6) = v7 & in(v7, v0) = 0 & % 10.99/2.24 in(v6, v2) = 0 & $i(v7) & $i(v6))))) & ! [v1: $i] : ! [v2: $i] : % 10.99/2.24 ( ~ (relation_inverse_image(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ( ! % 10.99/2.24 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | % 10.99/2.24 ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = v6) | ~ % 10.99/2.24 (in(v6, v0) = 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & % 10.99/2.24 in(v5, v1) = v7))) & ! [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ % 10.99/2.24 $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v3, v4) = v5 & % 10.99/2.24 in(v5, v0) = 0 & in(v4, v1) = 0 & $i(v5) & $i(v4))))))) % 10.99/2.24 % 10.99/2.24 (d3_tarski) % 10.99/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 10.99/2.24 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 10.99/2.24 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.99/2.24 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 10.99/2.24 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 10.99/2.24 % 10.99/2.24 (d4_relat_1) % 10.99/2.25 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 10.99/2.25 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 10.99/2.25 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 10.99/2.25 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 10.99/2.25 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 10.99/2.25 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6) % 10.99/2.25 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 10.99/2.25 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 10.99/2.25 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 10.99/2.25 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 10.99/2.25 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & % 10.99/2.25 $i(v3))))))) % 10.99/2.25 % 10.99/2.25 (fc5_relat_1) % 10.99/2.25 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 10.99/2.25 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 & % 10.99/2.25 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 10.99/2.25 % 10.99/2.25 (t167_relat_1) % 10.99/2.25 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 10.99/2.25 = 0) & relation_dom(v1) = v3 & subset(v2, v3) = v4 & % 10.99/2.25 relation_inverse_image(v1, v0) = v2 & relation(v1) = 0 & $i(v3) & $i(v2) & % 10.99/2.25 $i(v1) & $i(v0)) % 10.99/2.25 % 10.99/2.25 (function-axioms) % 10.99/2.25 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.99/2.25 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 10.99/2.25 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.99/2.25 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 10.99/2.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.99/2.25 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = % 10.99/2.25 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 10.99/2.25 ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 10.99/2.25 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.99/2.25 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 10.99/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.99/2.25 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 10.99/2.25 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 10.99/2.25 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 10.99/2.25 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 10.99/2.25 : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = % 10.99/2.25 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.99/2.25 $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: % 10.99/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.99/2.25 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 10.99/2.25 % 10.99/2.25 Further assumptions not needed in the proof: % 10.99/2.25 -------------------------------------------- % 10.99/2.25 antisymmetry_r2_hidden, cc1_relat_1, commutativity_k2_tarski, d5_tarski, % 10.99/2.25 dt_k10_relat_1, dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, % 10.99/2.25 dt_k2_tarski, dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, % 10.99/2.25 fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1, fc3_subset_1, fc4_relat_1, % 10.99/2.25 fc7_relat_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_subset_1, % 10.99/2.25 rc2_xboole_0, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, % 10.99/2.25 t5_subset, t6_boole, t7_boole, t8_boole % 10.99/2.25 % 10.99/2.25 Those formulas are unsatisfiable: % 10.99/2.25 --------------------------------- % 10.99/2.25 % 10.99/2.25 Begin of proof % 10.99/2.26 | % 10.99/2.26 | ALPHA: (d3_tarski) implies: % 10.99/2.26 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 10.99/2.26 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 10.99/2.26 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 10.99/2.26 | % 10.99/2.26 | ALPHA: (function-axioms) implies: % 10.99/2.26 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.99/2.26 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 10.99/2.26 | % 10.99/2.26 | DELTA: instantiating (t167_relat_1) with fresh symbols all_38_0, all_38_1, % 10.99/2.26 | all_38_2, all_38_3, all_38_4 gives: % 10.99/2.26 | (3) ~ (all_38_0 = 0) & relation_dom(all_38_3) = all_38_1 & % 10.99/2.26 | subset(all_38_2, all_38_1) = all_38_0 & % 10.99/2.26 | relation_inverse_image(all_38_3, all_38_4) = all_38_2 & % 10.99/2.26 | relation(all_38_3) = 0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & % 10.99/2.26 | $i(all_38_4) % 10.99/2.26 | % 10.99/2.26 | ALPHA: (3) implies: % 10.99/2.26 | (4) ~ (all_38_0 = 0) % 10.99/2.26 | (5) $i(all_38_4) % 10.99/2.26 | (6) $i(all_38_3) % 10.99/2.26 | (7) $i(all_38_2) % 10.99/2.26 | (8) $i(all_38_1) % 10.99/2.26 | (9) relation(all_38_3) = 0 % 10.99/2.26 | (10) relation_inverse_image(all_38_3, all_38_4) = all_38_2 % 10.99/2.26 | (11) subset(all_38_2, all_38_1) = all_38_0 % 10.99/2.26 | (12) relation_dom(all_38_3) = all_38_1 % 10.99/2.26 | % 10.99/2.26 | GROUND_INST: instantiating (d14_relat_1) with all_38_3, simplifying with (6), % 10.99/2.26 | (9) gives: % 10.99/2.26 | (13) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 10.99/2.26 | (relation_inverse_image(all_38_3, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 10.99/2.26 | | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = % 10.99/2.26 | 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 10.99/2.26 | v6) | ~ (in(v6, all_38_3) = 0) | ~ $i(v5) | ? [v7: int] : % 10.99/2.26 | ( ~ (v7 = 0) & in(v5, v1) = v7))) & (v4 = 0 | ? [v5: $i] : ? % 10.99/2.26 | [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, all_38_3) = 0 & % 10.99/2.26 | in(v5, v1) = 0 & $i(v6) & $i(v5))))) & ! [v0: $i] : ! [v1: % 10.99/2.26 | $i] : ( ~ (relation_inverse_image(all_38_3, v0) = v1) | ~ $i(v1) | % 10.99/2.26 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) = % 10.99/2.26 | v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 10.99/2.26 | (ordered_pair(v2, v4) = v5) | ~ (in(v5, all_38_3) = 0) | ~ % 10.99/2.26 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & ! % 10.99/2.26 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? % 10.99/2.26 | [v4: $i] : (ordered_pair(v2, v3) = v4 & in(v4, all_38_3) = 0 & % 10.99/2.26 | in(v3, v0) = 0 & $i(v4) & $i(v3))))) % 10.99/2.26 | % 10.99/2.26 | ALPHA: (13) implies: % 10.99/2.27 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_38_3, v0) % 10.99/2.27 | = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 % 10.99/2.27 | = 0 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: % 10.99/2.27 | $i] : ( ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, all_38_3) = % 10.99/2.27 | 0) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = % 10.99/2.27 | v6))) & ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? % 10.99/2.27 | [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & in(v4, % 10.99/2.27 | all_38_3) = 0 & in(v3, v0) = 0 & $i(v4) & $i(v3))))) % 10.99/2.27 | % 10.99/2.27 | GROUND_INST: instantiating (1) with all_38_2, all_38_1, all_38_0, simplifying % 10.99/2.27 | with (7), (8), (11) gives: % 10.99/2.27 | (15) all_38_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 10.99/2.27 | all_38_1) = v1 & in(v0, all_38_2) = 0 & $i(v0)) % 10.99/2.27 | % 10.99/2.27 | GROUND_INST: instantiating (fc5_relat_1) with all_38_3, all_38_1, simplifying % 10.99/2.27 | with (6), (12) gives: % 10.99/2.27 | (16) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_38_3) = v1 % 10.99/2.27 | & empty(all_38_1) = v2 & empty(all_38_3) = v0 & ( ~ (v2 = 0) | ~ % 10.99/2.27 | (v1 = 0) | v0 = 0)) % 10.99/2.27 | % 10.99/2.27 | GROUND_INST: instantiating (d4_relat_1) with all_38_3, all_38_1, simplifying % 10.99/2.27 | with (6), (12) gives: % 10.99/2.27 | (17) ? [v0: int] : ( ~ (v0 = 0) & relation(all_38_3) = v0) | ( ? [v0: any] % 10.99/2.27 | : (v0 = all_38_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 10.99/2.27 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : % 10.99/2.27 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_38_3) = 0) | % 10.99/2.27 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : % 10.99/2.27 | (ordered_pair(v1, v3) = v4 & in(v4, all_38_3) = 0 & $i(v4) & % 10.99/2.27 | $i(v3))))) & ( ~ $i(all_38_1) | ( ! [v0: $i] : ! [v1: int] % 10.99/2.27 | : (v1 = 0 | ~ (in(v0, all_38_1) = v1) | ~ $i(v0) | ! [v2: $i] % 10.99/2.27 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 10.99/2.27 | all_38_3) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 10.99/2.27 | all_38_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 10.99/2.27 | (ordered_pair(v0, v1) = v2 & in(v2, all_38_3) = 0 & $i(v2) & % 10.99/2.27 | $i(v1)))))) % 10.99/2.27 | % 10.99/2.27 | GROUND_INST: instantiating (14) with all_38_4, all_38_2, simplifying with (5), % 10.99/2.27 | (7), (10) gives: % 10.99/2.27 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_38_2) = v1) | ~ % 10.99/2.27 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) % 10.99/2.27 | | ~ (in(v3, all_38_3) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 10.99/2.27 | 0) & in(v2, all_38_4) = v4))) & ! [v0: $i] : ( ~ (in(v0, % 10.99/2.27 | all_38_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 10.99/2.27 | (ordered_pair(v0, v1) = v2 & in(v2, all_38_3) = 0 & in(v1, all_38_4) % 10.99/2.27 | = 0 & $i(v2) & $i(v1))) % 10.99/2.27 | % 10.99/2.27 | ALPHA: (18) implies: % 10.99/2.27 | (19) ! [v0: $i] : ( ~ (in(v0, all_38_2) = 0) | ~ $i(v0) | ? [v1: $i] : % 10.99/2.27 | ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_38_3) = 0 & % 10.99/2.27 | in(v1, all_38_4) = 0 & $i(v2) & $i(v1))) % 10.99/2.27 | % 10.99/2.27 | DELTA: instantiating (16) with fresh symbols all_51_0, all_51_1, all_51_2 % 10.99/2.27 | gives: % 10.99/2.27 | (20) relation(all_38_3) = all_51_1 & empty(all_38_1) = all_51_0 & % 10.99/2.28 | empty(all_38_3) = all_51_2 & ( ~ (all_51_0 = 0) | ~ (all_51_1 = 0) | % 10.99/2.28 | all_51_2 = 0) % 10.99/2.28 | % 10.99/2.28 | ALPHA: (20) implies: % 10.99/2.28 | (21) relation(all_38_3) = all_51_1 % 10.99/2.28 | % 10.99/2.28 | BETA: splitting (15) gives: % 10.99/2.28 | % 10.99/2.28 | Case 1: % 10.99/2.28 | | % 10.99/2.28 | | (22) all_38_0 = 0 % 10.99/2.28 | | % 10.99/2.28 | | REDUCE: (4), (22) imply: % 10.99/2.28 | | (23) $false % 10.99/2.28 | | % 10.99/2.28 | | CLOSE: (23) is inconsistent. % 10.99/2.28 | | % 10.99/2.28 | Case 2: % 10.99/2.28 | | % 10.99/2.28 | | (24) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_38_1) = v1 & % 10.99/2.28 | | in(v0, all_38_2) = 0 & $i(v0)) % 10.99/2.28 | | % 10.99/2.28 | | DELTA: instantiating (24) with fresh symbols all_67_0, all_67_1 gives: % 10.99/2.28 | | (25) ~ (all_67_0 = 0) & in(all_67_1, all_38_1) = all_67_0 & in(all_67_1, % 10.99/2.28 | | all_38_2) = 0 & $i(all_67_1) % 10.99/2.28 | | % 10.99/2.28 | | ALPHA: (25) implies: % 10.99/2.28 | | (26) ~ (all_67_0 = 0) % 10.99/2.28 | | (27) $i(all_67_1) % 10.99/2.28 | | (28) in(all_67_1, all_38_2) = 0 % 10.99/2.28 | | (29) in(all_67_1, all_38_1) = all_67_0 % 10.99/2.28 | | % 10.99/2.28 | | GROUND_INST: instantiating (2) with 0, all_51_1, all_38_3, simplifying with % 10.99/2.28 | | (9), (21) gives: % 10.99/2.28 | | (30) all_51_1 = 0 % 10.99/2.28 | | % 10.99/2.28 | | BETA: splitting (17) gives: % 10.99/2.28 | | % 10.99/2.28 | | Case 1: % 10.99/2.28 | | | % 10.99/2.28 | | | (31) ? [v0: int] : ( ~ (v0 = 0) & relation(all_38_3) = v0) % 10.99/2.28 | | | % 10.99/2.28 | | | DELTA: instantiating (31) with fresh symbol all_76_0 gives: % 10.99/2.28 | | | (32) ~ (all_76_0 = 0) & relation(all_38_3) = all_76_0 % 10.99/2.28 | | | % 10.99/2.28 | | | ALPHA: (32) implies: % 10.99/2.28 | | | (33) ~ (all_76_0 = 0) % 10.99/2.28 | | | (34) relation(all_38_3) = all_76_0 % 10.99/2.28 | | | % 10.99/2.28 | | | GROUND_INST: instantiating (2) with 0, all_76_0, all_38_3, simplifying % 10.99/2.28 | | | with (9), (34) gives: % 10.99/2.28 | | | (35) all_76_0 = 0 % 10.99/2.28 | | | % 10.99/2.28 | | | REDUCE: (33), (35) imply: % 10.99/2.28 | | | (36) $false % 10.99/2.28 | | | % 10.99/2.28 | | | CLOSE: (36) is inconsistent. % 10.99/2.28 | | | % 10.99/2.28 | | Case 2: % 10.99/2.28 | | | % 11.34/2.28 | | | (37) ? [v0: any] : (v0 = all_38_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: % 11.34/2.28 | | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] % 11.34/2.28 | | | : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, % 11.34/2.28 | | | all_38_3) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 11.34/2.28 | | | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_38_3) % 11.34/2.28 | | | = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_38_1) | ( ! [v0: % 11.34/2.28 | | | $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_38_1) = v1) | % 11.34/2.28 | | | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, % 11.34/2.28 | | | v2) = v3) | ~ (in(v3, all_38_3) = 0) | ~ $i(v2))) & % 11.34/2.28 | | | ! [v0: $i] : ( ~ (in(v0, all_38_1) = 0) | ~ $i(v0) | ? [v1: % 11.34/2.28 | | | $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, % 11.34/2.28 | | | all_38_3) = 0 & $i(v2) & $i(v1))))) % 11.34/2.28 | | | % 11.34/2.28 | | | ALPHA: (37) implies: % 11.34/2.29 | | | (38) ~ $i(all_38_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 11.34/2.29 | | | (in(v0, all_38_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 11.34/2.29 | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_38_3) % 11.34/2.29 | | | = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_38_1) = % 11.34/2.29 | | | 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 11.34/2.29 | | | (ordered_pair(v0, v1) = v2 & in(v2, all_38_3) = 0 & $i(v2) & % 11.34/2.29 | | | $i(v1)))) % 11.34/2.29 | | | % 11.34/2.29 | | | BETA: splitting (38) gives: % 11.34/2.29 | | | % 11.34/2.29 | | | Case 1: % 11.34/2.29 | | | | % 11.34/2.29 | | | | (39) ~ $i(all_38_1) % 11.34/2.29 | | | | % 11.34/2.29 | | | | PRED_UNIFY: (8), (39) imply: % 11.34/2.29 | | | | (40) $false % 11.34/2.29 | | | | % 11.34/2.29 | | | | CLOSE: (40) is inconsistent. % 11.34/2.29 | | | | % 11.34/2.29 | | | Case 2: % 11.34/2.29 | | | | % 11.34/2.29 | | | | (41) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_38_1) = % 11.34/2.29 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 11.34/2.29 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_38_3) = 0) | ~ % 11.34/2.29 | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_38_1) = 0) | ~ % 11.34/2.29 | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = % 11.34/2.29 | | | | v2 & in(v2, all_38_3) = 0 & $i(v2) & $i(v1))) % 11.34/2.29 | | | | % 11.34/2.29 | | | | ALPHA: (41) implies: % 11.34/2.29 | | | | (42) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_38_1) = % 11.34/2.29 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 11.34/2.29 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_38_3) = 0) | ~ % 11.34/2.29 | | | | $i(v2))) % 11.34/2.29 | | | | % 11.34/2.29 | | | | GROUND_INST: instantiating (19) with all_67_1, simplifying with (27), % 11.34/2.29 | | | | (28) gives: % 11.34/2.29 | | | | (43) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_67_1, v0) = v1 & % 11.34/2.29 | | | | in(v1, all_38_3) = 0 & in(v0, all_38_4) = 0 & $i(v1) & $i(v0)) % 11.34/2.29 | | | | % 11.34/2.29 | | | | GROUND_INST: instantiating (42) with all_67_1, all_67_0, simplifying % 11.34/2.29 | | | | with (27), (29) gives: % 11.34/2.29 | | | | (44) all_67_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 11.34/2.29 | | | | (ordered_pair(all_67_1, v0) = v1) | ~ (in(v1, all_38_3) = 0) % 11.34/2.29 | | | | | ~ $i(v0)) % 11.34/2.29 | | | | % 11.34/2.29 | | | | DELTA: instantiating (43) with fresh symbols all_90_0, all_90_1 gives: % 11.34/2.29 | | | | (45) ordered_pair(all_67_1, all_90_1) = all_90_0 & in(all_90_0, % 11.34/2.29 | | | | all_38_3) = 0 & in(all_90_1, all_38_4) = 0 & $i(all_90_0) & % 11.34/2.29 | | | | $i(all_90_1) % 11.34/2.29 | | | | % 11.34/2.29 | | | | ALPHA: (45) implies: % 11.34/2.29 | | | | (46) $i(all_90_1) % 11.34/2.29 | | | | (47) in(all_90_0, all_38_3) = 0 % 11.34/2.29 | | | | (48) ordered_pair(all_67_1, all_90_1) = all_90_0 % 11.34/2.29 | | | | % 11.34/2.29 | | | | BETA: splitting (44) gives: % 11.34/2.29 | | | | % 11.34/2.29 | | | | Case 1: % 11.34/2.29 | | | | | % 11.34/2.29 | | | | | (49) all_67_0 = 0 % 11.34/2.29 | | | | | % 11.34/2.29 | | | | | REDUCE: (26), (49) imply: % 11.34/2.29 | | | | | (50) $false % 11.34/2.29 | | | | | % 11.34/2.29 | | | | | CLOSE: (50) is inconsistent. % 11.34/2.29 | | | | | % 11.34/2.29 | | | | Case 2: % 11.34/2.29 | | | | | % 11.34/2.29 | | | | | (51) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(all_67_1, v0) = % 11.34/2.29 | | | | | v1) | ~ (in(v1, all_38_3) = 0) | ~ $i(v0)) % 11.34/2.29 | | | | | % 11.34/2.29 | | | | | GROUND_INST: instantiating (51) with all_90_1, all_90_0, simplifying % 11.34/2.29 | | | | | with (46), (47), (48) gives: % 11.34/2.29 | | | | | (52) $false % 11.34/2.29 | | | | | % 11.34/2.29 | | | | | CLOSE: (52) is inconsistent. % 11.34/2.29 | | | | | % 11.34/2.29 | | | | End of split % 11.34/2.29 | | | | % 11.34/2.29 | | | End of split % 11.34/2.29 | | | % 11.34/2.29 | | End of split % 11.34/2.29 | | % 11.34/2.29 | End of split % 11.34/2.29 | % 11.34/2.29 End of proof % 11.34/2.29 % SZS output end Proof for theBenchmark % 11.34/2.29 % 11.34/2.29 1720ms %------------------------------------------------------------------------------