%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV185+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 : n003.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 22:55:15 EDT 2023 % Result : Theorem 14.95s 2.65s % Output : Proof 18.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SWV185+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.08/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n003.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 10:30:40 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.65/0.62 Running up to 7 provers in parallel. % 0.65/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.65/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.65/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.65/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.65/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.65/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.65/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.63/1.43 Prover 4: Preprocessing ... % 6.02/1.47 Prover 1: Preprocessing ... % 6.02/1.49 Prover 5: Preprocessing ... % 6.02/1.49 Prover 6: Preprocessing ... % 6.02/1.49 Prover 2: Preprocessing ... % 6.02/1.50 Prover 0: Preprocessing ... % 6.02/1.51 Prover 3: Preprocessing ... % 11.97/2.26 Prover 1: Warning: ignoring some quantifiers % 11.97/2.30 Prover 3: Warning: ignoring some quantifiers % 11.97/2.32 Prover 1: Constructing countermodel ... % 11.97/2.33 Prover 6: Proving ... % 12.67/2.34 Prover 3: Constructing countermodel ... % 12.67/2.38 Prover 4: Warning: ignoring some quantifiers % 13.11/2.49 Prover 5: Proving ... % 13.11/2.49 Prover 4: Constructing countermodel ... % 13.99/2.53 Prover 2: Proving ... % 14.33/2.58 Prover 0: Proving ... % 14.95/2.65 Prover 3: proved (2023ms) % 14.95/2.65 % 14.95/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.95/2.65 % 14.95/2.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.95/2.65 Prover 5: stopped % 14.95/2.65 Prover 2: stopped % 14.95/2.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.95/2.65 Prover 0: stopped % 14.95/2.67 Prover 6: stopped % 15.25/2.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.25/2.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.25/2.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.35/2.83 Prover 8: Preprocessing ... % 16.67/2.86 Prover 10: Preprocessing ... % 16.67/2.87 Prover 7: Preprocessing ... % 16.67/2.87 Prover 11: Preprocessing ... % 16.67/2.87 Prover 1: Found proof (size 17) % 16.67/2.87 Prover 1: proved (2249ms) % 16.67/2.88 Prover 4: stopped % 16.67/2.90 Prover 13: Preprocessing ... % 17.29/2.95 Prover 10: stopped % 17.29/2.97 Prover 7: stopped % 17.57/2.99 Prover 11: stopped % 17.57/3.01 Prover 13: stopped % 17.57/3.05 Prover 8: Warning: ignoring some quantifiers % 18.06/3.07 Prover 8: Constructing countermodel ... % 18.06/3.09 Prover 8: stopped % 18.06/3.09 % 18.06/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.06/3.09 % 18.17/3.10 % SZS output start Proof for theBenchmark % 18.17/3.10 Assumptions after simplification: % 18.17/3.10 --------------------------------- % 18.17/3.10 % 18.17/3.10 (cl5_nebula_init_0101) % 18.17/3.13 gt(loopcounter, n1) = 0 & $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) % 18.17/3.13 & $i(center_init) & $i(sigma_init) & $i(mu_init) & $i(rho_init) & $i(init) & % 18.17/3.13 $i(q_init) & $i(n135299) & $i(loopcounter) & $i(n4) & $i(n1) & $i(n0) & ! % 18.17/3.13 [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(center_init, v0, n0) = v1) % 18.17/3.13 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) % 18.17/3.13 = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = % 18.17/3.13 init | ~ (a_select2(sigmaold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 18.17/3.13 ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = % 18.17/3.13 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 18.17/3.13 (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 18.17/3.13 : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! % 18.17/3.14 [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(muold_init, v0) = v1) | ~ % 18.17/3.14 $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 % 18.17/3.14 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | % 18.17/3.14 ~ (a_select2(sigma_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 18.17/3.14 any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = % 18.17/3.14 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 18.17/3.14 (a_select2(mu_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 18.17/3.14 (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! % 18.17/3.14 [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rho_init, v0) = v1) | ~ % 18.17/3.14 $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 % 18.17/3.14 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ (leq(v0, n135299) = 0) % 18.17/3.14 | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] % 18.17/3.14 : ! [v2: $i] : (v2 = init | ~ (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) % 18.17/3.14 | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ % 18.17/3.14 (v4 = 0) | ~ (v3 = 0))))) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 18.17/3.14 init) & a_select2(rhoold_init, v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = % 18.17/3.14 0 & $i(v1) & $i(v0)) % 18.17/3.14 % 18.17/3.14 (function-axioms) % 18.17/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.17/3.15 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 18.17/3.15 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.17/3.15 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 18.17/3.15 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.17/3.15 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 18.17/3.15 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.17/3.15 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 18.17/3.15 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.17/3.15 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 18.17/3.15 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.17/3.15 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 18.17/3.15 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 18.17/3.15 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 18.17/3.15 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 18.17/3.15 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.17/3.15 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 18.17/3.15 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 18.17/3.15 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 18.17/3.15 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 18.17/3.15 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 18.17/3.15 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 18.17/3.15 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 18.17/3.15 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 18.17/3.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.17/3.15 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 18.17/3.15 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 18.17/3.15 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 18.17/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.17/3.15 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 18.17/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.17/3.15 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 18.17/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.17/3.15 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 18.17/3.15 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 18.17/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 18.17/3.15 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.17/3.15 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.17/3.15 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 18.17/3.15 % 18.17/3.15 Further assumptions not needed in the proof: % 18.17/3.15 -------------------------------------------- % 18.17/3.15 const_array1_select, const_array2_select, defuse, finite_domain_0, % 18.17/3.15 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 18.17/3.15 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, % 18.17/3.15 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, % 18.17/3.15 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, % 18.17/3.15 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, % 18.17/3.15 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 18.17/3.15 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, % 18.17/3.15 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 18.17/3.15 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 18.17/3.15 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 18.17/3.15 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 18.17/3.15 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 18.17/3.15 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 18.17/3.15 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, % 18.17/3.15 successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 18.17/3.15 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue, % 18.17/3.15 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 18.17/3.15 % 18.17/3.15 Those formulas are unsatisfiable: % 18.17/3.15 --------------------------------- % 18.17/3.15 % 18.17/3.15 Begin of proof % 18.17/3.15 | % 18.17/3.15 | ALPHA: (cl5_nebula_init_0101) implies: % 18.17/3.15 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rhoold_init, v0) % 18.17/3.15 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 % 18.17/3.15 | & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 18.17/3.15 | (2) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(rhoold_init, % 18.17/3.15 | v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 18.17/3.15 | % 18.17/3.15 | ALPHA: (function-axioms) implies: % 18.17/3.15 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.17/3.15 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 18.17/3.15 | % 18.48/3.15 | DELTA: instantiating (2) with fresh symbols all_54_0, all_54_1 gives: % 18.48/3.16 | (4) ~ (all_54_0 = init) & a_select2(rhoold_init, all_54_1) = all_54_0 & % 18.48/3.16 | leq(all_54_1, n4) = 0 & leq(n0, all_54_1) = 0 & $i(all_54_0) & % 18.48/3.16 | $i(all_54_1) % 18.48/3.16 | % 18.48/3.16 | ALPHA: (4) implies: % 18.48/3.16 | (5) ~ (all_54_0 = init) % 18.48/3.16 | (6) $i(all_54_1) % 18.48/3.16 | (7) leq(n0, all_54_1) = 0 % 18.48/3.16 | (8) leq(all_54_1, n4) = 0 % 18.48/3.16 | (9) a_select2(rhoold_init, all_54_1) = all_54_0 % 18.48/3.16 | % 18.48/3.16 | GROUND_INST: instantiating (1) with all_54_1, all_54_0, simplifying with (6), % 18.48/3.16 | (9) gives: % 18.48/3.16 | (10) all_54_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_54_1, n4) = % 18.48/3.16 | v1 & leq(n0, all_54_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 18.48/3.16 | % 18.48/3.16 | BETA: splitting (10) gives: % 18.48/3.16 | % 18.48/3.16 | Case 1: % 18.48/3.16 | | % 18.48/3.16 | | (11) all_54_0 = init % 18.48/3.16 | | % 18.48/3.16 | | REDUCE: (5), (11) imply: % 18.48/3.16 | | (12) $false % 18.51/3.16 | | % 18.51/3.16 | | CLOSE: (12) is inconsistent. % 18.51/3.16 | | % 18.51/3.16 | Case 2: % 18.51/3.16 | | % 18.51/3.16 | | (13) ? [v0: any] : ? [v1: any] : (leq(all_54_1, n4) = v1 & leq(n0, % 18.51/3.16 | | all_54_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 18.51/3.16 | | % 18.51/3.16 | | DELTA: instantiating (13) with fresh symbols all_105_0, all_105_1 gives: % 18.51/3.16 | | (14) leq(all_54_1, n4) = all_105_0 & leq(n0, all_54_1) = all_105_1 & ( ~ % 18.51/3.16 | | (all_105_0 = 0) | ~ (all_105_1 = 0)) % 18.51/3.16 | | % 18.51/3.16 | | ALPHA: (14) implies: % 18.51/3.16 | | (15) leq(n0, all_54_1) = all_105_1 % 18.51/3.16 | | (16) leq(all_54_1, n4) = all_105_0 % 18.51/3.16 | | (17) ~ (all_105_0 = 0) | ~ (all_105_1 = 0) % 18.51/3.16 | | % 18.51/3.16 | | GROUND_INST: instantiating (3) with 0, all_105_1, all_54_1, n0, simplifying % 18.51/3.16 | | with (7), (15) gives: % 18.51/3.16 | | (18) all_105_1 = 0 % 18.51/3.16 | | % 18.51/3.16 | | GROUND_INST: instantiating (3) with 0, all_105_0, n4, all_54_1, simplifying % 18.51/3.16 | | with (8), (16) gives: % 18.51/3.16 | | (19) all_105_0 = 0 % 18.51/3.16 | | % 18.51/3.16 | | BETA: splitting (17) gives: % 18.51/3.16 | | % 18.51/3.16 | | Case 1: % 18.51/3.16 | | | % 18.51/3.16 | | | (20) ~ (all_105_0 = 0) % 18.51/3.16 | | | % 18.51/3.16 | | | REDUCE: (19), (20) imply: % 18.51/3.16 | | | (21) $false % 18.51/3.16 | | | % 18.51/3.16 | | | CLOSE: (21) is inconsistent. % 18.51/3.16 | | | % 18.51/3.16 | | Case 2: % 18.51/3.16 | | | % 18.51/3.16 | | | (22) ~ (all_105_1 = 0) % 18.51/3.16 | | | % 18.51/3.16 | | | REDUCE: (18), (22) imply: % 18.51/3.16 | | | (23) $false % 18.51/3.16 | | | % 18.51/3.16 | | | CLOSE: (23) is inconsistent. % 18.51/3.16 | | | % 18.51/3.16 | | End of split % 18.51/3.16 | | % 18.51/3.16 | End of split % 18.51/3.16 | % 18.51/3.16 End of proof % 18.51/3.16 % SZS output end Proof for theBenchmark % 18.51/3.16 % 18.51/3.16 2559ms %------------------------------------------------------------------------------