%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV133+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 : n010.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 22:55:03 EDT 2023 % Result : Theorem 15.07s 2.72s % Output : Proof 18.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWV133+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n010.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Tue Aug 29 05:24:19 EDT 2023 % 0.14/0.36 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.27/1.43 Prover 4: Preprocessing ... % 5.27/1.43 Prover 1: Preprocessing ... % 5.27/1.46 Prover 0: Preprocessing ... % 5.27/1.46 Prover 5: Preprocessing ... % 5.27/1.46 Prover 6: Preprocessing ... % 5.27/1.47 Prover 3: Preprocessing ... % 5.27/1.50 Prover 2: Preprocessing ... % 10.43/2.16 Prover 1: Warning: ignoring some quantifiers % 10.43/2.21 Prover 3: Warning: ignoring some quantifiers % 10.43/2.21 Prover 1: Constructing countermodel ... % 10.43/2.25 Prover 3: Constructing countermodel ... % 10.43/2.26 Prover 4: Warning: ignoring some quantifiers % 12.03/2.31 Prover 6: Proving ... % 12.11/2.35 Prover 4: Constructing countermodel ... % 12.11/2.37 Prover 0: Proving ... % 12.77/2.41 Prover 5: Proving ... % 12.77/2.48 Prover 2: Proving ... % 15.07/2.72 Prover 3: proved (2068ms) % 15.07/2.72 % 15.07/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.07/2.72 % 15.07/2.73 Prover 5: stopped % 15.07/2.73 Prover 0: stopped % 15.07/2.73 Prover 2: stopped % 15.07/2.73 Prover 6: stopped % 15.07/2.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.07/2.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.07/2.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.07/2.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.07/2.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.07/2.87 Prover 7: Preprocessing ... % 15.70/2.90 Prover 10: Preprocessing ... % 15.70/2.91 Prover 8: Preprocessing ... % 15.70/2.94 Prover 13: Preprocessing ... % 15.70/2.95 Prover 11: Preprocessing ... % 15.70/2.96 Prover 1: Found proof (size 57) % 15.70/2.96 Prover 1: proved (2312ms) % 15.70/2.96 Prover 4: stopped % 16.96/3.00 Prover 10: stopped % 16.96/3.01 Prover 7: stopped % 17.16/3.02 Prover 11: stopped % 17.26/3.07 Prover 13: stopped % 17.26/3.08 Prover 8: Warning: ignoring some quantifiers % 17.26/3.10 Prover 8: Constructing countermodel ... % 17.75/3.11 Prover 8: stopped % 17.75/3.11 % 17.75/3.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.75/3.12 % 17.75/3.13 % SZS output start Proof for theBenchmark % 17.75/3.13 Assumptions after simplification: % 17.75/3.13 --------------------------------- % 17.75/3.13 % 17.75/3.13 (gauss_array_0003) % 17.75/3.16 $i(s_sworst7) & $i(s_best7) & $i(s_worst7) & $i(pv1325) & $i(s_values7) & % 17.75/3.16 $i(n3) & $i(n2) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: % 17.75/3.16 $i] : ? [v4: int] : ( ~ (v4 = 0) & ~ (v2 = 0) & a_select2(s_values7, % 17.75/3.16 s_best7) = v3 & a_select2(s_values7, s_worst7) = v1 & a_select2(s_values7, % 17.75/3.16 pv1325) = v0 & leq(v0, v3) = 0 & leq(v0, v1) = v2 & leq(s_sworst7, n3) = 0 % 17.75/3.16 & leq(s_best7, n3) = 0 & leq(s_worst7, n3) = 0 & leq(pv1325, n3) = 0 & % 17.75/3.16 leq(n2, pv1325) = 0 & leq(n0, s_sworst7) = 0 & leq(n0, s_best7) = 0 & % 17.75/3.16 leq(n0, s_worst7) = 0 & leq(n0, pv1325) = v4 & $i(v3) & $i(v1) & $i(v0)) % 17.75/3.16 % 17.75/3.16 (gt_2_0) % 17.75/3.16 gt(n2, n0) = 0 & $i(n2) & $i(n0) % 17.75/3.16 % 17.75/3.16 (leq_gt1) % 17.75/3.16 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 17.75/3.16 leq(v0, v1) = 0) % 17.75/3.16 % 17.75/3.16 (leq_succ_gt) % 17.75/3.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2, % 17.75/3.16 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 17.75/3.16 % 17.75/3.16 (leq_succ_gt_equiv) % 17.75/3.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 17.75/3.16 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 17.75/3.16 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 17.75/3.16 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 17.75/3.16 leq(v0, v1) = 0) % 17.75/3.16 % 17.75/3.16 (successor_1) % 17.75/3.16 succ(n0) = n1 & $i(n1) & $i(n0) % 17.75/3.16 % 17.75/3.16 (successor_2) % 17.75/3.16 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 17.75/3.16 % 17.75/3.16 (successor_3) % 17.75/3.16 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 17.75/3.16 succ(n0) = v0 & $i(v1) & $i(v0)) % 17.75/3.16 % 17.75/3.16 (successor_4) % 17.75/3.17 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 17.75/3.17 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 17.75/3.17 % 17.75/3.17 (successor_5) % 17.75/3.17 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 17.75/3.17 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 17.75/3.17 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.75/3.17 % 17.75/3.17 (transitivity_leq) % 17.75/3.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (leq(v0, % 17.75/3.17 v2) = v3) | ~ (leq(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.75/3.17 ? [v4: int] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) % 17.75/3.17 % 17.75/3.17 (function-axioms) % 17.75/3.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.75/3.17 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 17.75/3.17 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.75/3.17 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 17.75/3.18 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.75/3.18 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 17.75/3.18 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.75/3.18 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 17.75/3.18 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.75/3.18 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 17.75/3.18 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.75/3.18 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 17.75/3.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.75/3.18 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 17.75/3.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 17.75/3.18 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.75/3.18 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 17.75/3.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 17.75/3.18 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 17.75/3.18 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 17.75/3.18 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 17.75/3.18 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 17.75/3.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.75/3.18 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 17.75/3.18 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.75/3.18 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 17.75/3.18 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.75/3.18 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 17.75/3.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.75/3.18 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 17.75/3.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.75/3.18 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 17.75/3.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.75/3.18 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 17.75/3.18 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 17.75/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 17.75/3.18 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.75/3.18 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.75/3.18 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 17.75/3.18 % 17.75/3.18 Further assumptions not needed in the proof: % 17.75/3.18 -------------------------------------------- % 17.75/3.18 const_array1_select, const_array2_select, defuse, finite_domain_0, % 17.75/3.18 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 17.75/3.18 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_1, % 17.75/3.18 gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1, % 17.75/3.18 gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, % 17.75/3.18 gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt2, leq_gt_pred, % 17.75/3.18 leq_minus, leq_succ, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 17.75/3.18 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 17.75/3.18 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 17.75/3.18 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 17.75/3.18 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 17.75/3.18 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 17.75/3.18 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, sum_plus_base, % 17.75/3.18 sum_plus_base_float, totality, transitivity_gt, ttrue, % 17.75/3.18 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 17.75/3.18 % 17.75/3.18 Those formulas are unsatisfiable: % 17.75/3.18 --------------------------------- % 17.75/3.18 % 17.75/3.18 Begin of proof % 17.75/3.18 | % 17.75/3.18 | ALPHA: (leq_succ_gt_equiv) implies: % 17.75/3.18 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 17.75/3.18 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0) % 17.75/3.18 | % 17.75/3.18 | ALPHA: (gt_2_0) implies: % 17.75/3.18 | (2) gt(n2, n0) = 0 % 17.75/3.18 | % 17.75/3.18 | ALPHA: (successor_4) implies: % 17.75/3.18 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 17.75/3.18 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 17.75/3.18 | % 17.75/3.18 | ALPHA: (successor_5) implies: % 17.75/3.18 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 17.75/3.18 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 17.75/3.18 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.75/3.18 | % 17.75/3.18 | ALPHA: (successor_1) implies: % 17.75/3.18 | (5) succ(n0) = n1 % 17.75/3.18 | % 17.75/3.18 | ALPHA: (successor_2) implies: % 17.75/3.18 | (6) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 17.75/3.18 | % 17.75/3.18 | ALPHA: (successor_3) implies: % 17.75/3.18 | (7) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) = % 17.75/3.18 | v0 & $i(v1) & $i(v0)) % 17.75/3.18 | % 17.75/3.18 | ALPHA: (gauss_array_0003) implies: % 17.75/3.18 | (8) $i(n0) % 17.75/3.18 | (9) $i(pv1325) % 17.75/3.18 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: int] % 17.75/3.18 | : ( ~ (v4 = 0) & ~ (v2 = 0) & a_select2(s_values7, s_best7) = v3 & % 17.75/3.18 | a_select2(s_values7, s_worst7) = v1 & a_select2(s_values7, pv1325) = % 17.75/3.18 | v0 & leq(v0, v3) = 0 & leq(v0, v1) = v2 & leq(s_sworst7, n3) = 0 & % 17.75/3.18 | leq(s_best7, n3) = 0 & leq(s_worst7, n3) = 0 & leq(pv1325, n3) = 0 & % 17.75/3.18 | leq(n2, pv1325) = 0 & leq(n0, s_sworst7) = 0 & leq(n0, s_best7) = 0 % 17.75/3.19 | & leq(n0, s_worst7) = 0 & leq(n0, pv1325) = v4 & $i(v3) & $i(v1) & % 17.75/3.19 | $i(v0)) % 17.75/3.19 | % 17.75/3.19 | ALPHA: (function-axioms) implies: % 18.10/3.19 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 18.10/3.19 | v1) | ~ (succ(v2) = v0)) % 18.10/3.19 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.10/3.19 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 18.10/3.19 | v0)) % 18.10/3.19 | % 18.10/3.19 | DELTA: instantiating (6) with fresh symbol all_49_0 gives: % 18.10/3.19 | (13) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0) % 18.10/3.19 | % 18.10/3.19 | ALPHA: (13) implies: % 18.10/3.19 | (14) $i(all_49_0) % 18.10/3.19 | (15) succ(n0) = all_49_0 % 18.10/3.19 | (16) succ(all_49_0) = n2 % 18.10/3.19 | % 18.10/3.19 | DELTA: instantiating (7) with fresh symbols all_51_0, all_51_1 gives: % 18.10/3.19 | (17) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1 % 18.10/3.19 | & $i(all_51_0) & $i(all_51_1) % 18.10/3.19 | % 18.10/3.19 | ALPHA: (17) implies: % 18.10/3.19 | (18) succ(n0) = all_51_1 % 18.10/3.19 | (19) succ(all_51_1) = all_51_0 % 18.10/3.19 | % 18.10/3.19 | DELTA: instantiating (3) with fresh symbols all_53_0, all_53_1, all_53_2 % 18.10/3.19 | gives: % 18.10/3.19 | (20) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) = % 18.10/3.19 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) & % 18.10/3.19 | $i(all_53_2) % 18.10/3.19 | % 18.10/3.19 | ALPHA: (20) implies: % 18.10/3.19 | (21) succ(n0) = all_53_2 % 18.10/3.19 | (22) succ(all_53_2) = all_53_1 % 18.10/3.19 | % 18.10/3.19 | DELTA: instantiating (4) with fresh symbols all_55_0, all_55_1, all_55_2, % 18.10/3.19 | all_55_3 gives: % 18.10/3.19 | (23) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) = % 18.10/3.19 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 & % 18.10/3.19 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) % 18.10/3.19 | % 18.10/3.19 | ALPHA: (23) implies: % 18.10/3.19 | (24) succ(n0) = all_55_3 % 18.10/3.19 | (25) succ(all_55_3) = all_55_2 % 18.10/3.19 | % 18.10/3.19 | DELTA: instantiating (10) with fresh symbols all_61_0, all_61_1, all_61_2, % 18.10/3.19 | all_61_3, all_61_4 gives: % 18.10/3.19 | (26) ~ (all_61_0 = 0) & ~ (all_61_2 = 0) & a_select2(s_values7, s_best7) % 18.10/3.19 | = all_61_1 & a_select2(s_values7, s_worst7) = all_61_3 & % 18.10/3.19 | a_select2(s_values7, pv1325) = all_61_4 & leq(all_61_4, all_61_1) = 0 % 18.10/3.19 | & leq(all_61_4, all_61_3) = all_61_2 & leq(s_sworst7, n3) = 0 & % 18.10/3.19 | leq(s_best7, n3) = 0 & leq(s_worst7, n3) = 0 & leq(pv1325, n3) = 0 & % 18.10/3.19 | leq(n2, pv1325) = 0 & leq(n0, s_sworst7) = 0 & leq(n0, s_best7) = 0 & % 18.10/3.19 | leq(n0, s_worst7) = 0 & leq(n0, pv1325) = all_61_0 & $i(all_61_1) & % 18.10/3.19 | $i(all_61_3) & $i(all_61_4) % 18.10/3.19 | % 18.10/3.19 | ALPHA: (26) implies: % 18.10/3.19 | (27) ~ (all_61_0 = 0) % 18.10/3.19 | (28) leq(n0, pv1325) = all_61_0 % 18.10/3.19 | (29) leq(n2, pv1325) = 0 % 18.10/3.19 | % 18.10/3.19 | GROUND_INST: instantiating (11) with all_51_1, all_53_2, n0, simplifying with % 18.10/3.19 | (18), (21) gives: % 18.10/3.19 | (30) all_53_2 = all_51_1 % 18.10/3.19 | % 18.10/3.19 | GROUND_INST: instantiating (11) with all_49_0, all_53_2, n0, simplifying with % 18.10/3.19 | (15), (21) gives: % 18.10/3.19 | (31) all_53_2 = all_49_0 % 18.10/3.19 | % 18.10/3.19 | GROUND_INST: instantiating (11) with all_51_1, all_55_3, n0, simplifying with % 18.10/3.19 | (18), (24) gives: % 18.10/3.19 | (32) all_55_3 = all_51_1 % 18.10/3.19 | % 18.10/3.20 | GROUND_INST: instantiating (11) with n1, all_55_3, n0, simplifying with (5), % 18.10/3.20 | (24) gives: % 18.10/3.20 | (33) all_55_3 = n1 % 18.10/3.20 | % 18.10/3.20 | COMBINE_EQS: (32), (33) imply: % 18.10/3.20 | (34) all_51_1 = n1 % 18.10/3.20 | % 18.10/3.20 | SIMP: (34) implies: % 18.10/3.20 | (35) all_51_1 = n1 % 18.10/3.20 | % 18.10/3.20 | COMBINE_EQS: (30), (31) imply: % 18.10/3.20 | (36) all_51_1 = all_49_0 % 18.10/3.20 | % 18.10/3.20 | SIMP: (36) implies: % 18.10/3.20 | (37) all_51_1 = all_49_0 % 18.10/3.20 | % 18.10/3.20 | COMBINE_EQS: (35), (37) imply: % 18.10/3.20 | (38) all_49_0 = n1 % 18.10/3.20 | % 18.10/3.20 | COMBINE_EQS: (31), (38) imply: % 18.10/3.20 | (39) all_53_2 = n1 % 18.10/3.20 | % 18.10/3.20 | REDUCE: (25), (33) imply: % 18.10/3.20 | (40) succ(n1) = all_55_2 % 18.10/3.20 | % 18.10/3.20 | REDUCE: (22), (39) imply: % 18.10/3.20 | (41) succ(n1) = all_53_1 % 18.10/3.20 | % 18.10/3.20 | REDUCE: (19), (35) imply: % 18.10/3.20 | (42) succ(n1) = all_51_0 % 18.10/3.20 | % 18.10/3.20 | REDUCE: (16), (38) imply: % 18.10/3.20 | (43) succ(n1) = n2 % 18.10/3.20 | % 18.10/3.20 | REDUCE: (14), (38) imply: % 18.10/3.20 | (44) $i(n1) % 18.10/3.20 | % 18.10/3.20 | GROUND_INST: instantiating (11) with all_51_0, all_53_1, n1, simplifying with % 18.10/3.20 | (41), (42) gives: % 18.10/3.20 | (45) all_53_1 = all_51_0 % 18.10/3.20 | % 18.10/3.20 | GROUND_INST: instantiating (11) with all_53_1, all_55_2, n1, simplifying with % 18.10/3.20 | (40), (41) gives: % 18.10/3.20 | (46) all_55_2 = all_53_1 % 18.10/3.20 | % 18.10/3.20 | GROUND_INST: instantiating (11) with n2, all_55_2, n1, simplifying with (40), % 18.10/3.20 | (43) gives: % 18.10/3.20 | (47) all_55_2 = n2 % 18.10/3.20 | % 18.10/3.20 | COMBINE_EQS: (46), (47) imply: % 18.10/3.20 | (48) all_53_1 = n2 % 18.10/3.20 | % 18.10/3.20 | SIMP: (48) implies: % 18.10/3.20 | (49) all_53_1 = n2 % 18.10/3.20 | % 18.10/3.20 | COMBINE_EQS: (45), (49) imply: % 18.10/3.20 | (50) all_51_0 = n2 % 18.10/3.20 | % 18.10/3.20 | SIMP: (50) implies: % 18.10/3.20 | (51) all_51_0 = n2 % 18.10/3.20 | % 18.10/3.20 | GROUND_INST: instantiating (leq_succ_gt) with n1, pv1325, n2, simplifying with % 18.10/3.20 | (9), (29), (43), (44) gives: % 18.10/3.20 | (52) gt(pv1325, n1) = 0 % 18.10/3.20 | % 18.10/3.20 | GROUND_INST: instantiating (1) with n0, n1, n2, simplifying with (2), (8), % 18.10/3.20 | (43), (44) gives: % 18.10/3.20 | (53) leq(n0, n1) = 0 % 18.10/3.20 | % 18.10/3.20 | GROUND_INST: instantiating (leq_gt1) with n1, pv1325, simplifying with (9), % 18.10/3.20 | (44), (52) gives: % 18.10/3.20 | (54) leq(n1, pv1325) = 0 % 18.10/3.20 | % 18.10/3.20 | GROUND_INST: instantiating (transitivity_leq) with n0, n1, pv1325, all_61_0, % 18.10/3.20 | simplifying with (8), (9), (28), (44), (53) gives: % 18.10/3.20 | (55) all_61_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & leq(n1, pv1325) = v0) % 18.10/3.20 | % 18.10/3.20 | BETA: splitting (55) gives: % 18.10/3.20 | % 18.10/3.20 | Case 1: % 18.10/3.20 | | % 18.10/3.20 | | (56) all_61_0 = 0 % 18.10/3.20 | | % 18.10/3.20 | | REDUCE: (27), (56) imply: % 18.10/3.20 | | (57) $false % 18.10/3.20 | | % 18.10/3.20 | | CLOSE: (57) is inconsistent. % 18.10/3.20 | | % 18.10/3.20 | Case 2: % 18.10/3.20 | | % 18.10/3.20 | | (58) ? [v0: int] : ( ~ (v0 = 0) & leq(n1, pv1325) = v0) % 18.10/3.20 | | % 18.10/3.20 | | DELTA: instantiating (58) with fresh symbol all_131_0 gives: % 18.10/3.20 | | (59) ~ (all_131_0 = 0) & leq(n1, pv1325) = all_131_0 % 18.10/3.20 | | % 18.10/3.20 | | ALPHA: (59) implies: % 18.10/3.21 | | (60) ~ (all_131_0 = 0) % 18.10/3.21 | | (61) leq(n1, pv1325) = all_131_0 % 18.10/3.21 | | % 18.10/3.21 | | GROUND_INST: instantiating (12) with 0, all_131_0, pv1325, n1, simplifying % 18.10/3.21 | | with (54), (61) gives: % 18.10/3.21 | | (62) all_131_0 = 0 % 18.10/3.21 | | % 18.10/3.21 | | REDUCE: (60), (62) imply: % 18.10/3.21 | | (63) $false % 18.10/3.21 | | % 18.10/3.21 | | CLOSE: (63) is inconsistent. % 18.10/3.21 | | % 18.10/3.21 | End of split % 18.10/3.21 | % 18.10/3.21 End of proof % 18.10/3.21 % SZS output end Proof for theBenchmark % 18.10/3.21 % 18.10/3.21 2577ms %------------------------------------------------------------------------------