%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV166+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 : n023.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 22:55:11 EDT 2023 % Result : Theorem 19.53s 3.37s % Output : Proof 24.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.10 % Problem : SWV166+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.08/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.30 % Computer : n023.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Tue Aug 29 09:04:25 EDT 2023 % 0.10/0.31 % CPUTime : % 0.52/0.57 ________ _____ % 0.52/0.57 ___ __ \_________(_)________________________________ % 0.52/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.57 % 0.52/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.57 (2023-06-19) % 0.52/0.57 % 0.52/0.57 (c) Philipp Rümmer, 2009-2023 % 0.52/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.57 Amanda Stjerna. % 0.52/0.57 Free software under BSD-3-Clause. % 0.52/0.57 % 0.52/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.57 % 0.52/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.52/0.59 Running up to 7 provers in parallel. % 0.52/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.52/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 5.40/1.47 Prover 1: Preprocessing ... % 5.40/1.49 Prover 4: Preprocessing ... % 5.98/1.53 Prover 2: Preprocessing ... % 5.98/1.53 Prover 6: Preprocessing ... % 5.98/1.53 Prover 3: Preprocessing ... % 5.98/1.53 Prover 5: Preprocessing ... % 5.98/1.55 Prover 0: Preprocessing ... % 14.69/2.69 Prover 1: Warning: ignoring some quantifiers % 15.32/2.84 Prover 3: Warning: ignoring some quantifiers % 15.32/2.84 Prover 1: Constructing countermodel ... % 16.12/2.88 Prover 3: Constructing countermodel ... % 16.12/2.92 Prover 6: Proving ... % 17.14/3.05 Prover 4: Warning: ignoring some quantifiers % 17.81/3.09 Prover 5: Proving ... % 18.13/3.14 Prover 4: Constructing countermodel ... % 18.92/3.24 Prover 0: Proving ... % 18.92/3.24 Prover 2: Proving ... % 19.53/3.36 Prover 3: proved (2765ms) % 19.53/3.36 % 19.53/3.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.53/3.37 % 19.53/3.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.53/3.37 Prover 0: stopped % 19.53/3.37 Prover 6: stopped % 19.53/3.37 Prover 5: stopped % 19.53/3.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 19.53/3.37 Prover 2: stopped % 19.53/3.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.14/3.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.14/3.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 21.23/3.58 Prover 13: Preprocessing ... % 21.23/3.60 Prover 11: Preprocessing ... % 21.23/3.62 Prover 8: Preprocessing ... % 21.23/3.63 Prover 7: Preprocessing ... % 22.00/3.63 Prover 1: Found proof (size 19) % 22.00/3.63 Prover 1: proved (3037ms) % 22.00/3.63 Prover 4: stopped % 22.00/3.65 Prover 10: Preprocessing ... % 22.64/3.75 Prover 7: stopped % 22.64/3.77 Prover 10: stopped % 23.25/3.83 Prover 13: stopped % 23.25/3.84 Prover 11: stopped % 23.95/3.97 Prover 8: Warning: ignoring some quantifiers % 23.95/4.00 Prover 8: Constructing countermodel ... % 24.38/4.03 Prover 8: stopped % 24.38/4.03 % 24.38/4.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 24.38/4.04 % 24.38/4.04 % SZS output start Proof for theBenchmark % 24.38/4.05 Assumptions after simplification: % 24.38/4.05 --------------------------------- % 24.38/4.05 % 24.38/4.05 (cl5_nebula_init_0006) % 24.76/4.10 $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(center_init) & % 24.76/4.10 $i(sigma_init) & $i(mu_init) & $i(rho_init) & $i(init) & $i(q_init) & % 24.76/4.10 $i(n135299) & $i(loopcounter) & $i(pv40) & $i(pv90) & $i(n4) & $i(n1) & $i(n0) % 24.76/4.10 & ? [v0: $i] : ( ~ (pv90 = n0) & pred(pv40) = v0 & leq(pv40, n4) = 0 & % 24.76/4.10 leq(n0, pv40) = 0 & gt(loopcounter, n1) = 0 & $i(v0) & ! [v1: $i] : ! [v2: % 24.76/4.10 $i] : (v2 = init | ~ (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | % 24.76/4.10 ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ % 24.76/4.10 (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | % 24.76/4.10 ~ (a_select2(sigmaold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 24.76/4.10 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 24.76/4.10 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 24.76/4.10 (a_select2(rhoold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 24.76/4.10 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 24.76/4.10 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 24.76/4.10 (a_select2(muold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] % 24.76/4.10 : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & % 24.76/4.10 ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select2(rho_init, v1) = v2) | % 24.76/4.10 ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = % 24.76/4.10 v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) % 24.76/4.10 | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : (a_select2(sigma_init, v1) = v3 % 24.76/4.10 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = init))) & ! [v1: $i] % 24.76/4.10 : ( ~ (leq(v1, v0) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : % 24.76/4.10 (a_select2(mu_init, v1) = v3 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | % 24.76/4.10 v3 = init))) & ! [v1: $i] : ( ~ (leq(v1, n135299) = 0) | ~ $i(v1) | % 24.76/4.10 ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] % 24.76/4.10 : (v3 = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4: % 24.76/4.10 any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = % 24.76/4.10 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 24.76/4.10 & a_select2(rhoold_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = 0 & % 24.76/4.10 $i(v2) & $i(v1))) % 24.76/4.10 % 24.76/4.10 (function-axioms) % 24.76/4.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 24.76/4.12 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 24.76/4.12 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 24.76/4.12 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 24.76/4.12 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 24.76/4.12 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 24.76/4.12 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 24.76/4.12 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 24.76/4.12 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 24.76/4.12 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 24.76/4.12 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 24.76/4.12 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 24.76/4.12 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 24.76/4.12 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 24.76/4.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 24.76/4.12 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 24.76/4.12 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 24.76/4.12 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 24.76/4.12 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 24.76/4.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 24.76/4.12 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 24.76/4.12 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 24.76/4.12 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 24.76/4.12 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 24.76/4.12 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 24.76/4.12 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 24.76/4.12 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 24.76/4.12 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 24.76/4.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 24.76/4.12 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 24.76/4.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 24.76/4.12 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 24.76/4.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 24.76/4.12 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 24.76/4.12 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 24.76/4.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 24.76/4.12 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.76/4.12 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 24.76/4.12 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 24.76/4.12 % 24.76/4.12 Further assumptions not needed in the proof: % 24.76/4.12 -------------------------------------------- % 24.76/4.12 const_array1_select, const_array2_select, defuse, finite_domain_0, % 24.76/4.12 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 24.76/4.12 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, % 24.76/4.12 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, % 24.76/4.12 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, % 24.76/4.12 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, % 24.76/4.12 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 24.76/4.12 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, % 24.76/4.12 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 24.76/4.12 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 24.76/4.12 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 24.76/4.12 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 24.76/4.12 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 24.76/4.12 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 24.76/4.12 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 24.76/4.12 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 24.76/4.12 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 24.76/4.12 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 24.76/4.12 % 24.76/4.12 Those formulas are unsatisfiable: % 24.76/4.12 --------------------------------- % 24.76/4.12 % 24.76/4.12 Begin of proof % 24.76/4.12 | % 24.76/4.12 | ALPHA: (cl5_nebula_init_0006) implies: % 24.76/4.13 | (1) ? [v0: $i] : ( ~ (pv90 = n0) & pred(pv40) = v0 & leq(pv40, n4) = 0 & % 24.76/4.13 | leq(n0, pv40) = 0 & gt(loopcounter, n1) = 0 & $i(v0) & ! [v1: $i] : % 24.76/4.13 | ! [v2: $i] : (v2 = init | ~ (a_select3(center_init, v1, n0) = v2) | % 24.76/4.13 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & % 24.76/4.13 | leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : % 24.76/4.13 | ! [v2: $i] : (v2 = init | ~ (a_select2(sigmaold_init, v1) = v2) | ~ % 24.76/4.13 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, % 24.76/4.13 | v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! % 24.76/4.13 | [v2: $i] : (v2 = init | ~ (a_select2(rhoold_init, v1) = v2) | ~ % 24.76/4.13 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, % 24.76/4.13 | v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! % 24.76/4.13 | [v2: $i] : (v2 = init | ~ (a_select2(muold_init, v1) = v2) | ~ % 24.76/4.13 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, % 24.76/4.13 | v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! % 24.76/4.13 | [v2: $i] : (v2 = init | ~ (a_select2(rho_init, v1) = v2) | ~ $i(v1) % 24.76/4.13 | | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = % 24.76/4.13 | v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, % 24.76/4.13 | v0) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : % 24.76/4.13 | (a_select2(sigma_init, v1) = v3 & leq(n0, v1) = v2 & $i(v3) & ( ~ % 24.76/4.13 | (v2 = 0) | v3 = init))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) | % 24.76/4.13 | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : (a_select2(mu_init, v1) = % 24.76/4.13 | v3 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = init))) & ! % 24.76/4.13 | [v1: $i] : ( ~ (leq(v1, n135299) = 0) | ~ $i(v1) | ? [v2: int] : ( % 24.76/4.13 | ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] : (v3 % 24.76/4.14 | = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? % 24.76/4.14 | [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & % 24.76/4.14 | ( ~ (v5 = 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( % 24.76/4.14 | ~ (v2 = init) & a_select2(rhoold_init, v1) = v2 & leq(v1, n4) = 0 & % 24.76/4.14 | leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 24.76/4.14 | % 24.76/4.14 | ALPHA: (function-axioms) implies: % 24.76/4.14 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 24.76/4.14 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 24.76/4.14 | % 24.76/4.14 | DELTA: instantiating (1) with fresh symbol all_76_0 gives: % 24.76/4.15 | (3) ~ (pv90 = n0) & pred(pv40) = all_76_0 & leq(pv40, n4) = 0 & leq(n0, % 24.76/4.15 | pv40) = 0 & gt(loopcounter, n1) = 0 & $i(all_76_0) & ! [v0: $i] : ! % 24.76/4.15 | [v1: $i] : (v1 = init | ~ (a_select3(center_init, v0, n0) = v1) | ~ % 24.76/4.15 | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, % 24.76/4.15 | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: % 24.76/4.15 | $i] : (v1 = init | ~ (a_select2(sigmaold_init, v0) = v1) | ~ $i(v0) % 24.76/4.15 | | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 % 24.76/4.15 | & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = % 24.76/4.15 | init | ~ (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ? [v2: % 24.76/4.15 | any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ % 24.76/4.15 | (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = % 24.76/4.15 | init | ~ (a_select2(muold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] % 24.76/4.15 | : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) % 24.76/4.15 | | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 24.76/4.15 | (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 24.76/4.15 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 24.76/4.15 | = 0)))) & ! [v0: $i] : ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0) % 24.76/4.15 | | ? [v1: any] : ? [v2: $i] : (a_select2(sigma_init, v0) = v2 & % 24.76/4.15 | leq(n0, v0) = v1 & $i(v2) & ( ~ (v1 = 0) | v2 = init))) & ! [v0: % 24.76/4.15 | $i] : ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 24.76/4.15 | [v2: $i] : (a_select2(mu_init, v0) = v2 & leq(n0, v0) = v1 & $i(v2) & % 24.76/4.15 | ( ~ (v1 = 0) | v2 = init))) & ! [v0: $i] : ( ~ (leq(v0, n135299) = % 24.76/4.15 | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | % 24.76/4.15 | ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select3(q_init, v0, v1) % 24.76/4.15 | = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = % 24.76/4.15 | v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ? [v0: % 24.76/4.15 | $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(rhoold_init, v0) = v1 % 24.76/4.15 | & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 24.76/4.15 | % 24.76/4.15 | ALPHA: (3) implies: % 24.76/4.15 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rhoold_init, v0) % 24.76/4.15 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 % 24.76/4.15 | & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 24.76/4.15 | (5) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(rhoold_init, % 24.76/4.15 | v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 24.76/4.15 | % 24.76/4.15 | DELTA: instantiating (5) with fresh symbols all_79_0, all_79_1 gives: % 24.76/4.15 | (6) ~ (all_79_0 = init) & a_select2(rhoold_init, all_79_1) = all_79_0 & % 24.76/4.15 | leq(all_79_1, n4) = 0 & leq(n0, all_79_1) = 0 & $i(all_79_0) & % 24.76/4.15 | $i(all_79_1) % 24.76/4.15 | % 24.76/4.15 | ALPHA: (6) implies: % 24.76/4.16 | (7) ~ (all_79_0 = init) % 24.76/4.16 | (8) $i(all_79_1) % 24.76/4.16 | (9) leq(n0, all_79_1) = 0 % 24.76/4.16 | (10) leq(all_79_1, n4) = 0 % 24.76/4.16 | (11) a_select2(rhoold_init, all_79_1) = all_79_0 % 24.76/4.16 | % 24.76/4.16 | GROUND_INST: instantiating (4) with all_79_1, all_79_0, simplifying with (8), % 24.76/4.16 | (11) gives: % 24.76/4.16 | (12) all_79_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = % 24.76/4.16 | v1 & leq(n0, all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 24.76/4.16 | % 24.76/4.16 | BETA: splitting (12) gives: % 24.76/4.16 | % 24.76/4.16 | Case 1: % 24.76/4.16 | | % 24.76/4.16 | | (13) all_79_0 = init % 24.76/4.16 | | % 24.76/4.16 | | REDUCE: (7), (13) imply: % 24.76/4.16 | | (14) $false % 24.76/4.16 | | % 24.76/4.16 | | CLOSE: (14) is inconsistent. % 24.76/4.16 | | % 24.76/4.16 | Case 2: % 24.76/4.16 | | % 24.76/4.16 | | (15) ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = v1 & leq(n0, % 24.76/4.16 | | all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 24.76/4.16 | | % 24.76/4.16 | | DELTA: instantiating (15) with fresh symbols all_107_0, all_107_1 gives: % 24.76/4.16 | | (16) leq(all_79_1, n4) = all_107_0 & leq(n0, all_79_1) = all_107_1 & ( ~ % 24.76/4.16 | | (all_107_0 = 0) | ~ (all_107_1 = 0)) % 24.76/4.16 | | % 24.76/4.16 | | ALPHA: (16) implies: % 24.76/4.17 | | (17) leq(n0, all_79_1) = all_107_1 % 24.76/4.17 | | (18) leq(all_79_1, n4) = all_107_0 % 24.76/4.17 | | (19) ~ (all_107_0 = 0) | ~ (all_107_1 = 0) % 24.76/4.17 | | % 24.76/4.17 | | GROUND_INST: instantiating (2) with 0, all_107_1, all_79_1, n0, simplifying % 24.76/4.17 | | with (9), (17) gives: % 24.76/4.17 | | (20) all_107_1 = 0 % 24.76/4.17 | | % 24.76/4.17 | | GROUND_INST: instantiating (2) with 0, all_107_0, n4, all_79_1, simplifying % 24.76/4.17 | | with (10), (18) gives: % 24.76/4.17 | | (21) all_107_0 = 0 % 24.76/4.17 | | % 24.76/4.17 | | BETA: splitting (19) gives: % 24.76/4.17 | | % 24.76/4.17 | | Case 1: % 24.76/4.17 | | | % 24.76/4.17 | | | (22) ~ (all_107_0 = 0) % 24.76/4.17 | | | % 24.76/4.17 | | | REDUCE: (21), (22) imply: % 24.76/4.17 | | | (23) $false % 24.76/4.17 | | | % 24.76/4.17 | | | CLOSE: (23) is inconsistent. % 24.76/4.17 | | | % 24.76/4.17 | | Case 2: % 24.76/4.17 | | | % 24.76/4.17 | | | (24) ~ (all_107_1 = 0) % 24.76/4.17 | | | % 24.76/4.17 | | | REDUCE: (20), (24) imply: % 24.76/4.17 | | | (25) $false % 24.76/4.17 | | | % 24.76/4.17 | | | CLOSE: (25) is inconsistent. % 24.76/4.17 | | | % 24.76/4.17 | | End of split % 24.76/4.17 | | % 24.76/4.17 | End of split % 24.76/4.17 | % 24.76/4.17 End of proof % 24.76/4.17 % SZS output end Proof for theBenchmark % 24.76/4.17 % 24.76/4.17 3600ms %------------------------------------------------------------------------------