%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV031+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 : n022.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 22:54:38 EDT 2023 % Result : Theorem 19.67s 3.38s % Output : Proof 28.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV031+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n022.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 10:04:08 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.92/1.37 Prover 1: Preprocessing ... % 4.92/1.37 Prover 4: Preprocessing ... % 4.92/1.40 Prover 5: Preprocessing ... % 4.92/1.40 Prover 6: Preprocessing ... % 4.92/1.40 Prover 0: Preprocessing ... % 4.92/1.40 Prover 3: Preprocessing ... % 4.92/1.41 Prover 2: Preprocessing ... % 11.91/2.33 Prover 1: Warning: ignoring some quantifiers % 12.46/2.43 Prover 3: Warning: ignoring some quantifiers % 12.46/2.46 Prover 3: Constructing countermodel ... % 12.46/2.46 Prover 6: Proving ... % 12.46/2.46 Prover 1: Constructing countermodel ... % 13.39/2.52 Prover 4: Warning: ignoring some quantifiers % 14.24/2.67 Prover 0: Proving ... % 14.24/2.67 Prover 4: Constructing countermodel ... % 14.58/2.68 Prover 5: Proving ... % 14.58/2.73 Prover 2: Proving ... % 19.67/3.38 Prover 3: proved (2724ms) % 19.67/3.38 % 19.67/3.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.67/3.38 % 19.67/3.38 Prover 5: stopped % 19.67/3.38 Prover 0: stopped % 19.67/3.38 Prover 2: stopped % 19.67/3.38 Prover 6: stopped % 19.67/3.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.67/3.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 19.67/3.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 19.67/3.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.67/3.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.33/3.53 Prover 13: Preprocessing ... % 20.33/3.54 Prover 11: Preprocessing ... % 21.12/3.54 Prover 10: Preprocessing ... % 21.12/3.57 Prover 7: Preprocessing ... % 21.12/3.59 Prover 8: Preprocessing ... % 22.44/3.76 Prover 10: Warning: ignoring some quantifiers % 22.44/3.78 Prover 10: Constructing countermodel ... % 23.08/3.87 Prover 8: Warning: ignoring some quantifiers % 23.08/3.87 Prover 7: Warning: ignoring some quantifiers % 23.08/3.89 Prover 13: Warning: ignoring some quantifiers % 23.08/3.89 Prover 7: Constructing countermodel ... % 23.08/3.90 Prover 8: Constructing countermodel ... % 23.86/3.91 Prover 13: Constructing countermodel ... % 23.86/3.93 Prover 11: Warning: ignoring some quantifiers % 23.86/3.97 Prover 11: Constructing countermodel ... % 27.71/4.43 Prover 1: Found proof (size 71) % 27.71/4.44 Prover 1: proved (3809ms) % 27.71/4.44 Prover 11: stopped % 27.71/4.44 Prover 7: stopped % 27.71/4.44 Prover 4: stopped % 27.71/4.44 Prover 13: stopped % 27.71/4.44 Prover 8: stopped % 27.71/4.44 Prover 10: stopped % 27.71/4.44 % 27.71/4.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 27.71/4.44 % 27.71/4.45 % SZS output start Proof for theBenchmark % 27.71/4.45 Assumptions after simplification: % 27.71/4.45 --------------------------------- % 27.71/4.45 % 27.71/4.45 (const_array2_select) % 27.71/4.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 27.71/4.48 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 27.71/4.48 (v10 = v6 | ~ (tptp_const_array2(v7, v8, v6) = v9) | ~ (a_select3(v9, v0, % 27.71/4.48 v3) = v10) | ~ (dim(v4, v5) = v8) | ~ (dim(v1, v2) = v7) | ~ $i(v6) | % 27.71/4.48 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 27.71/4.48 [v11: any] : ? [v12: any] : ? [v13: any] : ? [v14: any] : (leq(v4, v3) = % 27.71/4.48 v13 & leq(v3, v5) = v14 & leq(v1, v0) = v11 & leq(v0, v2) = v12 & ( ~ (v14 % 27.71/4.48 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) % 27.71/4.48 % 27.71/4.48 (gauss_init_0037) % 27.71/4.49 $i(s_values7_init) & $i(simplex7_init) & $i(n330) & $i(n410) & $i(pv10) & % 27.71/4.49 $i(pv9) & $i(init) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: % 27.71/4.49 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (minus(n330, % 27.71/4.49 n1) = v1 & minus(n410, n1) = v0 & tptp_const_array2(v2, v3, init) = v4 & % 27.71/4.49 a_select3(v4, pv9, pv10) = v5 & dim(n0, v1) = v3 & dim(n0, v0) = v2 & % 27.71/4.49 leq(pv10, v1) = 0 & leq(pv9, v0) = 0 & leq(n0, pv10) = 0 & leq(n0, pv9) = 0 % 27.71/4.49 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! % 27.71/4.49 [v7: $i] : (v7 = init | ~ (a_select2(s_values7_init, v6) = v7) | ~ $i(v6) % 27.71/4.49 | ? [v8: any] : ? [v9: any] : (leq(v6, n3) = v9 & leq(n0, v6) = v8 & ( ~ % 27.71/4.49 (v9 = 0) | ~ (v8 = 0)))) & ! [v6: $i] : ( ~ (leq(v6, n2) = 0) | ~ % 27.71/4.49 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & leq(n0, v6) = v7) | ! [v7: $i] : % 27.71/4.49 ! [v8: $i] : (v8 = init | ~ (a_select3(simplex7_init, v7, v6) = v8) | ~ % 27.71/4.49 $i(v7) | ? [v9: any] : ? [v10: any] : (leq(v7, n3) = v10 & leq(n0, v7) % 27.71/4.49 = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ( ~ (v5 = init) | ? [v6: $i] % 27.71/4.49 : ? [v7: $i] : ( ~ (v7 = init) & a_select2(s_values7_init, v6) = v7 & % 27.71/4.49 leq(v6, n3) = 0 & leq(n0, v6) = 0 & $i(v7) & $i(v6)) | ? [v6: $i] : % 27.71/4.49 (leq(v6, n2) = 0 & leq(n0, v6) = 0 & $i(v6) & ? [v7: $i] : ? [v8: $i] : % 27.71/4.49 ( ~ (v8 = init) & a_select3(simplex7_init, v7, v6) = v8 & leq(v7, n3) = % 27.71/4.49 0 & leq(n0, v7) = 0 & $i(v8) & $i(v7))))) % 27.71/4.49 % 27.71/4.49 (function-axioms) % 28.27/4.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 28.27/4.49 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 28.27/4.49 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.27/4.49 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 28.27/4.49 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 28.27/4.49 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 28.27/4.49 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 28.27/4.49 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 28.27/4.49 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 28.27/4.49 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 28.27/4.49 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 28.27/4.49 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 28.27/4.49 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 28.27/4.49 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 28.27/4.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 28.27/4.49 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 28.27/4.49 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 28.27/4.49 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 28.27/4.49 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 28.27/4.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 28.27/4.49 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 28.27/4.49 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 28.27/4.49 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 28.27/4.49 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 28.27/4.49 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.27/4.49 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 28.27/4.49 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 28.27/4.49 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 28.27/4.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.27/4.49 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 28.27/4.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.27/4.49 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 28.27/4.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.27/4.49 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 28.27/4.49 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 28.27/4.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 28.27/4.49 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.27/4.49 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.27/4.49 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 28.27/4.49 % 28.27/4.49 Further assumptions not needed in the proof: % 28.27/4.49 -------------------------------------------- % 28.27/4.50 const_array1_select, defuse, finite_domain_0, finite_domain_1, finite_domain_2, % 28.27/4.50 finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0, % 28.27/4.50 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_330_0, gt_330_1, % 28.27/4.50 gt_330_2, gt_330_3, gt_330_4, gt_330_5, gt_330_tptp_minus_1, gt_3_0, gt_3_1, % 28.27/4.50 gt_3_2, gt_3_tptp_minus_1, gt_410_0, gt_410_1, gt_410_2, gt_410_3, gt_410_330, % 28.27/4.50 gt_410_4, gt_410_5, gt_410_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, % 28.27/4.50 gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, % 28.27/4.50 gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, % 28.27/4.50 leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, lt_gt, % 28.27/4.50 matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 28.27/4.50 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 28.27/4.50 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 28.27/4.50 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 28.27/4.50 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 28.27/4.50 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 28.27/4.50 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2, % 28.27/4.50 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float, % 28.27/4.50 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 28.27/4.50 uniform_int_rand_ranges_lo % 28.27/4.50 % 28.27/4.50 Those formulas are unsatisfiable: % 28.27/4.50 --------------------------------- % 28.27/4.50 % 28.27/4.50 Begin of proof % 28.27/4.50 | % 28.27/4.50 | ALPHA: (gauss_init_0037) implies: % 28.27/4.50 | (1) $i(n0) % 28.27/4.50 | (2) $i(init) % 28.27/4.50 | (3) $i(pv9) % 28.27/4.50 | (4) $i(pv10) % 28.27/4.50 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 28.27/4.50 | ? [v5: $i] : (minus(n330, n1) = v1 & minus(n410, n1) = v0 & % 28.27/4.50 | tptp_const_array2(v2, v3, init) = v4 & a_select3(v4, pv9, pv10) = v5 % 28.27/4.50 | & dim(n0, v1) = v3 & dim(n0, v0) = v2 & leq(pv10, v1) = 0 & leq(pv9, % 28.27/4.50 | v0) = 0 & leq(n0, pv10) = 0 & leq(n0, pv9) = 0 & $i(v5) & $i(v4) & % 28.27/4.50 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7: $i] : (v7 = % 28.27/4.50 | init | ~ (a_select2(s_values7_init, v6) = v7) | ~ $i(v6) | ? % 28.27/4.50 | [v8: any] : ? [v9: any] : (leq(v6, n3) = v9 & leq(n0, v6) = v8 & ( % 28.27/4.50 | ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v6: $i] : ( ~ (leq(v6, n2) = % 28.27/4.50 | 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & leq(n0, v6) = v7) % 28.27/4.50 | | ! [v7: $i] : ! [v8: $i] : (v8 = init | ~ % 28.27/4.50 | (a_select3(simplex7_init, v7, v6) = v8) | ~ $i(v7) | ? [v9: % 28.27/4.50 | any] : ? [v10: any] : (leq(v7, n3) = v10 & leq(n0, v7) = v9 & % 28.27/4.50 | ( ~ (v10 = 0) | ~ (v9 = 0))))) & ( ~ (v5 = init) | ? [v6: $i] % 28.27/4.50 | : ? [v7: $i] : ( ~ (v7 = init) & a_select2(s_values7_init, v6) = % 28.27/4.50 | v7 & leq(v6, n3) = 0 & leq(n0, v6) = 0 & $i(v7) & $i(v6)) | ? % 28.27/4.50 | [v6: $i] : (leq(v6, n2) = 0 & leq(n0, v6) = 0 & $i(v6) & ? [v7: % 28.27/4.50 | $i] : ? [v8: $i] : ( ~ (v8 = init) & a_select3(simplex7_init, % 28.27/4.50 | v7, v6) = v8 & leq(v7, n3) = 0 & leq(n0, v7) = 0 & $i(v8) & % 28.27/4.50 | $i(v7))))) % 28.27/4.50 | % 28.27/4.50 | ALPHA: (function-axioms) implies: % 28.27/4.50 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 28.27/4.50 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 28.27/4.50 | % 28.27/4.50 | DELTA: instantiating (5) with fresh symbols all_74_0, all_74_1, all_74_2, % 28.27/4.50 | all_74_3, all_74_4, all_74_5 gives: % 28.27/4.51 | (7) minus(n330, n1) = all_74_4 & minus(n410, n1) = all_74_5 & % 28.27/4.51 | tptp_const_array2(all_74_3, all_74_2, init) = all_74_1 & % 28.27/4.51 | a_select3(all_74_1, pv9, pv10) = all_74_0 & dim(n0, all_74_4) = % 28.27/4.51 | all_74_2 & dim(n0, all_74_5) = all_74_3 & leq(pv10, all_74_4) = 0 & % 28.27/4.51 | leq(pv9, all_74_5) = 0 & leq(n0, pv10) = 0 & leq(n0, pv9) = 0 & % 28.27/4.51 | $i(all_74_0) & $i(all_74_1) & $i(all_74_2) & $i(all_74_3) & % 28.27/4.51 | $i(all_74_4) & $i(all_74_5) & ! [v0: $i] : ! [v1: $i] : (v1 = init | % 28.27/4.51 | ~ (a_select2(s_values7_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 28.27/4.51 | ? [v3: any] : (leq(v0, n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | % 28.27/4.51 | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | % 28.27/4.51 | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! % 28.27/4.51 | [v2: $i] : (v2 = init | ~ (a_select3(simplex7_init, v1, v0) = v2) | % 28.27/4.51 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n3) = v4 & % 28.27/4.51 | leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ( ~ (all_74_0 % 28.27/4.51 | = init) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 28.27/4.51 | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) % 28.27/4.51 | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, % 28.27/4.51 | v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 28.27/4.51 | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & leq(n0, % 28.27/4.51 | v1) = 0 & $i(v2) & $i(v1)))) % 28.27/4.51 | % 28.27/4.51 | ALPHA: (7) implies: % 28.27/4.51 | (8) $i(all_74_5) % 28.27/4.51 | (9) $i(all_74_4) % 28.27/4.51 | (10) leq(n0, pv9) = 0 % 28.27/4.51 | (11) leq(n0, pv10) = 0 % 28.27/4.51 | (12) leq(pv9, all_74_5) = 0 % 28.27/4.51 | (13) leq(pv10, all_74_4) = 0 % 28.27/4.51 | (14) dim(n0, all_74_5) = all_74_3 % 28.27/4.51 | (15) dim(n0, all_74_4) = all_74_2 % 28.27/4.51 | (16) a_select3(all_74_1, pv9, pv10) = all_74_0 % 28.27/4.51 | (17) tptp_const_array2(all_74_3, all_74_2, init) = all_74_1 % 28.27/4.51 | (18) ~ (all_74_0 = init) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 28.27/4.51 | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = % 28.27/4.51 | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) % 28.27/4.51 | = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 28.27/4.51 | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & leq(n0, % 28.27/4.51 | v1) = 0 & $i(v2) & $i(v1))) % 28.27/4.51 | (19) ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 28.27/4.51 | (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = % 28.27/4.51 | init | ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ? % 28.27/4.51 | [v3: any] : ? [v4: any] : (leq(v1, n3) = v4 & leq(n0, v1) = v3 & % 28.27/4.51 | ( ~ (v4 = 0) | ~ (v3 = 0))))) % 28.27/4.51 | (20) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 28.27/4.51 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, % 28.27/4.51 | n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 28.27/4.51 | % 28.27/4.51 | GROUND_INST: instantiating (const_array2_select) with pv9, n0, all_74_5, pv10, % 28.27/4.51 | n0, all_74_4, init, all_74_3, all_74_2, all_74_1, all_74_0, % 28.27/4.51 | simplifying with (1), (2), (3), (4), (8), (9), (14), (15), (16), % 28.27/4.51 | (17) gives: % 28.27/4.51 | (21) all_74_0 = init | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 28.27/4.51 | any] : (leq(pv10, all_74_4) = v3 & leq(pv9, all_74_5) = v1 & leq(n0, % 28.27/4.51 | pv10) = v2 & leq(n0, pv9) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ % 28.27/4.51 | (v1 = 0) | ~ (v0 = 0))) % 28.27/4.51 | % 28.27/4.51 | BETA: splitting (21) gives: % 28.27/4.51 | % 28.27/4.51 | Case 1: % 28.27/4.51 | | % 28.27/4.51 | | (22) all_74_0 = init % 28.27/4.51 | | % 28.27/4.51 | | BETA: splitting (18) gives: % 28.27/4.51 | | % 28.27/4.51 | | Case 1: % 28.27/4.51 | | | % 28.27/4.51 | | | (23) ~ (all_74_0 = init) % 28.27/4.51 | | | % 28.27/4.51 | | | REDUCE: (22), (23) imply: % 28.27/4.51 | | | (24) $false % 28.27/4.52 | | | % 28.27/4.52 | | | CLOSE: (24) is inconsistent. % 28.27/4.52 | | | % 28.27/4.52 | | Case 2: % 28.27/4.52 | | | % 28.27/4.52 | | | (25) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 28.27/4.52 | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, % 28.27/4.52 | | | v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 28.27/4.52 | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 28.27/4.52 | | | init) & a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) % 28.27/4.52 | | | = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 28.27/4.52 | | | % 28.27/4.52 | | | BETA: splitting (25) gives: % 28.27/4.52 | | | % 28.27/4.52 | | | Case 1: % 28.27/4.52 | | | | % 28.27/4.52 | | | | (26) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 28.27/4.52 | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, % 28.27/4.52 | | | | v0) = 0 & $i(v1) & $i(v0)) % 28.27/4.52 | | | | % 28.27/4.52 | | | | DELTA: instantiating (26) with fresh symbols all_400_0, all_400_1 gives: % 28.27/4.52 | | | | (27) ~ (all_400_0 = init) & a_select2(s_values7_init, all_400_1) = % 28.27/4.52 | | | | all_400_0 & leq(all_400_1, n3) = 0 & leq(n0, all_400_1) = 0 & % 28.27/4.52 | | | | $i(all_400_0) & $i(all_400_1) % 28.27/4.52 | | | | % 28.27/4.52 | | | | ALPHA: (27) implies: % 28.27/4.52 | | | | (28) ~ (all_400_0 = init) % 28.27/4.52 | | | | (29) $i(all_400_1) % 28.27/4.52 | | | | (30) leq(n0, all_400_1) = 0 % 28.27/4.52 | | | | (31) leq(all_400_1, n3) = 0 % 28.27/4.52 | | | | (32) a_select2(s_values7_init, all_400_1) = all_400_0 % 28.27/4.52 | | | | % 28.27/4.52 | | | | GROUND_INST: instantiating (20) with all_400_1, all_400_0, simplifying % 28.27/4.52 | | | | with (29), (32) gives: % 28.27/4.52 | | | | (33) all_400_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_400_1, % 28.27/4.52 | | | | n3) = v1 & leq(n0, all_400_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 28.27/4.52 | | | | 0))) % 28.27/4.52 | | | | % 28.27/4.52 | | | | BETA: splitting (33) gives: % 28.27/4.52 | | | | % 28.27/4.52 | | | | Case 1: % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | (34) all_400_0 = init % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | REDUCE: (28), (34) imply: % 28.27/4.52 | | | | | (35) $false % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | CLOSE: (35) is inconsistent. % 28.27/4.52 | | | | | % 28.27/4.52 | | | | Case 2: % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | (36) ? [v0: any] : ? [v1: any] : (leq(all_400_1, n3) = v1 & % 28.27/4.52 | | | | | leq(n0, all_400_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | DELTA: instantiating (36) with fresh symbols all_412_0, all_412_1 % 28.27/4.52 | | | | | gives: % 28.27/4.52 | | | | | (37) leq(all_400_1, n3) = all_412_0 & leq(n0, all_400_1) = % 28.27/4.52 | | | | | all_412_1 & ( ~ (all_412_0 = 0) | ~ (all_412_1 = 0)) % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | ALPHA: (37) implies: % 28.27/4.52 | | | | | (38) leq(n0, all_400_1) = all_412_1 % 28.27/4.52 | | | | | (39) leq(all_400_1, n3) = all_412_0 % 28.27/4.52 | | | | | (40) ~ (all_412_0 = 0) | ~ (all_412_1 = 0) % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | GROUND_INST: instantiating (6) with 0, all_412_1, all_400_1, n0, % 28.27/4.52 | | | | | simplifying with (30), (38) gives: % 28.27/4.52 | | | | | (41) all_412_1 = 0 % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | GROUND_INST: instantiating (6) with 0, all_412_0, n3, all_400_1, % 28.27/4.52 | | | | | simplifying with (31), (39) gives: % 28.27/4.52 | | | | | (42) all_412_0 = 0 % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | BETA: splitting (40) gives: % 28.27/4.52 | | | | | % 28.27/4.52 | | | | | Case 1: % 28.27/4.52 | | | | | | % 28.27/4.52 | | | | | | (43) ~ (all_412_0 = 0) % 28.27/4.52 | | | | | | % 28.27/4.52 | | | | | | REDUCE: (42), (43) imply: % 28.27/4.52 | | | | | | (44) $false % 28.27/4.52 | | | | | | % 28.27/4.52 | | | | | | CLOSE: (44) is inconsistent. % 28.27/4.52 | | | | | | % 28.27/4.52 | | | | | Case 2: % 28.27/4.52 | | | | | | % 28.27/4.52 | | | | | | (45) ~ (all_412_1 = 0) % 28.27/4.52 | | | | | | % 28.27/4.52 | | | | | | REDUCE: (41), (45) imply: % 28.27/4.52 | | | | | | (46) $false % 28.27/4.52 | | | | | | % 28.27/4.52 | | | | | | CLOSE: (46) is inconsistent. % 28.27/4.52 | | | | | | % 28.27/4.52 | | | | | End of split % 28.27/4.52 | | | | | % 28.27/4.52 | | | | End of split % 28.27/4.52 | | | | % 28.27/4.52 | | | Case 2: % 28.27/4.52 | | | | % 28.27/4.52 | | | | (47) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 28.27/4.52 | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 28.27/4.52 | | | | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & % 28.27/4.52 | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 28.27/4.52 | | | | % 28.27/4.52 | | | | DELTA: instantiating (47) with fresh symbol all_400_0 gives: % 28.27/4.52 | | | | (48) leq(all_400_0, n2) = 0 & leq(n0, all_400_0) = 0 & $i(all_400_0) % 28.27/4.52 | | | | & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 28.27/4.52 | | | | a_select3(simplex7_init, v0, all_400_0) = v1 & leq(v0, n3) = 0 % 28.27/4.52 | | | | & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 28.27/4.52 | | | | % 28.27/4.52 | | | | ALPHA: (48) implies: % 28.27/4.53 | | | | (49) $i(all_400_0) % 28.27/4.53 | | | | (50) leq(n0, all_400_0) = 0 % 28.27/4.53 | | | | (51) leq(all_400_0, n2) = 0 % 28.27/4.53 | | | | (52) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 28.27/4.53 | | | | a_select3(simplex7_init, v0, all_400_0) = v1 & leq(v0, n3) = 0 % 28.27/4.53 | | | | & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 28.27/4.53 | | | | % 28.27/4.53 | | | | DELTA: instantiating (52) with fresh symbols all_402_0, all_402_1 gives: % 28.27/4.53 | | | | (53) ~ (all_402_0 = init) & a_select3(simplex7_init, all_402_1, % 28.27/4.53 | | | | all_400_0) = all_402_0 & leq(all_402_1, n3) = 0 & leq(n0, % 28.27/4.53 | | | | all_402_1) = 0 & $i(all_402_0) & $i(all_402_1) % 28.27/4.53 | | | | % 28.27/4.53 | | | | ALPHA: (53) implies: % 28.27/4.53 | | | | (54) ~ (all_402_0 = init) % 28.27/4.53 | | | | (55) $i(all_402_1) % 28.27/4.53 | | | | (56) leq(n0, all_402_1) = 0 % 28.27/4.53 | | | | (57) leq(all_402_1, n3) = 0 % 28.27/4.53 | | | | (58) a_select3(simplex7_init, all_402_1, all_400_0) = all_402_0 % 28.27/4.53 | | | | % 28.27/4.53 | | | | GROUND_INST: instantiating (19) with all_400_0, simplifying with (49), % 28.27/4.53 | | | | (51) gives: % 28.27/4.53 | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_400_0) = v0) | ! [v0: % 28.27/4.53 | | | | $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(simplex7_init, % 28.27/4.53 | | | | v0, all_400_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 28.27/4.53 | | | | any] : (leq(v0, n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | % 28.27/4.53 | | | | ~ (v2 = 0)))) % 28.27/4.53 | | | | % 28.27/4.53 | | | | BETA: splitting (59) gives: % 28.27/4.53 | | | | % 28.27/4.53 | | | | Case 1: % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_400_0) = v0) % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | DELTA: instantiating (60) with fresh symbol all_413_0 gives: % 28.27/4.53 | | | | | (61) ~ (all_413_0 = 0) & leq(n0, all_400_0) = all_413_0 % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | ALPHA: (61) implies: % 28.27/4.53 | | | | | (62) ~ (all_413_0 = 0) % 28.27/4.53 | | | | | (63) leq(n0, all_400_0) = all_413_0 % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | GROUND_INST: instantiating (6) with 0, all_413_0, all_400_0, n0, % 28.27/4.53 | | | | | simplifying with (50), (63) gives: % 28.27/4.53 | | | | | (64) all_413_0 = 0 % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | REDUCE: (62), (64) imply: % 28.27/4.53 | | | | | (65) $false % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | CLOSE: (65) is inconsistent. % 28.27/4.53 | | | | | % 28.27/4.53 | | | | Case 2: % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | (66) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 28.27/4.53 | | | | | (a_select3(simplex7_init, v0, all_400_0) = v1) | ~ $i(v0) | % 28.27/4.53 | | | | | ? [v2: any] : ? [v3: any] : (leq(v0, n3) = v3 & leq(n0, % 28.27/4.53 | | | | | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | GROUND_INST: instantiating (66) with all_402_1, all_402_0, simplifying % 28.27/4.53 | | | | | with (55), (58) gives: % 28.27/4.53 | | | | | (67) all_402_0 = init | ? [v0: any] : ? [v1: any] : % 28.27/4.53 | | | | | (leq(all_402_1, n3) = v1 & leq(n0, all_402_1) = v0 & ( ~ (v1 = % 28.27/4.53 | | | | | 0) | ~ (v0 = 0))) % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | BETA: splitting (67) gives: % 28.27/4.53 | | | | | % 28.27/4.53 | | | | | Case 1: % 28.27/4.53 | | | | | | % 28.27/4.53 | | | | | | (68) all_402_0 = init % 28.27/4.53 | | | | | | % 28.27/4.53 | | | | | | REDUCE: (54), (68) imply: % 28.27/4.53 | | | | | | (69) $false % 28.27/4.53 | | | | | | % 28.27/4.53 | | | | | | CLOSE: (69) is inconsistent. % 28.27/4.53 | | | | | | % 28.27/4.53 | | | | | Case 2: % 28.27/4.53 | | | | | | % 28.27/4.53 | | | | | | (70) ? [v0: any] : ? [v1: any] : (leq(all_402_1, n3) = v1 & % 28.27/4.53 | | | | | | leq(n0, all_402_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 28.27/4.53 | | | | | | % 28.27/4.53 | | | | | | DELTA: instantiating (70) with fresh symbols all_522_0, all_522_1 % 28.27/4.53 | | | | | | gives: % 28.27/4.53 | | | | | | (71) leq(all_402_1, n3) = all_522_0 & leq(n0, all_402_1) = % 28.27/4.53 | | | | | | all_522_1 & ( ~ (all_522_0 = 0) | ~ (all_522_1 = 0)) % 28.27/4.53 | | | | | | % 28.27/4.53 | | | | | | ALPHA: (71) implies: % 28.27/4.53 | | | | | | (72) leq(n0, all_402_1) = all_522_1 % 28.27/4.53 | | | | | | (73) leq(all_402_1, n3) = all_522_0 % 28.27/4.53 | | | | | | (74) ~ (all_522_0 = 0) | ~ (all_522_1 = 0) % 28.27/4.53 | | | | | | % 28.27/4.53 | | | | | | GROUND_INST: instantiating (6) with 0, all_522_1, all_402_1, n0, % 28.27/4.53 | | | | | | simplifying with (56), (72) gives: % 28.27/4.53 | | | | | | (75) all_522_1 = 0 % 28.27/4.53 | | | | | | % 28.27/4.54 | | | | | | GROUND_INST: instantiating (6) with 0, all_522_0, n3, all_402_1, % 28.27/4.54 | | | | | | simplifying with (57), (73) gives: % 28.27/4.54 | | | | | | (76) all_522_0 = 0 % 28.27/4.54 | | | | | | % 28.27/4.54 | | | | | | BETA: splitting (74) gives: % 28.27/4.54 | | | | | | % 28.27/4.54 | | | | | | Case 1: % 28.27/4.54 | | | | | | | % 28.27/4.54 | | | | | | | (77) ~ (all_522_0 = 0) % 28.27/4.54 | | | | | | | % 28.27/4.54 | | | | | | | REDUCE: (76), (77) imply: % 28.27/4.54 | | | | | | | (78) $false % 28.27/4.54 | | | | | | | % 28.27/4.54 | | | | | | | CLOSE: (78) is inconsistent. % 28.27/4.54 | | | | | | | % 28.27/4.54 | | | | | | Case 2: % 28.27/4.54 | | | | | | | % 28.27/4.54 | | | | | | | (79) ~ (all_522_1 = 0) % 28.27/4.54 | | | | | | | % 28.27/4.54 | | | | | | | REDUCE: (75), (79) imply: % 28.27/4.54 | | | | | | | (80) $false % 28.27/4.54 | | | | | | | % 28.27/4.54 | | | | | | | CLOSE: (80) is inconsistent. % 28.27/4.54 | | | | | | | % 28.27/4.54 | | | | | | End of split % 28.27/4.54 | | | | | | % 28.27/4.54 | | | | | End of split % 28.27/4.54 | | | | | % 28.27/4.54 | | | | End of split % 28.27/4.54 | | | | % 28.27/4.54 | | | End of split % 28.27/4.54 | | | % 28.27/4.54 | | End of split % 28.27/4.54 | | % 28.27/4.54 | Case 2: % 28.27/4.54 | | % 28.27/4.54 | | (81) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 28.27/4.54 | | (leq(pv10, all_74_4) = v3 & leq(pv9, all_74_5) = v1 & leq(n0, pv10) % 28.27/4.54 | | = v2 & leq(n0, pv9) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = % 28.27/4.54 | | 0) | ~ (v0 = 0))) % 28.27/4.54 | | % 28.27/4.54 | | DELTA: instantiating (81) with fresh symbols all_105_0, all_105_1, % 28.27/4.54 | | all_105_2, all_105_3 gives: % 28.27/4.54 | | (82) leq(pv10, all_74_4) = all_105_0 & leq(pv9, all_74_5) = all_105_2 & % 28.27/4.54 | | leq(n0, pv10) = all_105_1 & leq(n0, pv9) = all_105_3 & ( ~ % 28.27/4.54 | | (all_105_0 = 0) | ~ (all_105_1 = 0) | ~ (all_105_2 = 0) | ~ % 28.27/4.54 | | (all_105_3 = 0)) % 28.27/4.54 | | % 28.27/4.54 | | ALPHA: (82) implies: % 28.27/4.54 | | (83) leq(n0, pv9) = all_105_3 % 28.27/4.54 | | (84) leq(n0, pv10) = all_105_1 % 28.27/4.54 | | (85) leq(pv9, all_74_5) = all_105_2 % 28.27/4.54 | | (86) leq(pv10, all_74_4) = all_105_0 % 28.27/4.54 | | (87) ~ (all_105_0 = 0) | ~ (all_105_1 = 0) | ~ (all_105_2 = 0) | ~ % 28.27/4.54 | | (all_105_3 = 0) % 28.27/4.54 | | % 28.27/4.54 | | GROUND_INST: instantiating (6) with 0, all_105_3, pv9, n0, simplifying with % 28.27/4.54 | | (10), (83) gives: % 28.27/4.54 | | (88) all_105_3 = 0 % 28.27/4.54 | | % 28.27/4.54 | | GROUND_INST: instantiating (6) with 0, all_105_1, pv10, n0, simplifying with % 28.27/4.54 | | (11), (84) gives: % 28.27/4.54 | | (89) all_105_1 = 0 % 28.27/4.54 | | % 28.27/4.54 | | GROUND_INST: instantiating (6) with 0, all_105_2, all_74_5, pv9, simplifying % 28.27/4.54 | | with (12), (85) gives: % 28.27/4.54 | | (90) all_105_2 = 0 % 28.27/4.54 | | % 28.27/4.54 | | GROUND_INST: instantiating (6) with 0, all_105_0, all_74_4, pv10, % 28.27/4.54 | | simplifying with (13), (86) gives: % 28.27/4.54 | | (91) all_105_0 = 0 % 28.27/4.54 | | % 28.27/4.54 | | BETA: splitting (87) gives: % 28.27/4.54 | | % 28.27/4.54 | | Case 1: % 28.27/4.54 | | | % 28.27/4.54 | | | (92) ~ (all_105_0 = 0) % 28.27/4.54 | | | % 28.27/4.54 | | | REDUCE: (91), (92) imply: % 28.27/4.54 | | | (93) $false % 28.27/4.54 | | | % 28.27/4.54 | | | CLOSE: (93) is inconsistent. % 28.27/4.54 | | | % 28.27/4.54 | | Case 2: % 28.27/4.54 | | | % 28.27/4.54 | | | (94) ~ (all_105_1 = 0) | ~ (all_105_2 = 0) | ~ (all_105_3 = 0) % 28.27/4.54 | | | % 28.27/4.54 | | | BETA: splitting (94) gives: % 28.27/4.54 | | | % 28.27/4.54 | | | Case 1: % 28.27/4.54 | | | | % 28.27/4.54 | | | | (95) ~ (all_105_1 = 0) % 28.27/4.54 | | | | % 28.27/4.54 | | | | REDUCE: (89), (95) imply: % 28.27/4.54 | | | | (96) $false % 28.27/4.54 | | | | % 28.27/4.54 | | | | CLOSE: (96) is inconsistent. % 28.27/4.54 | | | | % 28.27/4.54 | | | Case 2: % 28.27/4.54 | | | | % 28.27/4.54 | | | | (97) ~ (all_105_2 = 0) | ~ (all_105_3 = 0) % 28.27/4.54 | | | | % 28.27/4.54 | | | | BETA: splitting (97) gives: % 28.27/4.54 | | | | % 28.27/4.54 | | | | Case 1: % 28.27/4.54 | | | | | % 28.27/4.54 | | | | | (98) ~ (all_105_2 = 0) % 28.27/4.54 | | | | | % 28.27/4.54 | | | | | REDUCE: (90), (98) imply: % 28.27/4.54 | | | | | (99) $false % 28.27/4.54 | | | | | % 28.27/4.54 | | | | | CLOSE: (99) is inconsistent. % 28.27/4.54 | | | | | % 28.27/4.54 | | | | Case 2: % 28.27/4.54 | | | | | % 28.27/4.54 | | | | | (100) ~ (all_105_3 = 0) % 28.27/4.54 | | | | | % 28.27/4.54 | | | | | REDUCE: (88), (100) imply: % 28.27/4.54 | | | | | (101) $false % 28.27/4.54 | | | | | % 28.27/4.54 | | | | | CLOSE: (101) is inconsistent. % 28.27/4.54 | | | | | % 28.27/4.54 | | | | End of split % 28.27/4.54 | | | | % 28.27/4.54 | | | End of split % 28.27/4.54 | | | % 28.27/4.54 | | End of split % 28.27/4.54 | | % 28.27/4.54 | End of split % 28.27/4.54 | % 28.27/4.54 End of proof % 28.27/4.54 % SZS output end Proof for theBenchmark % 28.27/4.54 % 28.27/4.54 3937ms %------------------------------------------------------------------------------