%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU056+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n006.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 17:42:25 EDT 2023 % Result : Theorem 8.33s 1.86s % Output : Proof 10.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU056+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n006.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Wed Aug 23 18:26:23 EDT 2023 % 0.13/0.34 % CPUTime : % 0.18/0.59 ________ _____ % 0.18/0.59 ___ __ \_________(_)________________________________ % 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.59 % 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.59 (2023-06-19) % 0.18/0.59 % 0.18/0.59 (c) Philipp Rümmer, 2009-2023 % 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.59 Amanda Stjerna. % 0.18/0.59 Free software under BSD-3-Clause. % 0.18/0.59 % 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.59 % 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.52/1.04 Prover 1: Preprocessing ... % 2.52/1.04 Prover 4: Preprocessing ... % 2.77/1.08 Prover 3: Preprocessing ... % 2.77/1.08 Prover 6: Preprocessing ... % 2.77/1.08 Prover 2: Preprocessing ... % 2.77/1.08 Prover 5: Preprocessing ... % 2.77/1.08 Prover 0: Preprocessing ... % 5.43/1.49 Prover 1: Warning: ignoring some quantifiers % 5.43/1.53 Prover 2: Proving ... % 6.07/1.54 Prover 5: Proving ... % 6.07/1.54 Prover 1: Constructing countermodel ... % 6.07/1.54 Prover 6: Proving ... % 6.07/1.55 Prover 3: Warning: ignoring some quantifiers % 6.07/1.57 Prover 3: Constructing countermodel ... % 6.45/1.59 Prover 4: Warning: ignoring some quantifiers % 6.45/1.62 Prover 4: Constructing countermodel ... % 6.91/1.66 Prover 0: Proving ... % 8.33/1.85 Prover 3: proved (1237ms) % 8.33/1.85 % 8.33/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.33/1.86 % 8.33/1.86 Prover 0: stopped % 8.33/1.86 Prover 2: stopped % 8.33/1.86 Prover 5: stopped % 8.33/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.33/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.33/1.87 Prover 6: stopped % 8.72/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.72/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.72/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.72/1.90 Prover 7: Preprocessing ... % 8.72/1.91 Prover 8: Preprocessing ... % 8.72/1.91 Prover 11: Preprocessing ... % 8.72/1.92 Prover 10: Preprocessing ... % 9.21/1.95 Prover 13: Preprocessing ... % 9.21/2.05 Prover 7: Warning: ignoring some quantifiers % 9.21/2.06 Prover 10: Warning: ignoring some quantifiers % 9.74/2.06 Prover 7: Constructing countermodel ... % 9.74/2.07 Prover 10: Constructing countermodel ... % 9.74/2.09 Prover 13: Warning: ignoring some quantifiers % 9.74/2.09 Prover 1: Found proof (size 47) % 9.74/2.09 Prover 1: proved (1480ms) % 9.74/2.09 Prover 13: Constructing countermodel ... % 9.74/2.10 Prover 10: stopped % 9.74/2.10 Prover 4: stopped % 9.74/2.10 Prover 13: stopped % 9.74/2.10 Prover 7: stopped % 10.33/2.12 Prover 8: Warning: ignoring some quantifiers % 10.33/2.13 Prover 8: Constructing countermodel ... % 10.33/2.14 Prover 8: stopped % 10.54/2.15 Prover 11: Warning: ignoring some quantifiers % 10.54/2.16 Prover 11: Constructing countermodel ... % 10.54/2.17 Prover 11: stopped % 10.54/2.17 % 10.54/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.54/2.17 % 10.54/2.18 % SZS output start Proof for theBenchmark % 10.54/2.18 Assumptions after simplification: % 10.54/2.18 --------------------------------- % 10.54/2.19 % 10.54/2.19 (cc2_funct_1) % 10.54/2.21 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 10.54/2.21 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) = % 10.54/2.21 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 10.54/2.21 % 10.54/2.21 (d7_xboole_0) % 10.54/2.21 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 10.54/2.21 (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = % 10.54/2.21 empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : % 10.54/2.21 ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 10.54/2.21 set_intersection2(v0, v1) = empty_set) % 10.54/2.21 % 10.54/2.21 (t121_funct_1) % 10.54/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 10.54/2.21 $i] : ( ~ (relation_image(v2, v1) = v4) | ~ (relation_image(v2, v0) = v3) | % 10.54/2.21 ~ (set_intersection2(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 10.54/2.21 [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : % 10.54/2.22 (relation_image(v2, v9) = v10 & set_intersection2(v0, v1) = v9 & % 10.54/2.22 one_to_one(v2) = v8 & relation(v2) = v6 & function(v2) = v7 & $i(v10) & % 10.54/2.22 $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v10 = v5))) % 10.54/2.22 % 10.54/2.22 (t125_funct_1) % 10.54/2.22 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 10.54/2.22 int] : ( ~ (v5 = 0) & relation_image(v2, v1) = v4 & relation_image(v2, v0) = % 10.54/2.22 v3 & disjoint(v3, v4) = v5 & disjoint(v0, v1) = 0 & one_to_one(v2) = 0 & % 10.54/2.22 relation(v2) = 0 & function(v2) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 10.54/2.22 $i(v0)) % 10.54/2.22 % 10.54/2.22 (t149_relat_1) % 10.54/2.22 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 10.54/2.22 (relation_image(v0, empty_set) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 10.54/2.22 0) & relation(v0) = v2)) % 10.54/2.22 % 10.54/2.22 (function-axioms) % 10.54/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.54/2.23 (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0: % 10.54/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.54/2.23 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 10.54/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.54/2.23 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: % 10.54/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.54/2.23 : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! % 10.54/2.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.54/2.23 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 10.54/2.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.54/2.23 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] % 10.54/2.23 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 10.54/2.23 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.54/2.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 10.54/2.23 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 10.54/2.23 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 10.54/2.23 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: % 10.54/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.54/2.23 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 10.54/2.23 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) % 10.54/2.23 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.54/2.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 10.54/2.23 (empty(v2) = v0)) % 10.54/2.23 % 10.54/2.23 Further assumptions not needed in the proof: % 10.54/2.23 -------------------------------------------- % 10.54/2.23 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, commutativity_k3_xboole_0, % 10.54/2.23 existence_m1_subset_1, fc12_relat_1, fc1_relat_1, fc1_subset_1, fc1_xboole_0, % 10.54/2.23 fc4_relat_1, idempotence_k3_xboole_0, rc1_funct_1, rc1_relat_1, rc1_subset_1, % 10.54/2.23 rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, % 10.54/2.23 rc3_relat_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, t1_subset, t2_boole, % 10.54/2.23 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 10.54/2.23 % 10.54/2.23 Those formulas are unsatisfiable: % 10.54/2.23 --------------------------------- % 10.54/2.23 % 10.54/2.23 Begin of proof % 10.54/2.23 | % 10.54/2.23 | ALPHA: (d7_xboole_0) implies: % 10.54/2.23 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ % 10.54/2.23 | $i(v0) | set_intersection2(v0, v1) = empty_set) % 10.54/2.23 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 10.54/2.23 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = % 10.54/2.23 | empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) % 10.54/2.23 | % 10.54/2.23 | ALPHA: (t149_relat_1) implies: % 10.54/2.23 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ (relation_image(v0, % 10.54/2.23 | empty_set) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 10.54/2.23 | relation(v0) = v2)) % 10.54/2.23 | % 10.54/2.23 | ALPHA: (function-axioms) implies: % 10.54/2.23 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.54/2.23 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 10.54/2.23 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.54/2.23 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 10.54/2.23 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.54/2.23 | (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 10.96/2.23 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.96/2.23 | (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = % 10.96/2.23 | v0)) % 10.96/2.23 | % 10.96/2.23 | DELTA: instantiating (t125_funct_1) with fresh symbols all_47_0, all_47_1, % 10.96/2.23 | all_47_2, all_47_3, all_47_4, all_47_5 gives: % 10.96/2.24 | (8) ~ (all_47_0 = 0) & relation_image(all_47_3, all_47_4) = all_47_1 & % 10.96/2.24 | relation_image(all_47_3, all_47_5) = all_47_2 & disjoint(all_47_2, % 10.96/2.24 | all_47_1) = all_47_0 & disjoint(all_47_5, all_47_4) = 0 & % 10.96/2.24 | one_to_one(all_47_3) = 0 & relation(all_47_3) = 0 & function(all_47_3) % 10.96/2.24 | = 0 & $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) & % 10.96/2.24 | $i(all_47_5) % 10.96/2.24 | % 10.96/2.24 | ALPHA: (8) implies: % 10.96/2.24 | (9) ~ (all_47_0 = 0) % 10.96/2.24 | (10) $i(all_47_5) % 10.96/2.24 | (11) $i(all_47_4) % 10.96/2.24 | (12) $i(all_47_3) % 10.96/2.24 | (13) $i(all_47_2) % 10.96/2.24 | (14) $i(all_47_1) % 10.96/2.24 | (15) function(all_47_3) = 0 % 10.96/2.24 | (16) relation(all_47_3) = 0 % 10.96/2.24 | (17) one_to_one(all_47_3) = 0 % 10.96/2.24 | (18) disjoint(all_47_5, all_47_4) = 0 % 10.96/2.24 | (19) disjoint(all_47_2, all_47_1) = all_47_0 % 10.96/2.24 | (20) relation_image(all_47_3, all_47_5) = all_47_2 % 10.96/2.24 | (21) relation_image(all_47_3, all_47_4) = all_47_1 % 10.96/2.24 | % 10.96/2.24 | GROUND_INST: instantiating (cc2_funct_1) with all_47_3, 0, simplifying with % 10.96/2.24 | (12), (17) gives: % 10.96/2.24 | (22) ? [v0: MultipleValueBool] : ? [v1: MultipleValueBool] : ? [v2: % 10.96/2.24 | MultipleValueBool] : (relation(all_47_3) = v0 & function(all_47_3) = % 10.96/2.24 | v2 & empty(all_47_3) = v1) % 10.96/2.24 | % 10.96/2.24 | GROUND_INST: instantiating (1) with all_47_5, all_47_4, simplifying with (10), % 10.96/2.24 | (11), (18) gives: % 10.96/2.24 | (23) set_intersection2(all_47_5, all_47_4) = empty_set % 10.96/2.24 | % 10.96/2.24 | GROUND_INST: instantiating (2) with all_47_2, all_47_1, all_47_0, simplifying % 10.96/2.24 | with (13), (14), (19) gives: % 10.96/2.24 | (24) all_47_0 = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) & % 10.96/2.24 | set_intersection2(all_47_2, all_47_1) = v0 & $i(v0)) % 10.96/2.24 | % 10.96/2.24 | DELTA: instantiating (22) with fresh symbols all_55_0, all_55_1, all_55_2 % 10.96/2.24 | gives: % 10.96/2.24 | (25) relation(all_47_3) = all_55_2 & function(all_47_3) = all_55_0 & % 10.96/2.24 | empty(all_47_3) = all_55_1 % 10.96/2.24 | % 10.96/2.24 | ALPHA: (25) implies: % 10.96/2.24 | (26) function(all_47_3) = all_55_0 % 10.96/2.24 | (27) relation(all_47_3) = all_55_2 % 10.96/2.24 | % 10.96/2.24 | BETA: splitting (24) gives: % 10.96/2.24 | % 10.96/2.24 | Case 1: % 10.96/2.24 | | % 10.96/2.24 | | (28) all_47_0 = 0 % 10.96/2.24 | | % 10.96/2.24 | | REDUCE: (9), (28) imply: % 10.96/2.24 | | (29) $false % 10.96/2.24 | | % 10.96/2.24 | | CLOSE: (29) is inconsistent. % 10.96/2.24 | | % 10.96/2.24 | Case 2: % 10.96/2.24 | | % 10.96/2.24 | | (30) ? [v0: $i] : ( ~ (v0 = empty_set) & set_intersection2(all_47_2, % 10.96/2.24 | | all_47_1) = v0 & $i(v0)) % 10.96/2.24 | | % 10.96/2.24 | | DELTA: instantiating (30) with fresh symbol all_63_0 gives: % 10.96/2.24 | | (31) ~ (all_63_0 = empty_set) & set_intersection2(all_47_2, all_47_1) = % 10.96/2.24 | | all_63_0 & $i(all_63_0) % 10.96/2.24 | | % 10.96/2.24 | | ALPHA: (31) implies: % 10.96/2.24 | | (32) ~ (all_63_0 = empty_set) % 10.96/2.25 | | (33) set_intersection2(all_47_2, all_47_1) = all_63_0 % 10.96/2.25 | | % 10.96/2.25 | | GROUND_INST: instantiating (4) with 0, all_55_0, all_47_3, simplifying with % 10.96/2.25 | | (15), (26) gives: % 10.96/2.25 | | (34) all_55_0 = 0 % 10.96/2.25 | | % 10.96/2.25 | | GROUND_INST: instantiating (5) with 0, all_55_2, all_47_3, simplifying with % 10.96/2.25 | | (16), (27) gives: % 10.96/2.25 | | (35) all_55_2 = 0 % 10.96/2.25 | | % 10.96/2.25 | | GROUND_INST: instantiating (t121_funct_1) with all_47_5, all_47_4, all_47_3, % 10.96/2.25 | | all_47_2, all_47_1, all_63_0, simplifying with (10), (11), % 10.96/2.25 | | (12), (20), (21), (33) gives: % 10.96/2.25 | | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 10.96/2.25 | | $i] : (relation_image(all_47_3, v3) = v4 & % 10.96/2.25 | | set_intersection2(all_47_5, all_47_4) = v3 & one_to_one(all_47_3) % 10.96/2.25 | | = v2 & relation(all_47_3) = v0 & function(all_47_3) = v1 & $i(v4) % 10.96/2.25 | | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = % 10.96/2.25 | | all_63_0)) % 10.96/2.25 | | % 10.96/2.25 | | DELTA: instantiating (36) with fresh symbols all_79_0, all_79_1, all_79_2, % 10.96/2.25 | | all_79_3, all_79_4 gives: % 10.96/2.25 | | (37) relation_image(all_47_3, all_79_1) = all_79_0 & % 10.96/2.25 | | set_intersection2(all_47_5, all_47_4) = all_79_1 & % 10.96/2.25 | | one_to_one(all_47_3) = all_79_2 & relation(all_47_3) = all_79_4 & % 10.96/2.25 | | function(all_47_3) = all_79_3 & $i(all_79_0) & $i(all_79_1) & ( ~ % 10.96/2.25 | | (all_79_2 = 0) | ~ (all_79_3 = 0) | ~ (all_79_4 = 0) | all_79_0 % 10.96/2.25 | | = all_63_0) % 10.96/2.25 | | % 10.96/2.25 | | ALPHA: (37) implies: % 10.96/2.25 | | (38) function(all_47_3) = all_79_3 % 10.96/2.25 | | (39) relation(all_47_3) = all_79_4 % 10.96/2.25 | | (40) one_to_one(all_47_3) = all_79_2 % 10.96/2.25 | | (41) set_intersection2(all_47_5, all_47_4) = all_79_1 % 10.96/2.25 | | (42) relation_image(all_47_3, all_79_1) = all_79_0 % 10.96/2.25 | | (43) ~ (all_79_2 = 0) | ~ (all_79_3 = 0) | ~ (all_79_4 = 0) | all_79_0 % 10.96/2.25 | | = all_63_0 % 10.96/2.25 | | % 10.96/2.25 | | GROUND_INST: instantiating (4) with 0, all_79_3, all_47_3, simplifying with % 10.96/2.25 | | (15), (38) gives: % 10.96/2.25 | | (44) all_79_3 = 0 % 10.96/2.25 | | % 10.96/2.25 | | GROUND_INST: instantiating (5) with 0, all_79_4, all_47_3, simplifying with % 10.96/2.25 | | (16), (39) gives: % 10.96/2.25 | | (45) all_79_4 = 0 % 10.96/2.25 | | % 10.96/2.25 | | GROUND_INST: instantiating (6) with 0, all_79_2, all_47_3, simplifying with % 10.96/2.25 | | (17), (40) gives: % 10.96/2.25 | | (46) all_79_2 = 0 % 10.96/2.25 | | % 10.96/2.25 | | GROUND_INST: instantiating (7) with empty_set, all_79_1, all_47_4, all_47_5, % 10.96/2.25 | | simplifying with (23), (41) gives: % 10.96/2.25 | | (47) all_79_1 = empty_set % 10.96/2.25 | | % 10.96/2.25 | | REDUCE: (42), (47) imply: % 10.96/2.25 | | (48) relation_image(all_47_3, empty_set) = all_79_0 % 10.96/2.25 | | % 10.96/2.25 | | BETA: splitting (43) gives: % 10.96/2.25 | | % 10.96/2.25 | | Case 1: % 10.96/2.25 | | | % 10.96/2.25 | | | (49) ~ (all_79_2 = 0) % 10.96/2.25 | | | % 10.96/2.25 | | | REDUCE: (46), (49) imply: % 10.96/2.25 | | | (50) $false % 10.96/2.25 | | | % 10.96/2.25 | | | CLOSE: (50) is inconsistent. % 10.96/2.25 | | | % 10.96/2.25 | | Case 2: % 10.96/2.25 | | | % 10.96/2.25 | | | (51) ~ (all_79_3 = 0) | ~ (all_79_4 = 0) | all_79_0 = all_63_0 % 10.96/2.25 | | | % 10.96/2.25 | | | BETA: splitting (51) gives: % 10.96/2.25 | | | % 10.96/2.25 | | | Case 1: % 10.96/2.25 | | | | % 10.96/2.25 | | | | (52) ~ (all_79_3 = 0) % 10.96/2.25 | | | | % 10.96/2.25 | | | | REDUCE: (44), (52) imply: % 10.96/2.25 | | | | (53) $false % 10.96/2.25 | | | | % 10.96/2.25 | | | | CLOSE: (53) is inconsistent. % 10.96/2.25 | | | | % 10.96/2.25 | | | Case 2: % 10.96/2.25 | | | | % 10.96/2.25 | | | | (54) ~ (all_79_4 = 0) | all_79_0 = all_63_0 % 10.96/2.25 | | | | % 10.96/2.25 | | | | BETA: splitting (54) gives: % 10.96/2.25 | | | | % 10.96/2.25 | | | | Case 1: % 10.96/2.25 | | | | | % 10.96/2.25 | | | | | (55) ~ (all_79_4 = 0) % 10.96/2.25 | | | | | % 10.96/2.25 | | | | | REDUCE: (45), (55) imply: % 10.96/2.25 | | | | | (56) $false % 10.96/2.25 | | | | | % 10.96/2.25 | | | | | CLOSE: (56) is inconsistent. % 10.96/2.25 | | | | | % 10.96/2.25 | | | | Case 2: % 10.96/2.25 | | | | | % 10.96/2.25 | | | | | (57) all_79_0 = all_63_0 % 10.96/2.25 | | | | | % 10.96/2.25 | | | | | REDUCE: (48), (57) imply: % 10.96/2.25 | | | | | (58) relation_image(all_47_3, empty_set) = all_63_0 % 10.96/2.25 | | | | | % 10.96/2.25 | | | | | GROUND_INST: instantiating (3) with all_47_3, all_63_0, simplifying % 10.96/2.25 | | | | | with (12), (58) gives: % 10.96/2.26 | | | | | (59) all_63_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & % 10.96/2.26 | | | | | relation(all_47_3) = v0) % 10.96/2.26 | | | | | % 10.96/2.26 | | | | | BETA: splitting (59) gives: % 10.96/2.26 | | | | | % 10.96/2.26 | | | | | Case 1: % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | | (60) all_63_0 = empty_set % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | | REDUCE: (32), (60) imply: % 10.96/2.26 | | | | | | (61) $false % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | | CLOSE: (61) is inconsistent. % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | Case 2: % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | | (62) ? [v0: int] : ( ~ (v0 = 0) & relation(all_47_3) = v0) % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | | DELTA: instantiating (62) with fresh symbol all_110_0 gives: % 10.96/2.26 | | | | | | (63) ~ (all_110_0 = 0) & relation(all_47_3) = all_110_0 % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | | ALPHA: (63) implies: % 10.96/2.26 | | | | | | (64) ~ (all_110_0 = 0) % 10.96/2.26 | | | | | | (65) relation(all_47_3) = all_110_0 % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | | GROUND_INST: instantiating (5) with 0, all_110_0, all_47_3, % 10.96/2.26 | | | | | | simplifying with (16), (65) gives: % 10.96/2.26 | | | | | | (66) all_110_0 = 0 % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | | REDUCE: (64), (66) imply: % 10.96/2.26 | | | | | | (67) $false % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | | CLOSE: (67) is inconsistent. % 10.96/2.26 | | | | | | % 10.96/2.26 | | | | | End of split % 10.96/2.26 | | | | | % 10.96/2.26 | | | | End of split % 10.96/2.26 | | | | % 10.96/2.26 | | | End of split % 10.96/2.26 | | | % 10.96/2.26 | | End of split % 10.96/2.26 | | % 10.96/2.26 | End of split % 10.96/2.26 | % 10.96/2.26 End of proof % 10.96/2.26 % SZS output end Proof for theBenchmark % 10.96/2.26 % 10.96/2.26 1664ms %------------------------------------------------------------------------------