%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV174+1 : TPTP v8.1.2. Bugfixed v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 22:55:13 EDT 2023 % Result : Theorem 16.16s 2.87s % Output : Proof 19.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SWV174+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.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 : Tue Aug 29 07:15:20 EDT 2023 % 0.13/0.34 % CPUTime : % 0.64/0.61 ________ _____ % 0.64/0.61 ___ __ \_________(_)________________________________ % 0.64/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.64/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.64/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.64/0.61 % 0.64/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.64/0.61 (2023-06-19) % 0.64/0.61 % 0.64/0.61 (c) Philipp Rümmer, 2009-2023 % 0.64/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.64/0.61 Amanda Stjerna. % 0.64/0.61 Free software under BSD-3-Clause. % 0.64/0.61 % 0.64/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.64/0.61 % 0.64/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.64/0.62 Running up to 7 provers in parallel. % 0.64/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.64/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.64/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.64/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.64/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.64/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.64/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.11/1.44 Prover 1: Preprocessing ... % 5.11/1.44 Prover 4: Preprocessing ... % 5.70/1.47 Prover 2: Preprocessing ... % 5.70/1.47 Prover 0: Preprocessing ... % 5.70/1.47 Prover 6: Preprocessing ... % 5.70/1.47 Prover 3: Preprocessing ... % 5.70/1.47 Prover 5: Preprocessing ... % 10.60/2.10 Prover 1: Warning: ignoring some quantifiers % 11.54/2.22 Prover 1: Constructing countermodel ... % 11.54/2.27 Prover 3: Warning: ignoring some quantifiers % 12.07/2.29 Prover 3: Constructing countermodel ... % 12.07/2.30 Prover 6: Proving ... % 12.07/2.35 Prover 4: Warning: ignoring some quantifiers % 13.06/2.49 Prover 4: Constructing countermodel ... % 13.73/2.52 Prover 5: Proving ... % 13.73/2.52 Prover 0: Proving ... % 13.73/2.55 Prover 2: Proving ... % 16.16/2.87 Prover 3: proved (2237ms) % 16.16/2.87 % 16.16/2.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.16/2.87 % 16.16/2.87 Prover 2: stopped % 16.16/2.87 Prover 6: stopped % 16.16/2.87 Prover 0: stopped % 16.16/2.88 Prover 5: stopped % 16.16/2.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.16/2.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.16/2.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.16/2.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.16/2.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.42/3.07 Prover 7: Preprocessing ... % 17.42/3.07 Prover 11: Preprocessing ... % 18.11/3.08 Prover 10: Preprocessing ... % 18.11/3.08 Prover 1: Found proof (size 29) % 18.11/3.08 Prover 1: proved (2455ms) % 18.11/3.08 Prover 4: stopped % 18.11/3.09 Prover 8: Preprocessing ... % 18.25/3.09 Prover 13: Preprocessing ... % 18.43/3.14 Prover 10: stopped % 18.43/3.14 Prover 7: stopped % 18.43/3.17 Prover 11: stopped % 18.43/3.18 Prover 13: stopped % 18.98/3.26 Prover 8: Warning: ignoring some quantifiers % 19.34/3.28 Prover 8: Constructing countermodel ... % 19.34/3.30 Prover 8: stopped % 19.34/3.30 % 19.34/3.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.34/3.30 % 19.34/3.30 % SZS output start Proof for theBenchmark % 19.34/3.31 Assumptions after simplification: % 19.34/3.31 --------------------------------- % 19.34/3.31 % 19.34/3.31 (cl5_nebula_init_0046) % 19.34/3.34 $i(center_init) & $i(init) & $i(q_init) & $i(n135299) & $i(pv10) & $i(n4) & % 19.34/3.34 $i(n0) & ? [v0: $i] : (pred(pv10) = v0 & leq(pv10, n135299) = 0 & leq(n0, % 19.34/3.34 pv10) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 19.34/3.34 (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 19.34/3.34 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 19.34/3.34 0)))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) | ~ $i(v1) | ? [v2: % 19.34/3.34 int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] : % 19.34/3.34 (v3 = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4: % 19.34/3.34 any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = % 19.34/3.34 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( % 19.34/3.34 ~ (v3 = init) & a_select3(q_init, v1, v2) = v3 & leq(v2, n4) = 0 & leq(v1, % 19.34/3.34 n135299) = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & gt(pv10, v1) = 0 & % 19.34/3.34 $i(v3) & $i(v2) & $i(v1))) % 19.34/3.34 % 19.34/3.34 (leq_succ_gt_equiv) % 19.34/3.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.34/3.34 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 19.34/3.34 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 19.34/3.34 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 19.34/3.34 leq(v0, v1) = 0) % 19.34/3.34 % 19.34/3.34 (succ_pred) % 19.34/3.34 ! [v0: $i] : ! [v1: $i] : ( ~ (pred(v0) = v1) | ~ $i(v0) | succ(v1) = v0) % 19.34/3.34 % 19.34/3.34 (function-axioms) % 19.34/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.34/3.35 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.34/3.35 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.34/3.35 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.34/3.35 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.34/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.34/3.35 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.34/3.35 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.34/3.35 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.34/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.34/3.35 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.34/3.35 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 19.34/3.35 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.34/3.35 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 19.34/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 19.34/3.35 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.34/3.35 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 19.34/3.35 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.34/3.35 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 19.34/3.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 19.34/3.35 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.34/3.35 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 19.34/3.35 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.34/3.35 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 19.34/3.35 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.34/3.35 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 19.34/3.35 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.34/3.35 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.34/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.34/3.35 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.34/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.34/3.35 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.34/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.34/3.35 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.34/3.35 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 19.34/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 19.34/3.35 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.34/3.35 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.34/3.35 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 19.34/3.35 % 19.34/3.35 Further assumptions not needed in the proof: % 19.34/3.35 -------------------------------------------- % 19.34/3.35 const_array1_select, const_array2_select, defuse, finite_domain_0, % 19.34/3.35 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 19.34/3.35 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, % 19.34/3.35 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, % 19.34/3.35 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, % 19.34/3.35 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, % 19.34/3.35 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 19.34/3.35 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, % 19.34/3.35 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 19.34/3.35 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.34/3.35 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 19.34/3.35 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 19.34/3.35 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 19.34/3.35 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 19.34/3.35 succ_plus_5_r, succ_tptp_minus_1, successor_1, successor_2, successor_3, % 19.34/3.35 successor_4, successor_5, sum_plus_base, sum_plus_base_float, totality, % 19.34/3.35 transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 19.34/3.35 uniform_int_rand_ranges_lo % 19.34/3.35 % 19.34/3.35 Those formulas are unsatisfiable: % 19.34/3.35 --------------------------------- % 19.34/3.35 % 19.34/3.35 Begin of proof % 19.34/3.35 | % 19.34/3.35 | ALPHA: (leq_succ_gt_equiv) implies: % 19.34/3.36 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 19.34/3.36 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0) % 19.34/3.36 | % 19.34/3.36 | ALPHA: (cl5_nebula_init_0046) implies: % 19.34/3.36 | (2) $i(pv10) % 19.34/3.36 | (3) ? [v0: $i] : (pred(pv10) = v0 & leq(pv10, n135299) = 0 & leq(n0, pv10) % 19.34/3.36 | = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 19.34/3.36 | (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | ? [v3: any] : % 19.34/3.36 | ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 19.34/3.36 | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) | ~ % 19.34/3.36 | $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: % 19.34/3.36 | $i] : ! [v3: $i] : (v3 = init | ~ (a_select3(q_init, v1, v2) = % 19.34/3.36 | v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : (leq(v2, n4) = % 19.34/3.36 | v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ? % 19.34/3.36 | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = init) & % 19.34/3.36 | a_select3(q_init, v1, v2) = v3 & leq(v2, n4) = 0 & leq(v1, n135299) % 19.34/3.36 | = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & gt(pv10, v1) = 0 & $i(v3) % 19.34/3.36 | & $i(v2) & $i(v1))) % 19.34/3.36 | % 19.34/3.36 | ALPHA: (function-axioms) implies: % 19.34/3.36 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.34/3.36 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 19.34/3.36 | % 19.34/3.36 | DELTA: instantiating (3) with fresh symbol all_67_0 gives: % 19.34/3.36 | (5) pred(pv10) = all_67_0 & leq(pv10, n135299) = 0 & leq(n0, pv10) = 0 & % 19.34/3.36 | $i(all_67_0) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 19.34/3.36 | (a_select3(center_init, v0, n0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 19.34/3.36 | [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 19.34/3.36 | (v2 = 0)))) & ! [v0: $i] : ( ~ (leq(v0, all_67_0) = 0) | ~ % 19.34/3.36 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: % 19.34/3.36 | $i] : ! [v2: $i] : (v2 = init | ~ (a_select3(q_init, v0, v1) = % 19.34/3.36 | v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 % 19.34/3.36 | & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ? [v0: $i] % 19.34/3.36 | : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & a_select3(q_init, v0, % 19.34/3.36 | v1) = v2 & leq(v1, n4) = 0 & leq(v0, n135299) = 0 & leq(n0, v1) = 0 % 19.34/3.36 | & leq(n0, v0) = 0 & gt(pv10, v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 19.34/3.36 | % 19.34/3.36 | ALPHA: (5) implies: % 19.34/3.37 | (6) $i(all_67_0) % 19.34/3.37 | (7) pred(pv10) = all_67_0 % 19.34/3.37 | (8) ! [v0: $i] : ( ~ (leq(v0, all_67_0) = 0) | ~ $i(v0) | ? [v1: int] : % 19.34/3.37 | ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = % 19.34/3.37 | init | ~ (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) | ? [v3: % 19.34/3.37 | any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ % 19.34/3.37 | (v4 = 0) | ~ (v3 = 0))))) % 19.34/3.37 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 19.34/3.37 | a_select3(q_init, v0, v1) = v2 & leq(v1, n4) = 0 & leq(v0, n135299) = % 19.34/3.37 | 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & gt(pv10, v0) = 0 & $i(v2) & % 19.34/3.37 | $i(v1) & $i(v0)) % 19.34/3.37 | % 19.34/3.37 | DELTA: instantiating (9) with fresh symbols all_79_0, all_79_1, all_79_2 % 19.34/3.37 | gives: % 19.34/3.37 | (10) ~ (all_79_0 = init) & a_select3(q_init, all_79_2, all_79_1) = % 19.34/3.37 | all_79_0 & leq(all_79_1, n4) = 0 & leq(all_79_2, n135299) = 0 & % 19.34/3.37 | leq(n0, all_79_1) = 0 & leq(n0, all_79_2) = 0 & gt(pv10, all_79_2) = 0 % 19.34/3.37 | & $i(all_79_0) & $i(all_79_1) & $i(all_79_2) % 19.34/3.37 | % 19.34/3.37 | ALPHA: (10) implies: % 19.34/3.37 | (11) ~ (all_79_0 = init) % 19.34/3.37 | (12) $i(all_79_2) % 19.34/3.37 | (13) $i(all_79_1) % 19.34/3.37 | (14) gt(pv10, all_79_2) = 0 % 19.34/3.37 | (15) leq(n0, all_79_2) = 0 % 19.34/3.37 | (16) leq(n0, all_79_1) = 0 % 19.34/3.37 | (17) leq(all_79_1, n4) = 0 % 19.34/3.37 | (18) a_select3(q_init, all_79_2, all_79_1) = all_79_0 % 19.34/3.37 | % 19.34/3.37 | GROUND_INST: instantiating (succ_pred) with pv10, all_67_0, simplifying with % 19.34/3.37 | (2), (7) gives: % 19.34/3.37 | (19) succ(all_67_0) = pv10 % 19.34/3.37 | % 19.34/3.37 | GROUND_INST: instantiating (1) with all_79_2, all_67_0, pv10, simplifying with % 19.34/3.37 | (6), (12), (14), (19) gives: % 19.34/3.37 | (20) leq(all_79_2, all_67_0) = 0 % 19.34/3.37 | % 19.34/3.37 | GROUND_INST: instantiating (8) with all_79_2, simplifying with (12), (20) % 19.34/3.37 | gives: % 19.34/3.37 | (21) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_79_2) = v0) | ! [v0: $i] : % 19.34/3.37 | ! [v1: $i] : (v1 = init | ~ (a_select3(q_init, all_79_2, v0) = v1) | % 19.34/3.37 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, % 19.34/3.37 | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 19.34/3.37 | % 19.34/3.37 | BETA: splitting (21) gives: % 19.34/3.37 | % 19.34/3.37 | Case 1: % 19.34/3.37 | | % 19.80/3.38 | | (22) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_79_2) = v0) % 19.80/3.38 | | % 19.80/3.38 | | DELTA: instantiating (22) with fresh symbol all_118_0 gives: % 19.80/3.38 | | (23) ~ (all_118_0 = 0) & leq(n0, all_79_2) = all_118_0 % 19.80/3.38 | | % 19.80/3.38 | | ALPHA: (23) implies: % 19.80/3.38 | | (24) ~ (all_118_0 = 0) % 19.80/3.38 | | (25) leq(n0, all_79_2) = all_118_0 % 19.80/3.38 | | % 19.80/3.38 | | GROUND_INST: instantiating (4) with 0, all_118_0, all_79_2, n0, simplifying % 19.80/3.38 | | with (15), (25) gives: % 19.80/3.38 | | (26) all_118_0 = 0 % 19.80/3.38 | | % 19.80/3.38 | | REDUCE: (24), (26) imply: % 19.80/3.38 | | (27) $false % 19.80/3.38 | | % 19.80/3.38 | | CLOSE: (27) is inconsistent. % 19.80/3.38 | | % 19.80/3.38 | Case 2: % 19.80/3.38 | | % 19.80/3.38 | | (28) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(q_init, % 19.80/3.38 | | all_79_2, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 19.80/3.38 | | : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = % 19.80/3.38 | | 0)))) % 19.80/3.38 | | % 19.80/3.38 | | GROUND_INST: instantiating (28) with all_79_1, all_79_0, simplifying with % 19.80/3.38 | | (13), (18) gives: % 19.80/3.38 | | (29) all_79_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = % 19.80/3.38 | | v1 & leq(n0, all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 19.80/3.38 | | % 19.80/3.38 | | BETA: splitting (29) gives: % 19.80/3.38 | | % 19.80/3.38 | | Case 1: % 19.80/3.38 | | | % 19.80/3.38 | | | (30) all_79_0 = init % 19.80/3.38 | | | % 19.80/3.38 | | | REDUCE: (11), (30) imply: % 19.80/3.38 | | | (31) $false % 19.80/3.38 | | | % 19.80/3.38 | | | CLOSE: (31) is inconsistent. % 19.80/3.38 | | | % 19.80/3.38 | | Case 2: % 19.80/3.38 | | | % 19.80/3.38 | | | (32) ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = v1 & leq(n0, % 19.80/3.38 | | | all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 19.80/3.38 | | | % 19.80/3.38 | | | DELTA: instantiating (32) with fresh symbols all_122_0, all_122_1 gives: % 19.80/3.38 | | | (33) leq(all_79_1, n4) = all_122_0 & leq(n0, all_79_1) = all_122_1 & ( % 19.80/3.38 | | | ~ (all_122_0 = 0) | ~ (all_122_1 = 0)) % 19.80/3.38 | | | % 19.80/3.38 | | | ALPHA: (33) implies: % 19.80/3.38 | | | (34) leq(n0, all_79_1) = all_122_1 % 19.80/3.38 | | | (35) leq(all_79_1, n4) = all_122_0 % 19.80/3.38 | | | (36) ~ (all_122_0 = 0) | ~ (all_122_1 = 0) % 19.80/3.38 | | | % 19.80/3.38 | | | GROUND_INST: instantiating (4) with 0, all_122_1, all_79_1, n0, % 19.80/3.38 | | | simplifying with (16), (34) gives: % 19.80/3.38 | | | (37) all_122_1 = 0 % 19.80/3.38 | | | % 19.80/3.38 | | | GROUND_INST: instantiating (4) with 0, all_122_0, n4, all_79_1, % 19.80/3.38 | | | simplifying with (17), (35) gives: % 19.80/3.38 | | | (38) all_122_0 = 0 % 19.80/3.38 | | | % 19.80/3.38 | | | BETA: splitting (36) gives: % 19.80/3.38 | | | % 19.80/3.38 | | | Case 1: % 19.80/3.38 | | | | % 19.80/3.38 | | | | (39) ~ (all_122_0 = 0) % 19.80/3.38 | | | | % 19.80/3.38 | | | | REDUCE: (38), (39) imply: % 19.80/3.38 | | | | (40) $false % 19.80/3.38 | | | | % 19.80/3.38 | | | | CLOSE: (40) is inconsistent. % 19.80/3.38 | | | | % 19.80/3.38 | | | Case 2: % 19.80/3.38 | | | | % 19.80/3.38 | | | | (41) ~ (all_122_1 = 0) % 19.80/3.38 | | | | % 19.80/3.38 | | | | REDUCE: (37), (41) imply: % 19.80/3.38 | | | | (42) $false % 19.80/3.38 | | | | % 19.80/3.38 | | | | CLOSE: (42) is inconsistent. % 19.80/3.38 | | | | % 19.80/3.38 | | | End of split % 19.80/3.38 | | | % 19.80/3.38 | | End of split % 19.80/3.38 | | % 19.80/3.38 | End of split % 19.80/3.38 | % 19.80/3.38 End of proof % 19.80/3.38 % SZS output end Proof for theBenchmark % 19.80/3.38 % 19.80/3.38 2773ms %------------------------------------------------------------------------------