%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV188+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 : n006.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 22:55:16 EDT 2023 % Result : Theorem 16.76s 2.93s % Output : Proof 19.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV188+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n006.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 04:08:06 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.58/1.33 Prover 4: Preprocessing ... % 4.58/1.33 Prover 1: Preprocessing ... % 5.09/1.37 Prover 3: Preprocessing ... % 5.09/1.37 Prover 0: Preprocessing ... % 5.09/1.37 Prover 2: Preprocessing ... % 5.09/1.37 Prover 6: Preprocessing ... % 5.09/1.37 Prover 5: Preprocessing ... % 10.78/2.16 Prover 1: Warning: ignoring some quantifiers % 11.90/2.27 Prover 1: Constructing countermodel ... % 11.90/2.28 Prover 3: Warning: ignoring some quantifiers % 11.90/2.30 Prover 6: Proving ... % 12.29/2.34 Prover 3: Constructing countermodel ... % 12.29/2.37 Prover 4: Warning: ignoring some quantifiers % 12.29/2.37 Prover 5: Proving ... % 12.64/2.45 Prover 4: Constructing countermodel ... % 13.40/2.50 Prover 0: Proving ... % 13.40/2.52 Prover 2: Proving ... % 16.76/2.93 Prover 3: proved (2319ms) % 16.76/2.93 % 16.76/2.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.76/2.93 % 16.76/2.94 Prover 5: stopped % 16.76/2.94 Prover 0: stopped % 16.76/2.95 Prover 2: stopped % 16.76/2.95 Prover 6: stopped % 16.76/2.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.76/2.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.76/2.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.76/2.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.76/2.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.06/3.12 Prover 11: Preprocessing ... % 18.27/3.14 Prover 7: Preprocessing ... % 18.27/3.15 Prover 1: Found proof (size 25) % 18.27/3.15 Prover 1: proved (2535ms) % 18.27/3.15 Prover 4: stopped % 18.27/3.15 Prover 8: Preprocessing ... % 18.27/3.15 Prover 10: Preprocessing ... % 18.27/3.16 Prover 13: Preprocessing ... % 18.27/3.19 Prover 7: stopped % 18.27/3.20 Prover 11: stopped % 18.27/3.21 Prover 10: stopped % 18.96/3.24 Prover 13: stopped % 19.27/3.33 Prover 8: Warning: ignoring some quantifiers % 19.27/3.35 Prover 8: Constructing countermodel ... % 19.61/3.36 Prover 8: stopped % 19.61/3.36 % 19.61/3.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.61/3.36 % 19.61/3.37 % SZS output start Proof for theBenchmark % 19.64/3.37 Assumptions after simplification: % 19.64/3.37 --------------------------------- % 19.64/3.37 % 19.64/3.37 (cl5_nebula_init_0116) % 19.79/3.40 $i(mu_init) & $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & % 19.79/3.40 $i(loopcounter) & $i(center_init) & $i(rho_init) & $i(init) & $i(q_init) & % 19.79/3.40 $i(n135299) & $i(n4) & $i(n1) & $i(tptp_minus_1) & $i(n0) & ? [v0: any] : % 19.79/3.40 (gt(loopcounter, n1) = v0 & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 19.79/3.40 (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 19.79/3.41 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 19.79/3.41 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 19.79/3.41 (a_select2(rho_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : % 19.79/3.41 (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! % 19.79/3.41 [v1: $i] : ( ~ (leq(v1, n135299) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = % 19.79/3.41 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 19.79/3.41 (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: % 19.79/3.41 any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 19.79/3.41 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 19.79/3.41 a_select2(mu_init, v1) = v2 & leq(v1, tptp_minus_1) = 0 & leq(n0, v1) = 0 % 19.79/3.41 & $i(v2) & $i(v1)) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init % 19.79/3.41 | ~ (a_select2(sigmaold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 19.79/3.41 [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 % 19.79/3.41 = 0))))) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 19.79/3.41 ~ (a_select2(rhoold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 19.79/3.41 [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 % 19.79/3.41 = 0))))) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 19.79/3.41 ~ (a_select2(muold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 19.79/3.41 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 19.79/3.41 0)))))) % 19.79/3.41 % 19.79/3.41 (finite_domain_0) % 19.79/3.41 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.79/3.41 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.79/3.41 % 19.79/3.41 (irreflexivity_gt) % 19.79/3.41 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 19.79/3.41 % 19.79/3.41 (leq_gt1) % 19.79/3.41 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 19.79/3.41 leq(v0, v1) = 0) % 19.79/3.41 % 19.79/3.41 (leq_gt_pred) % 19.79/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.79/3.41 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 19.79/3.41 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 19.79/3.41 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 19.79/3.41 | gt(v1, v0) = 0) % 19.79/3.41 % 19.79/3.41 (pred_succ) % 19.79/3.41 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 19.79/3.41 % 19.79/3.41 (succ_tptp_minus_1) % 19.79/3.41 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 19.79/3.41 % 19.79/3.41 (function-axioms) % 19.79/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.79/3.42 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.79/3.42 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.79/3.42 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.79/3.42 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.79/3.42 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.79/3.42 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.79/3.42 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.79/3.42 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.79/3.42 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.79/3.42 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.79/3.42 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 19.79/3.42 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.79/3.42 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 19.79/3.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 19.79/3.42 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.79/3.42 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 19.79/3.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.79/3.42 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 19.79/3.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 19.79/3.42 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.79/3.42 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 19.79/3.42 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.79/3.42 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 19.79/3.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.79/3.42 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 19.79/3.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.79/3.42 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.79/3.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.79/3.42 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.79/3.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.79/3.42 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.79/3.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.79/3.42 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.79/3.42 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 19.79/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 19.79/3.42 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.79/3.42 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.79/3.42 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 19.79/3.42 % 19.79/3.42 Further assumptions not needed in the proof: % 19.79/3.42 -------------------------------------------- % 19.79/3.42 const_array1_select, const_array2_select, defuse, finite_domain_1, % 19.79/3.42 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 19.79/3.42 gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, gt_135299_3, % 19.79/3.42 gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, % 19.79/3.42 gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, % 19.79/3.42 gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, % 19.79/3.42 gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, leq_geq, leq_gt2, leq_minus, % 19.79/3.42 leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, lt_gt, % 19.79/3.42 matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 19.79/3.42 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.79/3.42 matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1, % 19.79/3.42 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, % 19.79/3.42 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, % 19.79/3.42 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, % 19.79/3.42 succ_pred, successor_1, successor_2, successor_3, successor_4, successor_5, % 19.79/3.42 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 19.79/3.42 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 19.79/3.42 % 19.79/3.42 Those formulas are unsatisfiable: % 19.79/3.42 --------------------------------- % 19.79/3.42 % 19.79/3.42 Begin of proof % 19.79/3.42 | % 19.79/3.43 | ALPHA: (leq_gt_pred) implies: % 19.79/3.43 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 19.79/3.43 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 19.79/3.43 | % 19.79/3.43 | ALPHA: (succ_tptp_minus_1) implies: % 19.79/3.43 | (2) succ(tptp_minus_1) = n0 % 19.79/3.43 | % 19.79/3.43 | ALPHA: (finite_domain_0) implies: % 19.79/3.43 | (3) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.79/3.43 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.79/3.43 | % 19.79/3.43 | ALPHA: (cl5_nebula_init_0116) implies: % 19.79/3.43 | (4) $i(n0) % 19.79/3.43 | (5) $i(tptp_minus_1) % 19.93/3.44 | (6) ? [v0: any] : (gt(loopcounter, n1) = v0 & ! [v1: $i] : ! [v2: $i] : % 19.93/3.44 | (v2 = init | ~ (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | % 19.93/3.44 | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & % 19.93/3.44 | ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = % 19.93/3.44 | init | ~ (a_select2(rho_init, v1) = v2) | ~ $i(v1) | ? [v3: any] % 19.93/3.44 | : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = % 19.93/3.44 | 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, n135299) = % 19.93/3.44 | 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) % 19.93/3.44 | | ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ (a_select3(q_init, % 19.93/3.44 | v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : % 19.93/3.44 | (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = % 19.93/3.44 | 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 19.93/3.44 | a_select2(mu_init, v1) = v2 & leq(v1, tptp_minus_1) = 0 & leq(n0, % 19.93/3.44 | v1) = 0 & $i(v2) & $i(v1)) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: % 19.93/3.44 | $i] : (v2 = init | ~ (a_select2(sigmaold_init, v1) = v2) | ~ % 19.93/3.44 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & % 19.93/3.44 | leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ( ~ (v0 = % 19.93/3.44 | 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 19.93/3.44 | (a_select2(rhoold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 19.93/3.44 | [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 19.93/3.44 | ~ (v3 = 0))))) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : % 19.93/3.44 | (v2 = init | ~ (a_select2(muold_init, v1) = v2) | ~ $i(v1) | ? % 19.93/3.44 | [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & % 19.93/3.44 | ( ~ (v4 = 0) | ~ (v3 = 0)))))) % 19.93/3.44 | % 19.93/3.44 | ALPHA: (function-axioms) implies: % 19.93/3.44 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.93/3.44 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 19.93/3.44 | % 19.93/3.44 | DELTA: instantiating (6) with fresh symbol all_74_0 gives: % 19.93/3.44 | (8) gt(loopcounter, n1) = all_74_0 & ! [v0: $i] : ! [v1: $i] : (v1 = init % 19.93/3.44 | | ~ (a_select3(center_init, v0, n0) = v1) | ~ $i(v0) | ? [v2: any] % 19.93/3.44 | : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) % 19.93/3.44 | | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 19.93/3.44 | (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 19.93/3.44 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 % 19.93/3.44 | = 0)))) & ! [v0: $i] : ( ~ (leq(v0, n135299) = 0) | ~ $i(v0) % 19.93/3.44 | | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! % 19.93/3.44 | [v2: $i] : (v2 = init | ~ (a_select3(q_init, v0, v1) = v2) | ~ % 19.93/3.44 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, % 19.93/3.44 | v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ? [v0: $i] : ? % 19.93/3.44 | [v1: $i] : ( ~ (v1 = init) & a_select2(mu_init, v0) = v1 & leq(v0, % 19.93/3.44 | tptp_minus_1) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) & ( ~ % 19.93/3.44 | (all_74_0 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 19.93/3.44 | (a_select2(sigmaold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 19.93/3.44 | [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | % 19.93/3.44 | ~ (v2 = 0))))) & ( ~ (all_74_0 = 0) | ! [v0: $i] : ! [v1: $i] % 19.93/3.44 | : (v1 = init | ~ (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ? % 19.93/3.44 | [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( % 19.93/3.44 | ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ (all_74_0 = 0) | ! [v0: $i] % 19.93/3.44 | : ! [v1: $i] : (v1 = init | ~ (a_select2(muold_init, v0) = v1) | ~ % 19.93/3.44 | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, % 19.93/3.44 | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 19.93/3.44 | % 19.93/3.44 | ALPHA: (8) implies: % 19.93/3.45 | (9) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(mu_init, v0) = % 19.93/3.45 | v1 & leq(v0, tptp_minus_1) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 19.93/3.45 | % 19.93/3.45 | DELTA: instantiating (9) with fresh symbols all_79_0, all_79_1 gives: % 19.93/3.45 | (10) ~ (all_79_0 = init) & a_select2(mu_init, all_79_1) = all_79_0 & % 19.93/3.45 | leq(all_79_1, tptp_minus_1) = 0 & leq(n0, all_79_1) = 0 & $i(all_79_0) % 19.93/3.45 | & $i(all_79_1) % 19.93/3.45 | % 19.93/3.45 | ALPHA: (10) implies: % 19.93/3.45 | (11) $i(all_79_1) % 19.93/3.45 | (12) leq(n0, all_79_1) = 0 % 19.93/3.45 | (13) leq(all_79_1, tptp_minus_1) = 0 % 19.93/3.45 | % 19.93/3.45 | GROUND_INST: instantiating (3) with all_79_1, simplifying with (11), (12) % 19.93/3.45 | gives: % 19.93/3.45 | (14) all_79_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0) % 19.93/3.45 | % 19.93/3.45 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with % 19.93/3.45 | (2), (5) gives: % 19.93/3.45 | (15) pred(n0) = tptp_minus_1 % 19.93/3.45 | % 19.93/3.45 | GROUND_INST: instantiating (1) with all_79_1, n0, tptp_minus_1, simplifying % 19.93/3.45 | with (4), (11), (13), (15) gives: % 19.93/3.45 | (16) gt(n0, all_79_1) = 0 % 19.93/3.45 | % 19.93/3.45 | GROUND_INST: instantiating (leq_gt1) with all_79_1, n0, simplifying with (4), % 19.93/3.45 | (11), (16) gives: % 19.93/3.45 | (17) leq(all_79_1, n0) = 0 % 19.93/3.45 | % 19.93/3.45 | BETA: splitting (14) gives: % 19.93/3.45 | % 19.93/3.45 | Case 1: % 19.93/3.45 | | % 19.93/3.45 | | (18) all_79_1 = n0 % 19.93/3.45 | | % 19.93/3.45 | | REDUCE: (16), (18) imply: % 19.93/3.45 | | (19) gt(n0, n0) = 0 % 19.93/3.45 | | % 19.93/3.45 | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with (4), % 19.93/3.45 | | (19) gives: % 19.93/3.45 | | (20) $false % 19.93/3.45 | | % 19.93/3.45 | | CLOSE: (20) is inconsistent. % 19.93/3.45 | | % 19.93/3.45 | Case 2: % 19.93/3.45 | | % 19.93/3.45 | | (21) ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0) % 19.93/3.45 | | % 19.93/3.45 | | DELTA: instantiating (21) with fresh symbol all_132_0 gives: % 19.93/3.45 | | (22) ~ (all_132_0 = 0) & leq(all_79_1, n0) = all_132_0 % 19.93/3.45 | | % 19.93/3.45 | | ALPHA: (22) implies: % 19.93/3.45 | | (23) ~ (all_132_0 = 0) % 19.93/3.45 | | (24) leq(all_79_1, n0) = all_132_0 % 19.93/3.45 | | % 19.93/3.45 | | GROUND_INST: instantiating (7) with 0, all_132_0, n0, all_79_1, simplifying % 19.93/3.45 | | with (17), (24) gives: % 19.93/3.45 | | (25) all_132_0 = 0 % 19.93/3.45 | | % 19.93/3.45 | | REDUCE: (23), (25) imply: % 19.93/3.45 | | (26) $false % 19.93/3.45 | | % 19.93/3.45 | | CLOSE: (26) is inconsistent. % 19.93/3.45 | | % 19.93/3.45 | End of split % 19.93/3.45 | % 19.93/3.45 End of proof % 19.93/3.45 % SZS output end Proof for theBenchmark % 19.93/3.45 % 19.93/3.45 2864ms %------------------------------------------------------------------------------