%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV182+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 : n007.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 13.39s 2.48s % Output : Proof 17.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV182+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n007.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 02:54:58 EDT 2023 % 0.13/0.33 % CPUTime : % 0.59/0.60 ________ _____ % 0.59/0.60 ___ __ \_________(_)________________________________ % 0.59/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.59/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.59/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.59/0.60 % 0.59/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.59/0.60 (2023-06-19) % 0.59/0.60 % 0.59/0.60 (c) Philipp Rümmer, 2009-2023 % 0.59/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.59/0.60 Amanda Stjerna. % 0.59/0.60 Free software under BSD-3-Clause. % 0.59/0.60 % 0.59/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.59/0.60 % 0.59/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.59/0.62 Running up to 7 provers in parallel. % 0.59/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.59/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.59/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.59/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.59/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.59/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.59/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.31/1.29 Prover 4: Preprocessing ... % 4.31/1.30 Prover 1: Preprocessing ... % 4.75/1.33 Prover 6: Preprocessing ... % 4.75/1.33 Prover 3: Preprocessing ... % 4.75/1.33 Prover 2: Preprocessing ... % 4.75/1.33 Prover 0: Preprocessing ... % 4.75/1.34 Prover 5: Preprocessing ... % 9.95/2.05 Prover 1: Warning: ignoring some quantifiers % 10.72/2.09 Prover 3: Warning: ignoring some quantifiers % 11.10/2.13 Prover 3: Constructing countermodel ... % 11.16/2.15 Prover 1: Constructing countermodel ... % 11.16/2.15 Prover 6: Proving ... % 11.16/2.19 Prover 4: Warning: ignoring some quantifiers % 12.30/2.29 Prover 4: Constructing countermodel ... % 12.30/2.30 Prover 5: Proving ... % 12.30/2.33 Prover 2: Proving ... % 12.30/2.34 Prover 0: Proving ... % 13.39/2.48 Prover 3: proved (1853ms) % 13.39/2.48 % 13.39/2.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.39/2.48 % 13.39/2.48 Prover 5: stopped % 13.39/2.48 Prover 2: stopped % 13.39/2.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.39/2.49 Prover 6: stopped % 13.39/2.50 Prover 0: stopped % 14.05/2.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.05/2.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.05/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.05/2.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.64/2.67 Prover 1: Found proof (size 48) % 14.64/2.67 Prover 1: proved (2044ms) % 15.33/2.67 Prover 4: stopped % 15.45/2.70 Prover 7: Preprocessing ... % 15.71/2.73 Prover 13: Preprocessing ... % 15.71/2.73 Prover 10: Preprocessing ... % 15.79/2.74 Prover 8: Preprocessing ... % 15.79/2.74 Prover 11: Preprocessing ... % 15.79/2.78 Prover 7: stopped % 15.79/2.80 Prover 10: stopped % 16.46/2.84 Prover 11: stopped % 16.46/2.84 Prover 13: stopped % 16.82/2.93 Prover 8: Warning: ignoring some quantifiers % 16.82/2.94 Prover 8: Constructing countermodel ... % 16.82/2.96 Prover 8: stopped % 17.19/2.96 % 17.19/2.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.19/2.96 % 17.19/2.97 % SZS output start Proof for theBenchmark % 17.26/2.98 Assumptions after simplification: % 17.26/2.98 --------------------------------- % 17.26/2.98 % 17.26/2.98 (cl5_nebula_init_0086) % 17.43/3.01 $i(sigma_init) & $i(rho_init) & $i(mu_init) & $i(center_init) & $i(init) & % 17.43/3.01 $i(q_init) & $i(n135299) & $i(loopcounter) & $i(pv76) & $i(tptp_float_0_001) & % 17.43/3.01 $i(n4) & $i(n1) & $i(n0) & ? [v0: any] : (leq(tptp_float_0_001, pv76) = 0 & % 17.43/3.01 leq(n1, loopcounter) = 0 & gt(loopcounter, n0) = v0 & ! [v1: $i] : ! [v2: % 17.43/3.01 $i] : (v2 = init | ~ (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | % 17.43/3.01 ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ % 17.43/3.01 (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, n135299) = 0) | % 17.43/3.01 ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] % 17.43/3.01 : ! [v3: $i] : (v3 = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ % 17.43/3.01 $i(v2) | ? [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = % 17.43/3.01 v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ % 17.43/3.01 (v2 = init) & a_select2(rho_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) % 17.43/3.01 = 0 & $i(v2) & $i(v1)) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 = % 17.43/3.01 init | ~ (a_select2(sigma_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : % 17.43/3.01 ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ % 17.43/3.01 (v3 = 0))))) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init % 17.43/3.01 | ~ (a_select2(rho_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 17.43/3.01 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 17.43/3.01 0))))) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 17.43/3.01 ~ (a_select2(mu_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 17.43/3.01 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 17.43/3.01 0)))))) % 17.43/3.01 % 17.43/3.01 (leq_succ_gt) % 17.43/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2, % 17.43/3.02 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 17.43/3.02 % 17.43/3.02 (successor_1) % 17.43/3.02 succ(n0) = n1 & $i(n1) & $i(n0) % 17.43/3.02 % 17.43/3.02 (successor_2) % 17.43/3.02 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 17.43/3.02 % 17.43/3.02 (successor_3) % 17.43/3.02 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 17.43/3.02 succ(n0) = v0 & $i(v1) & $i(v0)) % 17.43/3.02 % 17.43/3.02 (successor_4) % 17.43/3.02 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 17.43/3.02 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 17.43/3.02 % 17.43/3.02 (successor_5) % 17.43/3.02 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 17.43/3.02 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 17.43/3.02 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.43/3.02 % 17.43/3.02 (function-axioms) % 17.43/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.43/3.02 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 17.43/3.02 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.43/3.02 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 17.43/3.02 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.43/3.02 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 17.43/3.02 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.43/3.02 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 17.43/3.02 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.43/3.02 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 17.43/3.02 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.43/3.02 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 17.43/3.02 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.43/3.02 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 17.43/3.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 17.43/3.02 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.43/3.02 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 17.43/3.02 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 17.43/3.02 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 17.43/3.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 17.43/3.02 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 17.43/3.02 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 17.43/3.02 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.43/3.02 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 17.43/3.02 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.43/3.03 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 17.43/3.03 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.43/3.03 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 17.43/3.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.43/3.03 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 17.43/3.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.43/3.03 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 17.43/3.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.43/3.03 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 17.43/3.03 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 17.43/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 17.43/3.03 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.43/3.03 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.43/3.03 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 17.43/3.03 % 17.43/3.03 Further assumptions not needed in the proof: % 17.43/3.03 -------------------------------------------- % 17.43/3.03 const_array1_select, const_array2_select, defuse, finite_domain_0, % 17.43/3.03 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 17.43/3.03 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, % 17.43/3.03 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, % 17.43/3.03 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, % 17.43/3.03 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, % 17.43/3.03 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 17.43/3.03 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt_equiv, % 17.43/3.03 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 17.43/3.03 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 17.43/3.03 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 17.43/3.03 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 17.43/3.03 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 17.43/3.03 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 17.43/3.03 succ_plus_5_r, succ_pred, succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, % 17.43/3.03 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 17.43/3.03 uniform_int_rand_ranges_lo % 17.43/3.03 % 17.43/3.03 Those formulas are unsatisfiable: % 17.43/3.03 --------------------------------- % 17.43/3.03 % 17.43/3.03 Begin of proof % 17.43/3.03 | % 17.43/3.03 | ALPHA: (successor_4) implies: % 17.43/3.03 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 17.43/3.03 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 17.43/3.03 | % 17.43/3.03 | ALPHA: (successor_5) implies: % 17.43/3.03 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 17.43/3.03 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 17.43/3.03 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.43/3.03 | % 17.43/3.03 | ALPHA: (successor_1) implies: % 17.43/3.03 | (3) succ(n0) = n1 % 17.43/3.03 | % 17.43/3.03 | ALPHA: (successor_2) implies: % 17.43/3.03 | (4) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 17.43/3.03 | % 17.43/3.03 | ALPHA: (successor_3) implies: % 17.43/3.03 | (5) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) = % 17.43/3.03 | v0 & $i(v1) & $i(v0)) % 17.43/3.03 | % 17.43/3.03 | ALPHA: (cl5_nebula_init_0086) implies: % 17.43/3.03 | (6) $i(n0) % 17.43/3.03 | (7) $i(loopcounter) % 17.53/3.03 | (8) ? [v0: any] : (leq(tptp_float_0_001, pv76) = 0 & leq(n1, loopcounter) % 17.53/3.03 | = 0 & gt(loopcounter, n0) = v0 & ! [v1: $i] : ! [v2: $i] : (v2 = % 17.53/3.03 | init | ~ (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | ? % 17.53/3.03 | [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( % 17.53/3.03 | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, % 17.53/3.04 | n135299) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & % 17.53/3.04 | leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ % 17.53/3.04 | (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 17.53/3.04 | [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | % 17.53/3.04 | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 17.53/3.04 | & a_select2(rho_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = 0 % 17.53/3.04 | & $i(v2) & $i(v1)) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 % 17.53/3.04 | = init | ~ (a_select2(sigma_init, v1) = v2) | ~ $i(v1) | ? % 17.53/3.04 | [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & % 17.53/3.04 | ( ~ (v4 = 0) | ~ (v3 = 0))))) & ( ~ (v0 = 0) | ! [v1: $i] : % 17.53/3.04 | ! [v2: $i] : (v2 = init | ~ (a_select2(rho_init, v1) = v2) | ~ % 17.53/3.04 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & % 17.53/3.04 | leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ( ~ (v0 = % 17.53/3.04 | 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 17.53/3.04 | (a_select2(mu_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 17.53/3.04 | [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 17.53/3.04 | ~ (v3 = 0)))))) % 17.53/3.04 | % 17.53/3.04 | ALPHA: (function-axioms) implies: % 17.53/3.04 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) % 17.53/3.04 | | ~ (succ(v2) = v0)) % 17.53/3.04 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.53/3.04 | : ! [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = % 17.53/3.04 | v0)) % 17.53/3.04 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.53/3.04 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 17.53/3.04 | v0)) % 17.53/3.04 | % 17.53/3.04 | DELTA: instantiating (4) with fresh symbol all_49_0 gives: % 17.53/3.04 | (12) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0) % 17.53/3.04 | % 17.53/3.04 | ALPHA: (12) implies: % 17.53/3.04 | (13) succ(n0) = all_49_0 % 17.53/3.04 | % 17.53/3.04 | DELTA: instantiating (5) with fresh symbols all_51_0, all_51_1 gives: % 17.53/3.04 | (14) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1 % 17.53/3.04 | & $i(all_51_0) & $i(all_51_1) % 17.53/3.04 | % 17.53/3.04 | ALPHA: (14) implies: % 17.53/3.04 | (15) succ(n0) = all_51_1 % 17.53/3.04 | % 17.53/3.04 | DELTA: instantiating (1) with fresh symbols all_53_0, all_53_1, all_53_2 % 17.53/3.04 | gives: % 17.53/3.04 | (16) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) = % 17.53/3.04 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) & % 17.53/3.04 | $i(all_53_2) % 17.53/3.04 | % 17.53/3.04 | ALPHA: (16) implies: % 17.53/3.04 | (17) succ(n0) = all_53_2 % 17.53/3.04 | % 17.53/3.04 | DELTA: instantiating (2) with fresh symbols all_55_0, all_55_1, all_55_2, % 17.53/3.04 | all_55_3 gives: % 17.53/3.04 | (18) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) = % 17.53/3.04 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 & % 17.53/3.04 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) % 17.53/3.04 | % 17.53/3.04 | ALPHA: (18) implies: % 17.53/3.04 | (19) succ(n0) = all_55_3 % 17.53/3.04 | % 17.53/3.04 | DELTA: instantiating (8) with fresh symbol all_74_0 gives: % 17.53/3.04 | (20) leq(tptp_float_0_001, pv76) = 0 & leq(n1, loopcounter) = 0 & % 17.53/3.04 | gt(loopcounter, n0) = all_74_0 & ! [v0: $i] : ! [v1: $i] : (v1 = % 17.53/3.04 | init | ~ (a_select3(center_init, v0, n0) = v1) | ~ $i(v0) | ? % 17.53/3.04 | [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( % 17.53/3.04 | ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ (leq(v0, % 17.53/3.04 | n135299) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 17.53/3.04 | leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 17.53/3.04 | (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 17.53/3.04 | [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 17.53/3.04 | ~ (v3 = 0))))) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 17.53/3.04 | a_select2(rho_init, v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & % 17.53/3.04 | $i(v1) & $i(v0)) & ( ~ (all_74_0 = 0) | ! [v0: $i] : ! [v1: $i] : % 17.53/3.04 | (v1 = init | ~ (a_select2(sigma_init, v0) = v1) | ~ $i(v0) | ? % 17.53/3.04 | [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & % 17.53/3.04 | ( ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ (all_74_0 = 0) | ! [v0: % 17.53/3.04 | $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rho_init, v0) = v1) % 17.53/3.04 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & % 17.53/3.04 | leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ % 17.53/3.04 | (all_74_0 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 17.53/3.04 | (a_select2(mu_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 17.53/3.04 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 17.53/3.04 | (v2 = 0))))) % 17.53/3.04 | % 17.53/3.04 | ALPHA: (20) implies: % 17.53/3.05 | (21) gt(loopcounter, n0) = all_74_0 % 17.53/3.05 | (22) leq(n1, loopcounter) = 0 % 17.53/3.05 | (23) ~ (all_74_0 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 17.53/3.05 | (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 17.53/3.05 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 17.53/3.05 | (v2 = 0)))) % 17.53/3.05 | (24) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(rho_init, v0) % 17.53/3.05 | = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 17.53/3.05 | % 17.53/3.05 | DELTA: instantiating (24) with fresh symbols all_79_0, all_79_1 gives: % 17.53/3.05 | (25) ~ (all_79_0 = init) & a_select2(rho_init, all_79_1) = all_79_0 & % 17.53/3.05 | leq(all_79_1, n4) = 0 & leq(n0, all_79_1) = 0 & $i(all_79_0) & % 17.53/3.05 | $i(all_79_1) % 17.53/3.05 | % 17.53/3.05 | ALPHA: (25) implies: % 17.53/3.05 | (26) ~ (all_79_0 = init) % 17.53/3.05 | (27) $i(all_79_1) % 17.53/3.05 | (28) leq(n0, all_79_1) = 0 % 17.53/3.05 | (29) leq(all_79_1, n4) = 0 % 17.53/3.05 | (30) a_select2(rho_init, all_79_1) = all_79_0 % 17.53/3.05 | % 17.53/3.05 | GROUND_INST: instantiating (9) with all_51_1, all_53_2, n0, simplifying with % 17.53/3.05 | (15), (17) gives: % 17.53/3.05 | (31) all_53_2 = all_51_1 % 17.53/3.05 | % 17.53/3.05 | GROUND_INST: instantiating (9) with all_49_0, all_53_2, n0, simplifying with % 17.53/3.05 | (13), (17) gives: % 17.53/3.05 | (32) all_53_2 = all_49_0 % 17.53/3.05 | % 17.53/3.05 | GROUND_INST: instantiating (9) with all_53_2, all_55_3, n0, simplifying with % 17.53/3.05 | (17), (19) gives: % 17.53/3.05 | (33) all_55_3 = all_53_2 % 17.53/3.05 | % 17.53/3.05 | GROUND_INST: instantiating (9) with n1, all_55_3, n0, simplifying with (3), % 17.53/3.05 | (19) gives: % 17.53/3.05 | (34) all_55_3 = n1 % 17.53/3.05 | % 17.53/3.05 | COMBINE_EQS: (33), (34) imply: % 17.53/3.05 | (35) all_53_2 = n1 % 17.53/3.05 | % 17.53/3.05 | SIMP: (35) implies: % 17.53/3.05 | (36) all_53_2 = n1 % 17.53/3.05 | % 17.53/3.05 | COMBINE_EQS: (31), (36) imply: % 17.53/3.05 | (37) all_51_1 = n1 % 17.53/3.05 | % 17.53/3.05 | COMBINE_EQS: (31), (32) imply: % 17.53/3.05 | (38) all_51_1 = all_49_0 % 17.53/3.05 | % 17.53/3.05 | COMBINE_EQS: (37), (38) imply: % 17.53/3.05 | (39) all_49_0 = n1 % 17.53/3.05 | % 17.53/3.05 | GROUND_INST: instantiating (leq_succ_gt) with n0, loopcounter, n1, simplifying % 17.53/3.05 | with (3), (6), (7), (22) gives: % 17.53/3.05 | (40) gt(loopcounter, n0) = 0 % 17.53/3.05 | % 17.53/3.05 | GROUND_INST: instantiating (10) with all_74_0, 0, n0, loopcounter, simplifying % 17.53/3.05 | with (21), (40) gives: % 17.53/3.05 | (41) all_74_0 = 0 % 17.53/3.05 | % 17.53/3.05 | BETA: splitting (23) gives: % 17.53/3.05 | % 17.53/3.05 | Case 1: % 17.53/3.05 | | % 17.53/3.05 | | (42) ~ (all_74_0 = 0) % 17.53/3.05 | | % 17.53/3.05 | | REDUCE: (41), (42) imply: % 17.53/3.05 | | (43) $false % 17.53/3.05 | | % 17.53/3.05 | | CLOSE: (43) is inconsistent. % 17.53/3.05 | | % 17.53/3.05 | Case 2: % 17.53/3.05 | | % 17.53/3.05 | | (44) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rho_init, v0) % 17.53/3.05 | | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = % 17.53/3.05 | | v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 17.53/3.06 | | % 17.53/3.06 | | GROUND_INST: instantiating (44) with all_79_1, all_79_0, simplifying with % 17.53/3.06 | | (27), (30) gives: % 17.53/3.06 | | (45) all_79_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = % 17.53/3.06 | | v1 & leq(n0, all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 17.53/3.06 | | % 17.53/3.06 | | BETA: splitting (45) gives: % 17.53/3.06 | | % 17.53/3.06 | | Case 1: % 17.53/3.06 | | | % 17.53/3.06 | | | (46) all_79_0 = init % 17.53/3.06 | | | % 17.53/3.06 | | | REDUCE: (26), (46) imply: % 17.53/3.06 | | | (47) $false % 17.53/3.06 | | | % 17.53/3.06 | | | CLOSE: (47) is inconsistent. % 17.53/3.06 | | | % 17.53/3.06 | | Case 2: % 17.53/3.06 | | | % 17.53/3.06 | | | (48) ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = v1 & leq(n0, % 17.53/3.06 | | | all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 17.53/3.06 | | | % 17.53/3.06 | | | DELTA: instantiating (48) with fresh symbols all_124_0, all_124_1 gives: % 17.53/3.06 | | | (49) leq(all_79_1, n4) = all_124_0 & leq(n0, all_79_1) = all_124_1 & ( % 17.53/3.06 | | | ~ (all_124_0 = 0) | ~ (all_124_1 = 0)) % 17.53/3.06 | | | % 17.53/3.06 | | | ALPHA: (49) implies: % 17.53/3.06 | | | (50) leq(n0, all_79_1) = all_124_1 % 17.53/3.06 | | | (51) leq(all_79_1, n4) = all_124_0 % 17.53/3.06 | | | (52) ~ (all_124_0 = 0) | ~ (all_124_1 = 0) % 17.53/3.06 | | | % 17.53/3.06 | | | GROUND_INST: instantiating (11) with 0, all_124_1, all_79_1, n0, % 17.53/3.06 | | | simplifying with (28), (50) gives: % 17.53/3.06 | | | (53) all_124_1 = 0 % 17.53/3.06 | | | % 17.53/3.06 | | | GROUND_INST: instantiating (11) with 0, all_124_0, n4, all_79_1, % 17.53/3.06 | | | simplifying with (29), (51) gives: % 17.53/3.06 | | | (54) all_124_0 = 0 % 17.53/3.06 | | | % 17.53/3.06 | | | BETA: splitting (52) gives: % 17.53/3.06 | | | % 17.53/3.06 | | | Case 1: % 17.53/3.06 | | | | % 17.53/3.06 | | | | (55) ~ (all_124_0 = 0) % 17.53/3.06 | | | | % 17.53/3.06 | | | | REDUCE: (54), (55) imply: % 17.53/3.06 | | | | (56) $false % 17.53/3.06 | | | | % 17.53/3.06 | | | | CLOSE: (56) is inconsistent. % 17.53/3.06 | | | | % 17.53/3.06 | | | Case 2: % 17.53/3.06 | | | | % 17.53/3.06 | | | | (57) ~ (all_124_1 = 0) % 17.53/3.06 | | | | % 17.53/3.06 | | | | REDUCE: (53), (57) imply: % 17.53/3.06 | | | | (58) $false % 17.53/3.06 | | | | % 17.53/3.06 | | | | CLOSE: (58) is inconsistent. % 17.53/3.06 | | | | % 17.53/3.06 | | | End of split % 17.53/3.06 | | | % 17.53/3.06 | | End of split % 17.53/3.06 | | % 17.53/3.06 | End of split % 17.53/3.06 | % 17.53/3.06 End of proof % 17.53/3.06 % SZS output end Proof for theBenchmark % 17.53/3.06 % 17.53/3.06 2456ms %------------------------------------------------------------------------------