%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV385+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 : n027.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 22:56:07 EDT 2023 % Result : Theorem 8.96s 1.94s % Output : Proof 10.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWV385+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n027.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 04:03:38 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.59 ________ _____ % 0.21/0.59 ___ __ \_________(_)________________________________ % 0.21/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.59 % 0.21/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.59 (2023-06-19) % 0.21/0.59 % 0.21/0.59 (c) Philipp Rümmer, 2009-2023 % 0.21/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.59 Amanda Stjerna. % 0.21/0.59 Free software under BSD-3-Clause. % 0.21/0.59 % 0.21/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.59 % 0.21/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.37/1.16 Prover 1: Preprocessing ... % 3.37/1.17 Prover 4: Preprocessing ... % 3.67/1.20 Prover 6: Preprocessing ... % 3.67/1.20 Prover 3: Preprocessing ... % 3.67/1.21 Prover 0: Preprocessing ... % 3.67/1.21 Prover 2: Preprocessing ... % 3.67/1.21 Prover 5: Preprocessing ... % 6.79/1.67 Prover 1: Warning: ignoring some quantifiers % 7.53/1.75 Prover 3: Warning: ignoring some quantifiers % 7.53/1.78 Prover 3: Constructing countermodel ... % 7.53/1.78 Prover 5: Proving ... % 7.53/1.78 Prover 6: Proving ... % 7.98/1.80 Prover 0: Proving ... % 7.98/1.80 Prover 1: Constructing countermodel ... % 7.98/1.81 Prover 4: Constructing countermodel ... % 7.98/1.81 Prover 2: Proving ... % 8.74/1.92 Prover 5: proved (1308ms) % 8.74/1.93 % 8.96/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.96/1.94 % 8.96/1.94 Prover 6: proved (1313ms) % 8.96/1.94 % 8.96/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.96/1.94 % 8.96/1.94 Prover 3: stopped % 8.96/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.96/1.95 Prover 0: stopped % 8.96/1.95 Prover 2: stopped % 8.96/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.96/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.96/1.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.96/1.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.96/1.99 Prover 7: Preprocessing ... % 8.96/1.99 Prover 4: Found proof (size 39) % 8.96/1.99 Prover 4: proved (1375ms) % 8.96/1.99 Prover 1: Found proof (size 39) % 8.96/1.99 Prover 1: proved (1377ms) % 8.96/2.01 Prover 8: Preprocessing ... % 8.96/2.02 Prover 10: Preprocessing ... % 8.96/2.02 Prover 11: Preprocessing ... % 8.96/2.02 Prover 13: Preprocessing ... % 8.96/2.03 Prover 7: stopped % 8.96/2.05 Prover 10: stopped % 8.96/2.06 Prover 11: stopped % 8.96/2.08 Prover 13: stopped % 8.96/2.12 Prover 8: Warning: ignoring some quantifiers % 10.03/2.14 Prover 8: Constructing countermodel ... % 10.03/2.15 Prover 8: stopped % 10.03/2.15 % 10.03/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.03/2.15 % 10.03/2.16 % SZS output start Proof for theBenchmark % 10.03/2.17 Assumptions after simplification: % 10.03/2.17 --------------------------------- % 10.03/2.17 % 10.03/2.17 (l21_co) % 10.03/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 10.03/2.19 any] : ? [v6: $i] : (im_succ_cpq(v3) = v6 & ok(v6) = 0 & ok(v3) = v5 & % 10.03/2.19 triple(v0, v1, v2) = v3 & check_cpq(v6) = 0 & check_cpq(v3) = v4 & $i(v6) & % 10.03/2.19 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v5 = 0) | ~ (v4 = 0))) % 10.03/2.19 % 10.03/2.19 (l21_li1316) % 10.03/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, % 10.03/2.20 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 10.03/2.20 $i] : ? [v6: any] : (im_succ_cpq(v3) = v5 & ok(v5) = v6 & ok(v3) = v4 & % 10.03/2.20 $i(v5) & ( ~ (v6 = 0) | v4 = 0))) % 10.03/2.20 % 10.03/2.20 (l21_li2225) % 10.03/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, % 10.03/2.20 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 10.03/2.20 $i] : ? [v6: any] : ? [v7: any] : (im_succ_cpq(v3) = v5 & ok(v5) = v7 & % 10.03/2.20 check_cpq(v5) = v6 & check_cpq(v3) = v4 & $i(v5) & ( ~ (v7 = 0) | ~ (v6 = % 10.03/2.20 0) | v4 = 0))) % 10.03/2.20 % 10.03/2.20 (function-axioms) % 10.63/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 10.63/2.21 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 10.63/2.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.63/2.21 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 10.63/2.21 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 10.63/2.21 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 10.63/2.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 10.63/2.21 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 10.63/2.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.63/2.21 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 10.63/2.21 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.63/2.21 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 10.63/2.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 10.63/2.21 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.63/2.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 10.63/2.21 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 10.63/2.21 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 10.63/2.21 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 10.63/2.21 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 10.63/2.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 10.63/2.21 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 10.63/2.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.63/2.21 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 10.63/2.21 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.63/2.21 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 10.63/2.21 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 10.63/2.21 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.63/2.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.63/2.21 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 10.63/2.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.63/2.21 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 10.63/2.21 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (im_succ_cpq(v2) = % 10.63/2.21 v1) | ~ (im_succ_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 10.63/2.21 : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = % 10.63/2.21 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 10.63/2.21 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : % 10.63/2.21 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ % 10.63/2.21 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.63/2.21 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) % 10.63/2.21 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.63/2.21 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & ! % 10.63/2.21 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = % 10.63/2.21 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 10.63/2.21 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) % 10.63/2.21 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.63/2.21 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = % 10.63/2.21 v0)) % 10.63/2.21 % 10.63/2.21 Further assumptions not needed in the proof: % 10.63/2.21 -------------------------------------------- % 10.63/2.21 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 10.63/2.21 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax40, ax41, ax42, ax43, % 10.63/2.21 ax44, ax45, ax46, ax47, ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest, % 10.63/2.21 reflexivity, stricly_smaller_definition, totality, transitivity % 10.63/2.21 % 10.63/2.21 Those formulas are unsatisfiable: % 10.63/2.21 --------------------------------- % 10.63/2.21 % 10.63/2.21 Begin of proof % 10.63/2.22 | % 10.63/2.22 | ALPHA: (function-axioms) implies: % 10.63/2.22 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.63/2.22 | (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) % 10.63/2.22 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.63/2.22 | (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 10.63/2.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 10.63/2.22 | (im_succ_cpq(v2) = v1) | ~ (im_succ_cpq(v2) = v0)) % 10.63/2.22 | % 10.63/2.22 | DELTA: instantiating (l21_co) with fresh symbols all_48_0, all_48_1, all_48_2, % 10.63/2.22 | all_48_3, all_48_4, all_48_5, all_48_6 gives: % 10.63/2.22 | (4) im_succ_cpq(all_48_3) = all_48_0 & ok(all_48_0) = 0 & ok(all_48_3) = % 10.63/2.22 | all_48_1 & triple(all_48_6, all_48_5, all_48_4) = all_48_3 & % 10.63/2.22 | check_cpq(all_48_0) = 0 & check_cpq(all_48_3) = all_48_2 & $i(all_48_0) % 10.63/2.22 | & $i(all_48_3) & $i(all_48_4) & $i(all_48_5) & $i(all_48_6) & ( ~ % 10.63/2.22 | (all_48_1 = 0) | ~ (all_48_2 = 0)) % 10.63/2.22 | % 10.63/2.22 | ALPHA: (4) implies: % 10.63/2.22 | (5) $i(all_48_6) % 10.63/2.22 | (6) $i(all_48_5) % 10.63/2.22 | (7) $i(all_48_4) % 10.63/2.22 | (8) check_cpq(all_48_3) = all_48_2 % 10.63/2.22 | (9) check_cpq(all_48_0) = 0 % 10.63/2.22 | (10) triple(all_48_6, all_48_5, all_48_4) = all_48_3 % 10.63/2.22 | (11) ok(all_48_3) = all_48_1 % 10.63/2.22 | (12) ok(all_48_0) = 0 % 10.63/2.22 | (13) im_succ_cpq(all_48_3) = all_48_0 % 10.63/2.22 | (14) ~ (all_48_1 = 0) | ~ (all_48_2 = 0) % 10.63/2.22 | % 10.63/2.22 | GROUND_INST: instantiating (l21_li2225) with all_48_6, all_48_5, all_48_4, % 10.63/2.22 | all_48_3, simplifying with (5), (6), (7), (10) gives: % 10.63/2.23 | (15) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 10.63/2.23 | (im_succ_cpq(all_48_3) = v1 & ok(v1) = v3 & check_cpq(v1) = v2 & % 10.63/2.23 | check_cpq(all_48_3) = v0 & $i(v1) & ( ~ (v3 = 0) | ~ (v2 = 0) | v0 % 10.63/2.23 | = 0)) % 10.63/2.23 | % 10.63/2.23 | GROUND_INST: instantiating (l21_li1316) with all_48_6, all_48_5, all_48_4, % 10.63/2.23 | all_48_3, simplifying with (5), (6), (7), (10) gives: % 10.63/2.23 | (16) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (im_succ_cpq(all_48_3) = % 10.63/2.23 | v1 & ok(v1) = v2 & ok(all_48_3) = v0 & $i(v1) & ( ~ (v2 = 0) | v0 = % 10.63/2.23 | 0)) % 10.63/2.23 | % 10.63/2.23 | DELTA: instantiating (16) with fresh symbols all_55_0, all_55_1, all_55_2 % 10.63/2.23 | gives: % 10.63/2.23 | (17) im_succ_cpq(all_48_3) = all_55_1 & ok(all_55_1) = all_55_0 & % 10.63/2.23 | ok(all_48_3) = all_55_2 & $i(all_55_1) & ( ~ (all_55_0 = 0) | all_55_2 % 10.63/2.23 | = 0) % 10.63/2.23 | % 10.63/2.23 | ALPHA: (17) implies: % 10.63/2.23 | (18) ok(all_48_3) = all_55_2 % 10.63/2.23 | (19) ok(all_55_1) = all_55_0 % 10.63/2.23 | (20) im_succ_cpq(all_48_3) = all_55_1 % 10.63/2.23 | (21) ~ (all_55_0 = 0) | all_55_2 = 0 % 10.63/2.23 | % 10.63/2.23 | DELTA: instantiating (15) with fresh symbols all_57_0, all_57_1, all_57_2, % 10.63/2.23 | all_57_3 gives: % 10.63/2.23 | (22) im_succ_cpq(all_48_3) = all_57_2 & ok(all_57_2) = all_57_0 & % 10.63/2.23 | check_cpq(all_57_2) = all_57_1 & check_cpq(all_48_3) = all_57_3 & % 10.63/2.23 | $i(all_57_2) & ( ~ (all_57_0 = 0) | ~ (all_57_1 = 0) | all_57_3 = 0) % 10.63/2.23 | % 10.63/2.23 | ALPHA: (22) implies: % 10.63/2.23 | (23) check_cpq(all_48_3) = all_57_3 % 10.63/2.23 | (24) check_cpq(all_57_2) = all_57_1 % 10.63/2.23 | (25) ok(all_57_2) = all_57_0 % 10.63/2.23 | (26) im_succ_cpq(all_48_3) = all_57_2 % 10.63/2.23 | (27) ~ (all_57_0 = 0) | ~ (all_57_1 = 0) | all_57_3 = 0 % 10.63/2.23 | % 10.63/2.23 | GROUND_INST: instantiating (1) with all_48_2, all_57_3, all_48_3, simplifying % 10.63/2.23 | with (8), (23) gives: % 10.63/2.23 | (28) all_57_3 = all_48_2 % 10.63/2.23 | % 10.63/2.23 | GROUND_INST: instantiating (2) with all_48_1, all_55_2, all_48_3, simplifying % 10.63/2.23 | with (11), (18) gives: % 10.63/2.23 | (29) all_55_2 = all_48_1 % 10.63/2.23 | % 10.63/2.23 | GROUND_INST: instantiating (3) with all_48_0, all_57_2, all_48_3, simplifying % 10.63/2.23 | with (13), (26) gives: % 10.63/2.23 | (30) all_57_2 = all_48_0 % 10.63/2.23 | % 10.63/2.23 | GROUND_INST: instantiating (3) with all_55_1, all_57_2, all_48_3, simplifying % 10.63/2.23 | with (20), (26) gives: % 10.63/2.23 | (31) all_57_2 = all_55_1 % 10.63/2.23 | % 10.63/2.23 | COMBINE_EQS: (30), (31) imply: % 10.63/2.23 | (32) all_55_1 = all_48_0 % 10.63/2.23 | % 10.63/2.23 | REDUCE: (25), (30) imply: % 10.63/2.23 | (33) ok(all_48_0) = all_57_0 % 10.63/2.23 | % 10.63/2.23 | REDUCE: (19), (32) imply: % 10.63/2.23 | (34) ok(all_48_0) = all_55_0 % 10.63/2.23 | % 10.63/2.23 | REDUCE: (24), (30) imply: % 10.63/2.23 | (35) check_cpq(all_48_0) = all_57_1 % 10.63/2.23 | % 10.63/2.23 | GROUND_INST: instantiating (1) with 0, all_57_1, all_48_0, simplifying with % 10.63/2.23 | (9), (35) gives: % 10.63/2.23 | (36) all_57_1 = 0 % 10.63/2.23 | % 10.63/2.23 | GROUND_INST: instantiating (2) with 0, all_57_0, all_48_0, simplifying with % 10.63/2.23 | (12), (33) gives: % 10.63/2.23 | (37) all_57_0 = 0 % 10.63/2.23 | % 10.63/2.23 | GROUND_INST: instantiating (2) with all_55_0, all_57_0, all_48_0, simplifying % 10.63/2.23 | with (33), (34) gives: % 10.63/2.23 | (38) all_57_0 = all_55_0 % 10.63/2.23 | % 10.63/2.23 | COMBINE_EQS: (37), (38) imply: % 10.63/2.23 | (39) all_55_0 = 0 % 10.63/2.23 | % 10.63/2.23 | BETA: splitting (21) gives: % 10.63/2.23 | % 10.63/2.24 | Case 1: % 10.63/2.24 | | % 10.63/2.24 | | (40) ~ (all_55_0 = 0) % 10.63/2.24 | | % 10.63/2.24 | | REDUCE: (39), (40) imply: % 10.63/2.24 | | (41) $false % 10.63/2.24 | | % 10.63/2.24 | | CLOSE: (41) is inconsistent. % 10.63/2.24 | | % 10.63/2.24 | Case 2: % 10.63/2.24 | | % 10.63/2.24 | | (42) all_55_2 = 0 % 10.63/2.24 | | % 10.63/2.24 | | COMBINE_EQS: (29), (42) imply: % 10.63/2.24 | | (43) all_48_1 = 0 % 10.63/2.24 | | % 10.63/2.24 | | BETA: splitting (14) gives: % 10.63/2.24 | | % 10.63/2.24 | | Case 1: % 10.63/2.24 | | | % 10.63/2.24 | | | (44) ~ (all_48_1 = 0) % 10.63/2.24 | | | % 10.63/2.24 | | | REDUCE: (43), (44) imply: % 10.63/2.24 | | | (45) $false % 10.63/2.24 | | | % 10.63/2.24 | | | CLOSE: (45) is inconsistent. % 10.63/2.24 | | | % 10.63/2.24 | | Case 2: % 10.63/2.24 | | | % 10.63/2.24 | | | (46) ~ (all_48_2 = 0) % 10.63/2.24 | | | % 10.63/2.24 | | | BETA: splitting (27) gives: % 10.63/2.24 | | | % 10.63/2.24 | | | Case 1: % 10.63/2.24 | | | | % 10.63/2.24 | | | | (47) ~ (all_57_0 = 0) % 10.63/2.24 | | | | % 10.63/2.24 | | | | REDUCE: (37), (47) imply: % 10.63/2.24 | | | | (48) $false % 10.63/2.24 | | | | % 10.63/2.24 | | | | CLOSE: (48) is inconsistent. % 10.63/2.24 | | | | % 10.63/2.24 | | | Case 2: % 10.63/2.24 | | | | % 10.63/2.24 | | | | (49) ~ (all_57_1 = 0) | all_57_3 = 0 % 10.63/2.24 | | | | % 10.63/2.24 | | | | BETA: splitting (49) gives: % 10.63/2.24 | | | | % 10.63/2.24 | | | | Case 1: % 10.63/2.24 | | | | | % 10.63/2.24 | | | | | (50) ~ (all_57_1 = 0) % 10.63/2.24 | | | | | % 10.63/2.24 | | | | | REDUCE: (36), (50) imply: % 10.63/2.24 | | | | | (51) $false % 10.63/2.24 | | | | | % 10.63/2.24 | | | | | CLOSE: (51) is inconsistent. % 10.63/2.24 | | | | | % 10.63/2.24 | | | | Case 2: % 10.63/2.24 | | | | | % 10.63/2.24 | | | | | (52) all_57_3 = 0 % 10.63/2.24 | | | | | % 10.63/2.24 | | | | | COMBINE_EQS: (28), (52) imply: % 10.63/2.24 | | | | | (53) all_48_2 = 0 % 10.63/2.24 | | | | | % 10.63/2.24 | | | | | REDUCE: (46), (53) imply: % 10.63/2.24 | | | | | (54) $false % 10.63/2.24 | | | | | % 10.63/2.24 | | | | | CLOSE: (54) is inconsistent. % 10.63/2.24 | | | | | % 10.63/2.24 | | | | End of split % 10.63/2.24 | | | | % 10.63/2.24 | | | End of split % 10.63/2.24 | | | % 10.63/2.24 | | End of split % 10.63/2.24 | | % 10.63/2.24 | End of split % 10.63/2.24 | % 10.63/2.24 End of proof % 10.63/2.24 % SZS output end Proof for theBenchmark % 10.63/2.24 % 10.63/2.24 1645ms %------------------------------------------------------------------------------