%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV175+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 : n029.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 13.92s 2.84s % Output : Proof 18.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWV175+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n029.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 07:16:41 EDT 2023 % 0.12/0.34 % CPUTime : % 0.59/0.60 ________ _____ % 0.59/0.60 ___ __ \_________(_)________________________________ % 0.59/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.59/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.59/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.59/0.60 % 0.59/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.59/0.60 (2023-06-19) % 0.59/0.60 % 0.59/0.60 (c) Philipp Rümmer, 2009-2023 % 0.59/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.59/0.60 Amanda Stjerna. % 0.59/0.60 Free software under BSD-3-Clause. % 0.59/0.60 % 0.59/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.59/0.60 % 0.59/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.59/0.61 Running up to 7 provers in parallel. % 0.59/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.59/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.59/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.59/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.59/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.59/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.59/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 4.29/1.41 Prover 1: Preprocessing ... % 4.29/1.41 Prover 4: Preprocessing ... % 4.29/1.44 Prover 6: Preprocessing ... % 4.29/1.44 Prover 3: Preprocessing ... % 4.29/1.44 Prover 2: Preprocessing ... % 4.29/1.44 Prover 0: Preprocessing ... % 4.29/1.44 Prover 5: Preprocessing ... % 11.00/2.36 Prover 1: Warning: ignoring some quantifiers % 11.00/2.40 Prover 3: Warning: ignoring some quantifiers % 11.65/2.46 Prover 3: Constructing countermodel ... % 11.88/2.51 Prover 1: Constructing countermodel ... % 11.88/2.52 Prover 6: Proving ... % 12.14/2.55 Prover 4: Warning: ignoring some quantifiers % 12.59/2.65 Prover 5: Proving ... % 12.59/2.66 Prover 4: Constructing countermodel ... % 12.99/2.72 Prover 0: Proving ... % 12.99/2.75 Prover 2: Proving ... % 13.92/2.83 Prover 3: proved (2209ms) % 13.92/2.83 % 13.92/2.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.92/2.84 % 13.92/2.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.92/2.84 Prover 6: stopped % 14.22/2.85 Prover 5: stopped % 14.22/2.85 Prover 2: stopped % 14.22/2.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.22/2.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.22/2.87 Prover 0: stopped % 14.22/2.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.22/2.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.03/3.01 Prover 8: Preprocessing ... % 15.03/3.02 Prover 10: Preprocessing ... % 15.03/3.03 Prover 7: Preprocessing ... % 15.72/3.05 Prover 13: Preprocessing ... % 15.72/3.06 Prover 11: Preprocessing ... % 16.46/3.18 Prover 1: Found proof (size 24) % 16.46/3.18 Prover 1: proved (2560ms) % 16.46/3.18 Prover 4: stopped % 16.46/3.19 Prover 7: stopped % 16.91/3.22 Prover 10: stopped % 17.29/3.26 Prover 11: stopped % 17.29/3.29 Prover 13: stopped % 17.29/3.32 Prover 8: Warning: ignoring some quantifiers % 17.29/3.34 Prover 8: Constructing countermodel ... % 17.82/3.36 Prover 8: stopped % 17.82/3.36 % 17.82/3.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.82/3.36 % 17.82/3.37 % SZS output start Proof for theBenchmark % 17.82/3.37 Assumptions after simplification: % 17.82/3.37 --------------------------------- % 17.82/3.37 % 17.82/3.37 (cl5_nebula_init_0051) % 18.02/3.41 $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(loopcounter) & % 18.02/3.41 $i(center_init) & $i(rho_init) & $i(init) & $i(q_init) & $i(n135299) & % 18.02/3.41 $i(pv30) & $i(pv28) & $i(n4) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: any] : % 18.02/3.41 ? [v2: $i] : ( ~ (v2 = init) & a_select3(q_init, pv30, pv28) = v2 & pred(pv28) % 18.02/3.41 = v0 & leq(pv30, n135299) = 0 & leq(pv28, n4) = 0 & leq(n0, pv30) = 0 & % 18.02/3.41 leq(n0, pv28) = 0 & gt(loopcounter, n1) = v1 & $i(v2) & $i(v0) & ! [v3: $i] % 18.02/3.41 : ! [v4: $i] : (v4 = init | ~ (a_select3(center_init, v3, n0) = v4) | ~ % 18.02/3.41 $i(v3) | ? [v5: any] : ? [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = % 18.02/3.41 v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v3: $i] : ( ~ (leq(v3, v0) = 0) % 18.02/3.41 | ~ $i(v3) | ? [v4: any] : ? [v5: $i] : (a_select2(rho_init, v3) = v5 & % 18.02/3.41 leq(n0, v3) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = init))) & ! [v3: $i] : % 18.02/3.41 ( ~ (leq(v3, n135299) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 18.02/3.41 leq(n0, v3) = v4) | ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ % 18.02/3.41 (a_select3(q_init, v3, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: % 18.02/3.41 any] : (leq(v4, n4) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 18.02/3.41 0))))) & ( ~ (v1 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = init | % 18.02/3.41 ~ (a_select2(sigmaold_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? % 18.02/3.41 [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 % 18.02/3.41 = 0))))) & ( ~ (v1 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = init | % 18.02/3.41 ~ (a_select2(rhoold_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? % 18.02/3.41 [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 % 18.02/3.41 = 0))))) & ( ~ (v1 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = init | % 18.02/3.41 ~ (a_select2(muold_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: % 18.02/3.41 any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 18.02/3.41 0)))))) % 18.02/3.41 % 18.02/3.41 (function-axioms) % 18.02/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.02/3.42 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 18.02/3.42 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.02/3.42 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 18.02/3.42 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.02/3.42 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 18.02/3.42 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.02/3.42 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 18.02/3.42 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.02/3.42 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 18.02/3.42 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.02/3.42 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 18.02/3.42 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 18.02/3.42 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 18.02/3.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 18.02/3.42 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.02/3.42 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 18.02/3.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 18.02/3.42 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 18.02/3.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 18.02/3.42 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 18.02/3.42 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 18.02/3.42 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 18.02/3.42 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 18.02/3.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.02/3.42 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 18.02/3.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 18.02/3.42 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 18.02/3.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.02/3.42 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 18.02/3.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.02/3.42 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 18.02/3.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.02/3.42 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 18.02/3.42 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 18.02/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 18.02/3.42 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.02/3.42 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.02/3.42 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 18.02/3.42 % 18.02/3.42 Further assumptions not needed in the proof: % 18.02/3.42 -------------------------------------------- % 18.02/3.42 const_array1_select, const_array2_select, defuse, finite_domain_0, % 18.02/3.42 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 18.02/3.42 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, % 18.02/3.42 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, % 18.02/3.42 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, % 18.02/3.42 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, % 18.02/3.42 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 18.02/3.42 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, % 18.02/3.42 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 18.02/3.42 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 18.02/3.42 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 18.02/3.42 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 18.02/3.42 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 18.02/3.42 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 18.02/3.42 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 18.02/3.42 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 18.02/3.42 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 18.02/3.42 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 18.02/3.42 % 18.02/3.42 Those formulas are unsatisfiable: % 18.02/3.42 --------------------------------- % 18.02/3.42 % 18.02/3.42 Begin of proof % 18.02/3.42 | % 18.02/3.42 | ALPHA: (cl5_nebula_init_0051) implies: % 18.02/3.42 | (1) $i(pv28) % 18.02/3.42 | (2) $i(pv30) % 18.02/3.42 | (3) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ( ~ (v2 = init) & % 18.02/3.42 | a_select3(q_init, pv30, pv28) = v2 & pred(pv28) = v0 & leq(pv30, % 18.02/3.42 | n135299) = 0 & leq(pv28, n4) = 0 & leq(n0, pv30) = 0 & leq(n0, % 18.02/3.42 | pv28) = 0 & gt(loopcounter, n1) = v1 & $i(v2) & $i(v0) & ! [v3: % 18.02/3.42 | $i] : ! [v4: $i] : (v4 = init | ~ (a_select3(center_init, v3, n0) % 18.02/3.42 | = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : (leq(v3, n4) = % 18.02/3.42 | v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v3: % 18.02/3.42 | $i] : ( ~ (leq(v3, v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: % 18.02/3.42 | $i] : (a_select2(rho_init, v3) = v5 & leq(n0, v3) = v4 & $i(v5) & % 18.02/3.42 | ( ~ (v4 = 0) | v5 = init))) & ! [v3: $i] : ( ~ (leq(v3, n135299) % 18.02/3.42 | = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & leq(n0, v3) = % 18.02/3.42 | v4) | ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ % 18.02/3.42 | (a_select3(q_init, v3, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? % 18.02/3.42 | [v7: any] : (leq(v4, n4) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) | % 18.02/3.42 | ~ (v6 = 0))))) & ( ~ (v1 = 0) | ! [v3: $i] : ! [v4: $i] : % 18.02/3.42 | (v4 = init | ~ (a_select2(sigmaold_init, v3) = v4) | ~ $i(v3) | % 18.02/3.42 | ? [v5: any] : ? [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 % 18.02/3.42 | & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ( ~ (v1 = 0) | ! [v3: $i] : % 18.02/3.43 | ! [v4: $i] : (v4 = init | ~ (a_select2(rhoold_init, v3) = v4) | % 18.02/3.43 | ~ $i(v3) | ? [v5: any] : ? [v6: any] : (leq(v3, n4) = v6 & % 18.02/3.43 | leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ( ~ (v1 = % 18.02/3.43 | 0) | ! [v3: $i] : ! [v4: $i] : (v4 = init | ~ % 18.02/3.43 | (a_select2(muold_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? % 18.02/3.43 | [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | % 18.02/3.43 | ~ (v5 = 0)))))) % 18.02/3.43 | % 18.02/3.43 | ALPHA: (function-axioms) implies: % 18.02/3.43 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.02/3.43 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 18.02/3.43 | % 18.02/3.43 | DELTA: instantiating (3) with fresh symbols all_74_0, all_74_1, all_74_2 % 18.02/3.43 | gives: % 18.02/3.43 | (5) ~ (all_74_0 = init) & a_select3(q_init, pv30, pv28) = all_74_0 & % 18.02/3.43 | pred(pv28) = all_74_2 & leq(pv30, n135299) = 0 & leq(pv28, n4) = 0 & % 18.02/3.43 | leq(n0, pv30) = 0 & leq(n0, pv28) = 0 & gt(loopcounter, n1) = all_74_1 % 18.02/3.43 | & $i(all_74_0) & $i(all_74_2) & ! [v0: $i] : ! [v1: $i] : (v1 = init % 18.02/3.43 | | ~ (a_select3(center_init, v0, n0) = v1) | ~ $i(v0) | ? [v2: any] % 18.02/3.43 | : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) % 18.02/3.43 | | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ (leq(v0, all_74_2) = 0) | ~ % 18.02/3.43 | $i(v0) | ? [v1: any] : ? [v2: $i] : (a_select2(rho_init, v0) = v2 & % 18.02/3.43 | leq(n0, v0) = v1 & $i(v2) & ( ~ (v1 = 0) | v2 = init))) & ! [v0: % 18.02/3.43 | $i] : ( ~ (leq(v0, n135299) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 18.02/3.43 | = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = init % 18.02/3.43 | | ~ (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : % 18.02/3.43 | ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 18.02/3.43 | ~ (v3 = 0))))) & ( ~ (all_74_1 = 0) | ! [v0: $i] : ! [v1: % 18.02/3.43 | $i] : (v1 = init | ~ (a_select2(sigmaold_init, v0) = v1) | ~ % 18.02/3.43 | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, % 18.02/3.43 | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ (all_74_1 = 0) % 18.02/3.43 | | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rhoold_init, % 18.02/3.43 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, % 18.02/3.43 | n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & % 18.02/3.43 | ( ~ (all_74_1 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 18.02/3.43 | (a_select2(muold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 18.02/3.43 | [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | % 18.02/3.43 | ~ (v2 = 0))))) % 18.02/3.43 | % 18.02/3.43 | ALPHA: (5) implies: % 18.02/3.43 | (6) ~ (all_74_0 = init) % 18.02/3.43 | (7) leq(n0, pv28) = 0 % 18.02/3.43 | (8) leq(n0, pv30) = 0 % 18.02/3.43 | (9) leq(pv28, n4) = 0 % 18.02/3.43 | (10) leq(pv30, n135299) = 0 % 18.02/3.43 | (11) a_select3(q_init, pv30, pv28) = all_74_0 % 18.02/3.43 | (12) ! [v0: $i] : ( ~ (leq(v0, n135299) = 0) | ~ $i(v0) | ? [v1: int] : % 18.02/3.43 | ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = % 18.02/3.43 | init | ~ (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) | ? [v3: % 18.02/3.43 | any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ % 18.02/3.43 | (v4 = 0) | ~ (v3 = 0))))) % 18.02/3.43 | % 18.02/3.43 | GROUND_INST: instantiating (12) with pv30, simplifying with (2), (10) gives: % 18.02/3.44 | (13) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, pv30) = v0) | ! [v0: $i] : ! % 18.02/3.44 | [v1: $i] : (v1 = init | ~ (a_select3(q_init, pv30, v0) = v1) | ~ % 18.02/3.44 | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, % 18.02/3.44 | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 18.02/3.44 | % 18.02/3.44 | BETA: splitting (13) gives: % 18.02/3.44 | % 18.02/3.44 | Case 1: % 18.02/3.44 | | % 18.02/3.44 | | (14) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, pv30) = v0) % 18.02/3.44 | | % 18.02/3.44 | | DELTA: instantiating (14) with fresh symbol all_104_0 gives: % 18.02/3.44 | | (15) ~ (all_104_0 = 0) & leq(n0, pv30) = all_104_0 % 18.02/3.44 | | % 18.02/3.44 | | ALPHA: (15) implies: % 18.02/3.44 | | (16) ~ (all_104_0 = 0) % 18.02/3.44 | | (17) leq(n0, pv30) = all_104_0 % 18.02/3.44 | | % 18.02/3.44 | | GROUND_INST: instantiating (4) with 0, all_104_0, pv30, n0, simplifying with % 18.02/3.44 | | (8), (17) gives: % 18.02/3.44 | | (18) all_104_0 = 0 % 18.02/3.44 | | % 18.02/3.44 | | REDUCE: (16), (18) imply: % 18.02/3.44 | | (19) $false % 18.02/3.44 | | % 18.02/3.44 | | CLOSE: (19) is inconsistent. % 18.02/3.44 | | % 18.02/3.44 | Case 2: % 18.02/3.44 | | % 18.02/3.44 | | (20) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(q_init, pv30, % 18.02/3.44 | | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, % 18.02/3.44 | | n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 18.02/3.44 | | % 18.02/3.44 | | GROUND_INST: instantiating (20) with pv28, all_74_0, simplifying with (1), % 18.02/3.44 | | (11) gives: % 18.02/3.44 | | (21) all_74_0 = init | ? [v0: any] : ? [v1: any] : (leq(pv28, n4) = v1 % 18.02/3.44 | | & leq(n0, pv28) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 18.02/3.44 | | % 18.02/3.44 | | BETA: splitting (21) gives: % 18.02/3.44 | | % 18.02/3.44 | | Case 1: % 18.02/3.44 | | | % 18.02/3.44 | | | (22) all_74_0 = init % 18.02/3.44 | | | % 18.02/3.44 | | | REDUCE: (6), (22) imply: % 18.02/3.44 | | | (23) $false % 18.02/3.44 | | | % 18.02/3.44 | | | CLOSE: (23) is inconsistent. % 18.02/3.44 | | | % 18.02/3.44 | | Case 2: % 18.02/3.44 | | | % 18.02/3.44 | | | (24) ? [v0: any] : ? [v1: any] : (leq(pv28, n4) = v1 & leq(n0, pv28) % 18.02/3.44 | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 18.02/3.44 | | | % 18.02/3.44 | | | DELTA: instantiating (24) with fresh symbols all_108_0, all_108_1 gives: % 18.02/3.44 | | | (25) leq(pv28, n4) = all_108_0 & leq(n0, pv28) = all_108_1 & ( ~ % 18.02/3.44 | | | (all_108_0 = 0) | ~ (all_108_1 = 0)) % 18.02/3.44 | | | % 18.02/3.44 | | | ALPHA: (25) implies: % 18.02/3.44 | | | (26) leq(n0, pv28) = all_108_1 % 18.02/3.44 | | | (27) leq(pv28, n4) = all_108_0 % 18.02/3.44 | | | (28) ~ (all_108_0 = 0) | ~ (all_108_1 = 0) % 18.02/3.44 | | | % 18.02/3.44 | | | GROUND_INST: instantiating (4) with 0, all_108_1, pv28, n0, simplifying % 18.02/3.44 | | | with (7), (26) gives: % 18.02/3.44 | | | (29) all_108_1 = 0 % 18.02/3.44 | | | % 18.02/3.44 | | | GROUND_INST: instantiating (4) with 0, all_108_0, n4, pv28, simplifying % 18.02/3.44 | | | with (9), (27) gives: % 18.02/3.44 | | | (30) all_108_0 = 0 % 18.02/3.44 | | | % 18.02/3.44 | | | BETA: splitting (28) gives: % 18.02/3.44 | | | % 18.02/3.44 | | | Case 1: % 18.02/3.44 | | | | % 18.02/3.44 | | | | (31) ~ (all_108_0 = 0) % 18.02/3.44 | | | | % 18.02/3.44 | | | | REDUCE: (30), (31) imply: % 18.02/3.44 | | | | (32) $false % 18.02/3.44 | | | | % 18.02/3.44 | | | | CLOSE: (32) is inconsistent. % 18.02/3.44 | | | | % 18.02/3.44 | | | Case 2: % 18.02/3.44 | | | | % 18.02/3.44 | | | | (33) ~ (all_108_1 = 0) % 18.02/3.44 | | | | % 18.02/3.44 | | | | REDUCE: (29), (33) imply: % 18.02/3.44 | | | | (34) $false % 18.02/3.44 | | | | % 18.02/3.44 | | | | CLOSE: (34) is inconsistent. % 18.02/3.44 | | | | % 18.02/3.44 | | | End of split % 18.02/3.44 | | | % 18.02/3.44 | | End of split % 18.02/3.44 | | % 18.02/3.44 | End of split % 18.02/3.44 | % 18.02/3.44 End of proof % 18.02/3.44 % SZS output end Proof for theBenchmark % 18.02/3.44 % 18.02/3.44 2842ms %------------------------------------------------------------------------------