%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU355+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 : n001.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 17:44:15 EDT 2023 % Result : Theorem 10.27s 2.41s % Output : Proof 12.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SEU355+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n001.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Wed Aug 23 16:35:54 EDT 2023 % 0.12/0.32 % CPUTime : % 0.17/0.61 ________ _____ % 0.17/0.61 ___ __ \_________(_)________________________________ % 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.61 % 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.61 (2023-06-19) % 0.17/0.61 % 0.17/0.61 (c) Philipp Rümmer, 2009-2023 % 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.61 Amanda Stjerna. % 0.17/0.61 Free software under BSD-3-Clause. % 0.17/0.61 % 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.61 % 0.17/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.63 Running up to 7 provers in parallel. % 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.13/1.11 Prover 1: Preprocessing ... % 2.13/1.12 Prover 4: Preprocessing ... % 2.84/1.18 Prover 3: Preprocessing ... % 2.84/1.18 Prover 2: Preprocessing ... % 2.84/1.18 Prover 5: Preprocessing ... % 2.84/1.18 Prover 6: Preprocessing ... % 2.84/1.18 Prover 0: Preprocessing ... % 4.70/1.53 Prover 2: Proving ... % 4.70/1.57 Prover 5: Proving ... % 4.70/1.61 Prover 1: Warning: ignoring some quantifiers % 5.13/1.66 Prover 1: Constructing countermodel ... % 6.46/1.73 Prover 3: Warning: ignoring some quantifiers % 6.66/1.75 Prover 6: Proving ... % 6.66/1.77 Prover 3: Constructing countermodel ... % 7.27/1.87 Prover 4: Warning: ignoring some quantifiers % 7.71/1.91 Prover 4: Constructing countermodel ... % 7.71/1.93 Prover 0: Proving ... % 10.27/2.38 Prover 1: Found proof (size 68) % 10.27/2.39 Prover 1: proved (1745ms) % 10.27/2.39 Prover 6: stopped % 10.27/2.39 Prover 5: stopped % 10.27/2.39 Prover 2: stopped % 10.27/2.39 Prover 4: stopped % 10.27/2.39 Prover 3: stopped % 10.27/2.41 Prover 0: stopped % 10.27/2.41 % 10.27/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.27/2.41 % 11.44/2.43 % SZS output start Proof for theBenchmark % 11.44/2.44 Assumptions after simplification: % 11.44/2.44 --------------------------------- % 11.44/2.44 % 11.44/2.44 (d8_lattice3) % 11.51/2.49 ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 11.51/2.49 (the_carrier(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 11.51/2.49 ( ~ (relstr_element_smaller(v0, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? % 11.51/2.49 [v5: int] : ( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = 0) | ! % 11.51/2.49 [v5: $i] : ( ~ (element(v5, v1) = 0) | ~ $i(v5) | ? [v6: any] : ? % 11.51/2.49 [v7: any] : (related(v0, v3, v5) = v7 & in(v5, v2) = v6 & ( ~ (v6 % 11.51/2.49 = 0) | v7 = 0)))) & (v4 = 0 | ? [v5: $i] : ? [v6: int] : ( % 11.51/2.49 ~ (v6 = 0) & element(v5, v1) = 0 & related(v0, v3, v5) = v6 & % 11.51/2.49 in(v5, v2) = 0 & $i(v5))))))) % 11.51/2.49 % 11.51/2.49 (d9_lattice3) % 11.51/2.49 ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 11.51/2.49 (the_carrier(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 11.51/2.49 ( ~ (relstr_set_smaller(v0, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? % 11.51/2.49 [v5: int] : ( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = 0) | ! % 11.51/2.49 [v5: $i] : ( ~ (element(v5, v1) = 0) | ~ $i(v5) | ? [v6: any] : ? % 11.51/2.49 [v7: any] : (related(v0, v5, v3) = v7 & in(v5, v2) = v6 & ( ~ (v6 % 11.51/2.49 = 0) | v7 = 0)))) & (v4 = 0 | ? [v5: $i] : ? [v6: int] : ( % 11.51/2.50 ~ (v6 = 0) & element(v5, v1) = 0 & related(v0, v5, v3) = v6 & % 11.51/2.50 in(v5, v2) = 0 & $i(v5))))))) % 11.51/2.50 % 11.51/2.50 (rc1_xboole_0) % 11.51/2.50 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 11.51/2.50 % 11.51/2.50 (t6_boole) % 11.51/2.50 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 11.51/2.50 $i(v0)) % 11.51/2.50 % 11.51/2.50 (t6_yellow_0) % 11.51/2.50 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : (rel_str(v0) = 0 & the_carrier(v0) % 11.51/2.50 = v1 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 11.51/2.50 (relstr_set_smaller(v0, empty_set, v2) = v3 & relstr_element_smaller(v0, % 11.51/2.50 empty_set, v2) = v4 & element(v2, v1) = 0 & $i(v2) & ( ~ (v4 = 0) | ~ % 11.51/2.50 (v3 = 0)))) % 11.51/2.50 % 11.51/2.50 (t7_boole) % 11.51/2.50 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 11.51/2.50 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 11.51/2.50 % 11.51/2.50 (function-axioms) % 11.86/2.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.86/2.51 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relstr_set_smaller(v4, v3, v2) = v1) | % 11.86/2.51 ~ (relstr_set_smaller(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.86/2.51 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 11.86/2.51 ~ (relstr_element_smaller(v4, v3, v2) = v1) | ~ % 11.86/2.51 (relstr_element_smaller(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.86/2.51 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 11.86/2.51 ~ (related(v4, v3, v2) = v1) | ~ (related(v4, v3, v2) = v0)) & ! [v0: % 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.86/2.51 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: % 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.86/2.51 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 11.86/2.51 ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0: % 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 11.86/2.51 ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 11.86/2.51 ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 11.86/2.51 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 11.86/2.51 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) & ! [v0: % 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 11.86/2.51 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 11.86/2.51 % 11.86/2.51 Further assumptions not needed in the proof: % 11.86/2.51 -------------------------------------------- % 11.86/2.51 antisymmetry_r2_hidden, cc1_finset_1, dt_k1_xboole_0, dt_l1_orders_2, % 11.86/2.51 dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, existence_l1_orders_2, % 11.86/2.51 existence_l1_struct_0, existence_m1_subset_1, fc1_xboole_0, rc1_finset_1, % 11.86/2.52 rc2_xboole_0, t1_subset, t2_subset, t8_boole % 11.86/2.52 % 11.86/2.52 Those formulas are unsatisfiable: % 11.86/2.52 --------------------------------- % 11.86/2.52 % 11.86/2.52 Begin of proof % 11.86/2.52 | % 11.86/2.52 | ALPHA: (t6_boole) implies: % 11.86/2.52 | (1) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 11.86/2.52 | % 11.86/2.52 | ALPHA: (t6_yellow_0) implies: % 11.86/2.52 | (2) $i(empty_set) % 11.86/2.52 | (3) ? [v0: $i] : ? [v1: $i] : (rel_str(v0) = 0 & the_carrier(v0) = v1 & % 11.86/2.52 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 11.86/2.52 | (relstr_set_smaller(v0, empty_set, v2) = v3 & % 11.86/2.52 | relstr_element_smaller(v0, empty_set, v2) = v4 & element(v2, v1) = % 11.86/2.52 | 0 & $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 11.86/2.52 | % 11.86/2.52 | ALPHA: (function-axioms) implies: % 11.86/2.52 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.86/2.52 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 11.86/2.52 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 11.86/2.52 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 11.86/2.53 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.86/2.53 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 11.86/2.53 | v2) = v0)) % 11.86/2.53 | % 11.86/2.53 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_16_0 gives: % 11.86/2.53 | (7) empty(all_16_0) = 0 & $i(all_16_0) % 11.86/2.53 | % 11.86/2.53 | ALPHA: (7) implies: % 11.86/2.53 | (8) $i(all_16_0) % 11.86/2.53 | (9) empty(all_16_0) = 0 % 11.86/2.53 | % 11.86/2.53 | DELTA: instantiating (3) with fresh symbols all_25_0, all_25_1 gives: % 11.86/2.53 | (10) rel_str(all_25_1) = 0 & the_carrier(all_25_1) = all_25_0 & % 11.86/2.53 | $i(all_25_0) & $i(all_25_1) & ? [v0: $i] : ? [v1: any] : ? [v2: % 11.86/2.53 | any] : (relstr_set_smaller(all_25_1, empty_set, v0) = v1 & % 11.86/2.53 | relstr_element_smaller(all_25_1, empty_set, v0) = v2 & element(v0, % 11.86/2.53 | all_25_0) = 0 & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0))) % 11.86/2.53 | % 11.86/2.53 | ALPHA: (10) implies: % 11.86/2.53 | (11) $i(all_25_1) % 11.86/2.53 | (12) the_carrier(all_25_1) = all_25_0 % 11.86/2.53 | (13) rel_str(all_25_1) = 0 % 11.86/2.53 | (14) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 11.86/2.53 | (relstr_set_smaller(all_25_1, empty_set, v0) = v1 & % 11.86/2.53 | relstr_element_smaller(all_25_1, empty_set, v0) = v2 & element(v0, % 11.86/2.53 | all_25_0) = 0 & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0))) % 11.86/2.53 | % 11.86/2.53 | DELTA: instantiating (14) with fresh symbols all_27_0, all_27_1, all_27_2 % 11.86/2.53 | gives: % 11.86/2.53 | (15) relstr_set_smaller(all_25_1, empty_set, all_27_2) = all_27_1 & % 11.86/2.53 | relstr_element_smaller(all_25_1, empty_set, all_27_2) = all_27_0 & % 11.86/2.53 | element(all_27_2, all_25_0) = 0 & $i(all_27_2) & ( ~ (all_27_0 = 0) | % 11.86/2.54 | ~ (all_27_1 = 0)) % 11.86/2.54 | % 11.86/2.54 | ALPHA: (15) implies: % 11.86/2.54 | (16) $i(all_27_2) % 11.86/2.54 | (17) element(all_27_2, all_25_0) = 0 % 11.86/2.54 | (18) relstr_element_smaller(all_25_1, empty_set, all_27_2) = all_27_0 % 11.86/2.54 | (19) relstr_set_smaller(all_25_1, empty_set, all_27_2) = all_27_1 % 11.86/2.54 | (20) ~ (all_27_0 = 0) | ~ (all_27_1 = 0) % 11.86/2.54 | % 11.86/2.54 | GROUND_INST: instantiating (1) with all_16_0, simplifying with (8), (9) gives: % 11.86/2.54 | (21) all_16_0 = empty_set % 11.86/2.54 | % 11.86/2.54 | GROUND_INST: instantiating (d9_lattice3) with all_25_1, simplifying with (11), % 11.86/2.54 | (13) gives: % 11.86/2.54 | (22) ? [v0: $i] : (the_carrier(all_25_1) = v0 & $i(v0) & ! [v1: $i] : ! % 11.86/2.54 | [v2: $i] : ! [v3: any] : ( ~ (relstr_set_smaller(all_25_1, v1, v2) % 11.86/2.54 | = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & % 11.86/2.54 | element(v2, v0) = v4) | (( ~ (v3 = 0) | ! [v4: $i] : ( ~ % 11.86/2.54 | (element(v4, v0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: % 11.86/2.54 | any] : (related(all_25_1, v4, v2) = v6 & in(v4, v1) = v5 & % 11.86/2.54 | ( ~ (v5 = 0) | v6 = 0)))) & (v3 = 0 | ? [v4: $i] : ? % 11.86/2.54 | [v5: int] : ( ~ (v5 = 0) & element(v4, v0) = 0 & % 11.86/2.54 | related(all_25_1, v4, v2) = v5 & in(v4, v1) = 0 & % 11.86/2.54 | $i(v4)))))) % 11.86/2.54 | % 11.86/2.54 | GROUND_INST: instantiating (d8_lattice3) with all_25_1, simplifying with (11), % 11.86/2.54 | (13) gives: % 11.86/2.55 | (23) ? [v0: $i] : (the_carrier(all_25_1) = v0 & $i(v0) & ! [v1: $i] : ! % 11.86/2.55 | [v2: $i] : ! [v3: any] : ( ~ (relstr_element_smaller(all_25_1, v1, % 11.86/2.55 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = % 11.86/2.55 | 0) & element(v2, v0) = v4) | (( ~ (v3 = 0) | ! [v4: $i] : ( ~ % 11.86/2.55 | (element(v4, v0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: % 11.86/2.55 | any] : (related(all_25_1, v2, v4) = v6 & in(v4, v1) = v5 & % 11.86/2.55 | ( ~ (v5 = 0) | v6 = 0)))) & (v3 = 0 | ? [v4: $i] : ? % 11.86/2.55 | [v5: int] : ( ~ (v5 = 0) & element(v4, v0) = 0 & % 11.86/2.55 | related(all_25_1, v2, v4) = v5 & in(v4, v1) = 0 & % 11.86/2.55 | $i(v4)))))) % 11.86/2.55 | % 11.86/2.55 | DELTA: instantiating (23) with fresh symbol all_35_0 gives: % 11.86/2.55 | (24) the_carrier(all_25_1) = all_35_0 & $i(all_35_0) & ! [v0: $i] : ! % 11.86/2.55 | [v1: $i] : ! [v2: any] : ( ~ (relstr_element_smaller(all_25_1, v0, % 11.86/2.55 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 11.86/2.55 | & element(v1, all_35_0) = v3) | (( ~ (v2 = 0) | ! [v3: $i] : ( ~ % 11.86/2.55 | (element(v3, all_35_0) = 0) | ~ $i(v3) | ? [v4: any] : ? % 11.86/2.55 | [v5: any] : (related(all_25_1, v1, v3) = v5 & in(v3, v0) = v4 % 11.86/2.55 | & ( ~ (v4 = 0) | v5 = 0)))) & (v2 = 0 | ? [v3: $i] : ? % 11.86/2.55 | [v4: int] : ( ~ (v4 = 0) & element(v3, all_35_0) = 0 & % 11.86/2.55 | related(all_25_1, v1, v3) = v4 & in(v3, v0) = 0 & $i(v3))))) % 11.86/2.55 | % 11.86/2.55 | ALPHA: (24) implies: % 11.86/2.55 | (25) the_carrier(all_25_1) = all_35_0 % 11.86/2.56 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 11.86/2.56 | (relstr_element_smaller(all_25_1, v0, v1) = v2) | ~ $i(v1) | ~ % 11.86/2.56 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & element(v1, all_35_0) = v3) | % 11.86/2.56 | (( ~ (v2 = 0) | ! [v3: $i] : ( ~ (element(v3, all_35_0) = 0) | ~ % 11.86/2.56 | $i(v3) | ? [v4: any] : ? [v5: any] : (related(all_25_1, v1, % 11.86/2.56 | v3) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))) & % 11.86/2.56 | (v2 = 0 | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & element(v3, % 11.86/2.56 | all_35_0) = 0 & related(all_25_1, v1, v3) = v4 & in(v3, v0) % 11.86/2.56 | = 0 & $i(v3))))) % 11.86/2.56 | % 11.86/2.56 | GROUND_INST: instantiating (26) with empty_set, all_27_2, all_27_0, % 11.86/2.56 | simplifying with (2), (16), (18) gives: % 11.86/2.56 | (27) ? [v0: int] : ( ~ (v0 = 0) & element(all_27_2, all_35_0) = v0) | (( ~ % 11.86/2.56 | (all_27_0 = 0) | ! [v0: $i] : ( ~ (element(v0, all_35_0) = 0) | % 11.86/2.56 | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (related(all_25_1, % 11.86/2.56 | all_27_2, v0) = v2 & in(v0, empty_set) = v1 & ( ~ (v1 = 0) | % 11.86/2.56 | v2 = 0)))) & (all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( % 11.86/2.56 | ~ (v1 = 0) & element(v0, all_35_0) = 0 & related(all_25_1, % 11.86/2.56 | all_27_2, v0) = v1 & in(v0, empty_set) = 0 & $i(v0)))) % 11.86/2.56 | % 11.86/2.56 | DELTA: instantiating (22) with fresh symbol all_38_0 gives: % 11.86/2.57 | (28) the_carrier(all_25_1) = all_38_0 & $i(all_38_0) & ! [v0: $i] : ! % 11.86/2.57 | [v1: $i] : ! [v2: any] : ( ~ (relstr_set_smaller(all_25_1, v0, v1) = % 11.86/2.57 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 11.86/2.57 | element(v1, all_38_0) = v3) | (( ~ (v2 = 0) | ! [v3: $i] : ( ~ % 11.86/2.57 | (element(v3, all_38_0) = 0) | ~ $i(v3) | ? [v4: any] : ? % 11.86/2.57 | [v5: any] : (related(all_25_1, v3, v1) = v5 & in(v3, v0) = v4 % 11.86/2.57 | & ( ~ (v4 = 0) | v5 = 0)))) & (v2 = 0 | ? [v3: $i] : ? % 11.86/2.57 | [v4: int] : ( ~ (v4 = 0) & element(v3, all_38_0) = 0 & % 11.86/2.57 | related(all_25_1, v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))))) % 11.86/2.57 | % 11.86/2.57 | ALPHA: (28) implies: % 11.86/2.57 | (29) the_carrier(all_25_1) = all_38_0 % 12.13/2.57 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 12.13/2.57 | (relstr_set_smaller(all_25_1, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 12.13/2.57 | | ? [v3: int] : ( ~ (v3 = 0) & element(v1, all_38_0) = v3) | (( ~ % 12.13/2.57 | (v2 = 0) | ! [v3: $i] : ( ~ (element(v3, all_38_0) = 0) | ~ % 12.13/2.57 | $i(v3) | ? [v4: any] : ? [v5: any] : (related(all_25_1, v3, % 12.13/2.57 | v1) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))) & % 12.13/2.57 | (v2 = 0 | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & element(v3, % 12.13/2.57 | all_38_0) = 0 & related(all_25_1, v3, v1) = v4 & in(v3, v0) % 12.13/2.57 | = 0 & $i(v3))))) % 12.13/2.57 | % 12.13/2.57 | GROUND_INST: instantiating (30) with empty_set, all_27_2, all_27_1, % 12.13/2.57 | simplifying with (2), (16), (19) gives: % 12.13/2.57 | (31) ? [v0: int] : ( ~ (v0 = 0) & element(all_27_2, all_38_0) = v0) | (( ~ % 12.13/2.57 | (all_27_1 = 0) | ! [v0: $i] : ( ~ (element(v0, all_38_0) = 0) | % 12.13/2.57 | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (related(all_25_1, v0, % 12.13/2.57 | all_27_2) = v2 & in(v0, empty_set) = v1 & ( ~ (v1 = 0) | v2 % 12.13/2.57 | = 0)))) & (all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ % 12.13/2.57 | (v1 = 0) & element(v0, all_38_0) = 0 & related(all_25_1, v0, % 12.13/2.57 | all_27_2) = v1 & in(v0, empty_set) = 0 & $i(v0)))) % 12.13/2.57 | % 12.13/2.58 | REDUCE: (9), (21) imply: % 12.13/2.58 | (32) empty(empty_set) = 0 % 12.13/2.58 | % 12.13/2.58 | GROUND_INST: instantiating (5) with all_25_0, all_38_0, all_25_1, simplifying % 12.13/2.58 | with (12), (29) gives: % 12.13/2.58 | (33) all_38_0 = all_25_0 % 12.13/2.58 | % 12.13/2.58 | GROUND_INST: instantiating (5) with all_35_0, all_38_0, all_25_1, simplifying % 12.13/2.58 | with (25), (29) gives: % 12.13/2.58 | (34) all_38_0 = all_35_0 % 12.13/2.58 | % 12.13/2.58 | COMBINE_EQS: (33), (34) imply: % 12.13/2.58 | (35) all_35_0 = all_25_0 % 12.13/2.58 | % 12.13/2.58 | BETA: splitting (20) gives: % 12.13/2.58 | % 12.13/2.58 | Case 1: % 12.13/2.58 | | % 12.13/2.58 | | (36) ~ (all_27_0 = 0) % 12.13/2.58 | | % 12.13/2.58 | | BETA: splitting (27) gives: % 12.13/2.58 | | % 12.13/2.58 | | Case 1: % 12.13/2.58 | | | % 12.13/2.58 | | | (37) ? [v0: int] : ( ~ (v0 = 0) & element(all_27_2, all_35_0) = v0) % 12.13/2.58 | | | % 12.13/2.58 | | | DELTA: instantiating (37) with fresh symbol all_70_0 gives: % 12.13/2.58 | | | (38) ~ (all_70_0 = 0) & element(all_27_2, all_35_0) = all_70_0 % 12.13/2.58 | | | % 12.13/2.58 | | | ALPHA: (38) implies: % 12.13/2.58 | | | (39) ~ (all_70_0 = 0) % 12.13/2.58 | | | (40) element(all_27_2, all_35_0) = all_70_0 % 12.13/2.58 | | | % 12.13/2.58 | | | REDUCE: (35), (40) imply: % 12.13/2.58 | | | (41) element(all_27_2, all_25_0) = all_70_0 % 12.13/2.58 | | | % 12.13/2.58 | | | GROUND_INST: instantiating (6) with 0, all_70_0, all_25_0, all_27_2, % 12.13/2.58 | | | simplifying with (17), (41) gives: % 12.13/2.58 | | | (42) all_70_0 = 0 % 12.13/2.58 | | | % 12.13/2.58 | | | REDUCE: (39), (42) imply: % 12.13/2.58 | | | (43) $false % 12.13/2.59 | | | % 12.13/2.59 | | | CLOSE: (43) is inconsistent. % 12.13/2.59 | | | % 12.13/2.59 | | Case 2: % 12.13/2.59 | | | % 12.13/2.59 | | | (44) ( ~ (all_27_0 = 0) | ! [v0: $i] : ( ~ (element(v0, all_35_0) = 0) % 12.13/2.59 | | | | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (related(all_25_1, % 12.13/2.59 | | | all_27_2, v0) = v2 & in(v0, empty_set) = v1 & ( ~ (v1 = 0) % 12.13/2.59 | | | | v2 = 0)))) & (all_27_0 = 0 | ? [v0: $i] : ? [v1: int] % 12.13/2.59 | | | : ( ~ (v1 = 0) & element(v0, all_35_0) = 0 & related(all_25_1, % 12.13/2.59 | | | all_27_2, v0) = v1 & in(v0, empty_set) = 0 & $i(v0))) % 12.13/2.59 | | | % 12.13/2.59 | | | ALPHA: (44) implies: % 12.13/2.59 | | | (45) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.13/2.59 | | | element(v0, all_35_0) = 0 & related(all_25_1, all_27_2, v0) = v1 % 12.13/2.59 | | | & in(v0, empty_set) = 0 & $i(v0)) % 12.13/2.59 | | | % 12.13/2.59 | | | BETA: splitting (45) gives: % 12.13/2.59 | | | % 12.13/2.59 | | | Case 1: % 12.13/2.59 | | | | % 12.13/2.59 | | | | (46) all_27_0 = 0 % 12.13/2.59 | | | | % 12.13/2.59 | | | | REDUCE: (36), (46) imply: % 12.13/2.59 | | | | (47) $false % 12.13/2.59 | | | | % 12.13/2.59 | | | | CLOSE: (47) is inconsistent. % 12.13/2.59 | | | | % 12.13/2.59 | | | Case 2: % 12.13/2.59 | | | | % 12.13/2.59 | | | | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, % 12.13/2.59 | | | | all_35_0) = 0 & related(all_25_1, all_27_2, v0) = v1 & % 12.13/2.59 | | | | in(v0, empty_set) = 0 & $i(v0)) % 12.13/2.59 | | | | % 12.13/2.59 | | | | DELTA: instantiating (48) with fresh symbols all_73_0, all_73_1 gives: % 12.13/2.59 | | | | (49) ~ (all_73_0 = 0) & element(all_73_1, all_35_0) = 0 & % 12.13/2.59 | | | | related(all_25_1, all_27_2, all_73_1) = all_73_0 & in(all_73_1, % 12.13/2.59 | | | | empty_set) = 0 & $i(all_73_1) % 12.13/2.59 | | | | % 12.13/2.59 | | | | ALPHA: (49) implies: % 12.13/2.60 | | | | (50) $i(all_73_1) % 12.13/2.60 | | | | (51) in(all_73_1, empty_set) = 0 % 12.13/2.60 | | | | % 12.13/2.60 | | | | GROUND_INST: instantiating (t7_boole) with all_73_1, empty_set, % 12.13/2.60 | | | | simplifying with (2), (50), (51) gives: % 12.13/2.60 | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0) % 12.13/2.60 | | | | % 12.13/2.60 | | | | DELTA: instantiating (52) with fresh symbol all_83_0 gives: % 12.13/2.60 | | | | (53) ~ (all_83_0 = 0) & empty(empty_set) = all_83_0 % 12.13/2.60 | | | | % 12.13/2.60 | | | | ALPHA: (53) implies: % 12.13/2.60 | | | | (54) ~ (all_83_0 = 0) % 12.13/2.60 | | | | (55) empty(empty_set) = all_83_0 % 12.13/2.60 | | | | % 12.13/2.60 | | | | GROUND_INST: instantiating (4) with 0, all_83_0, empty_set, simplifying % 12.13/2.60 | | | | with (32), (55) gives: % 12.13/2.60 | | | | (56) all_83_0 = 0 % 12.13/2.60 | | | | % 12.13/2.60 | | | | REDUCE: (54), (56) imply: % 12.13/2.60 | | | | (57) $false % 12.13/2.60 | | | | % 12.13/2.60 | | | | CLOSE: (57) is inconsistent. % 12.13/2.60 | | | | % 12.13/2.60 | | | End of split % 12.13/2.60 | | | % 12.13/2.60 | | End of split % 12.13/2.60 | | % 12.13/2.60 | Case 2: % 12.13/2.60 | | % 12.13/2.60 | | (58) ~ (all_27_1 = 0) % 12.13/2.60 | | % 12.13/2.60 | | BETA: splitting (31) gives: % 12.13/2.60 | | % 12.13/2.60 | | Case 1: % 12.13/2.60 | | | % 12.13/2.60 | | | (59) ? [v0: int] : ( ~ (v0 = 0) & element(all_27_2, all_38_0) = v0) % 12.13/2.60 | | | % 12.13/2.60 | | | DELTA: instantiating (59) with fresh symbol all_71_0 gives: % 12.13/2.60 | | | (60) ~ (all_71_0 = 0) & element(all_27_2, all_38_0) = all_71_0 % 12.13/2.60 | | | % 12.13/2.60 | | | ALPHA: (60) implies: % 12.13/2.60 | | | (61) ~ (all_71_0 = 0) % 12.13/2.60 | | | (62) element(all_27_2, all_38_0) = all_71_0 % 12.13/2.60 | | | % 12.13/2.60 | | | REDUCE: (33), (62) imply: % 12.13/2.60 | | | (63) element(all_27_2, all_25_0) = all_71_0 % 12.13/2.60 | | | % 12.13/2.60 | | | GROUND_INST: instantiating (6) with 0, all_71_0, all_25_0, all_27_2, % 12.13/2.60 | | | simplifying with (17), (63) gives: % 12.13/2.60 | | | (64) all_71_0 = 0 % 12.13/2.60 | | | % 12.13/2.60 | | | REDUCE: (61), (64) imply: % 12.13/2.60 | | | (65) $false % 12.13/2.60 | | | % 12.13/2.60 | | | CLOSE: (65) is inconsistent. % 12.13/2.60 | | | % 12.13/2.60 | | Case 2: % 12.13/2.60 | | | % 12.13/2.61 | | | (66) ( ~ (all_27_1 = 0) | ! [v0: $i] : ( ~ (element(v0, all_38_0) = 0) % 12.13/2.61 | | | | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (related(all_25_1, % 12.13/2.61 | | | v0, all_27_2) = v2 & in(v0, empty_set) = v1 & ( ~ (v1 = 0) % 12.13/2.61 | | | | v2 = 0)))) & (all_27_1 = 0 | ? [v0: $i] : ? [v1: int] % 12.13/2.61 | | | : ( ~ (v1 = 0) & element(v0, all_38_0) = 0 & related(all_25_1, % 12.13/2.61 | | | v0, all_27_2) = v1 & in(v0, empty_set) = 0 & $i(v0))) % 12.13/2.61 | | | % 12.13/2.61 | | | ALPHA: (66) implies: % 12.13/2.61 | | | (67) all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.13/2.61 | | | element(v0, all_38_0) = 0 & related(all_25_1, v0, all_27_2) = v1 % 12.13/2.61 | | | & in(v0, empty_set) = 0 & $i(v0)) % 12.13/2.61 | | | % 12.13/2.61 | | | BETA: splitting (67) gives: % 12.13/2.61 | | | % 12.13/2.61 | | | Case 1: % 12.13/2.61 | | | | % 12.13/2.61 | | | | (68) all_27_1 = 0 % 12.13/2.61 | | | | % 12.13/2.61 | | | | REDUCE: (58), (68) imply: % 12.13/2.61 | | | | (69) $false % 12.13/2.61 | | | | % 12.13/2.61 | | | | CLOSE: (69) is inconsistent. % 12.13/2.61 | | | | % 12.13/2.61 | | | Case 2: % 12.13/2.61 | | | | % 12.13/2.61 | | | | (70) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, % 12.13/2.61 | | | | all_38_0) = 0 & related(all_25_1, v0, all_27_2) = v1 & % 12.13/2.61 | | | | in(v0, empty_set) = 0 & $i(v0)) % 12.13/2.61 | | | | % 12.13/2.61 | | | | DELTA: instantiating (70) with fresh symbols all_78_0, all_78_1 gives: % 12.13/2.61 | | | | (71) ~ (all_78_0 = 0) & element(all_78_1, all_38_0) = 0 & % 12.13/2.61 | | | | related(all_25_1, all_78_1, all_27_2) = all_78_0 & in(all_78_1, % 12.13/2.61 | | | | empty_set) = 0 & $i(all_78_1) % 12.13/2.61 | | | | % 12.13/2.61 | | | | ALPHA: (71) implies: % 12.13/2.61 | | | | (72) $i(all_78_1) % 12.13/2.61 | | | | (73) in(all_78_1, empty_set) = 0 % 12.13/2.61 | | | | % 12.13/2.61 | | | | GROUND_INST: instantiating (t7_boole) with all_78_1, empty_set, % 12.13/2.61 | | | | simplifying with (2), (72), (73) gives: % 12.13/2.61 | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0) % 12.13/2.61 | | | | % 12.13/2.61 | | | | DELTA: instantiating (74) with fresh symbol all_88_0 gives: % 12.13/2.61 | | | | (75) ~ (all_88_0 = 0) & empty(empty_set) = all_88_0 % 12.13/2.61 | | | | % 12.13/2.61 | | | | ALPHA: (75) implies: % 12.13/2.61 | | | | (76) ~ (all_88_0 = 0) % 12.13/2.62 | | | | (77) empty(empty_set) = all_88_0 % 12.13/2.62 | | | | % 12.13/2.62 | | | | GROUND_INST: instantiating (4) with 0, all_88_0, empty_set, simplifying % 12.13/2.62 | | | | with (32), (77) gives: % 12.13/2.62 | | | | (78) all_88_0 = 0 % 12.13/2.62 | | | | % 12.13/2.62 | | | | REDUCE: (76), (78) imply: % 12.13/2.62 | | | | (79) $false % 12.13/2.62 | | | | % 12.13/2.62 | | | | CLOSE: (79) is inconsistent. % 12.13/2.62 | | | | % 12.13/2.62 | | | End of split % 12.13/2.62 | | | % 12.13/2.62 | | End of split % 12.13/2.62 | | % 12.13/2.62 | End of split % 12.13/2.62 | % 12.13/2.62 End of proof % 12.13/2.62 % SZS output end Proof for theBenchmark % 12.13/2.62 % 12.13/2.62 2004ms %------------------------------------------------------------------------------