%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV137+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 : n023.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 22:55:04 EDT 2023 % Result : Theorem 18.43s 3.25s % Output : Proof 23.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SWV137+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.31 % Computer : n023.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.31 % CPULimit : 300 % 0.15/0.31 % WCLimit : 300 % 0.15/0.31 % DateTime : Tue Aug 29 09:21:25 EDT 2023 % 0.15/0.32 % CPUTime : % 0.16/0.59 ________ _____ % 0.16/0.59 ___ __ \_________(_)________________________________ % 0.16/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.59 % 0.16/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.59 (2023-06-19) % 0.16/0.59 % 0.16/0.59 (c) Philipp Rümmer, 2009-2023 % 0.16/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.59 Amanda Stjerna. % 0.16/0.59 Free software under BSD-3-Clause. % 0.16/0.59 % 0.16/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.59 % 0.16/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.61 Running up to 7 provers in parallel. % 0.61/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.36/1.34 Prover 4: Preprocessing ... % 4.36/1.34 Prover 1: Preprocessing ... % 4.52/1.40 Prover 3: Preprocessing ... % 4.52/1.40 Prover 6: Preprocessing ... % 4.52/1.40 Prover 2: Preprocessing ... % 4.52/1.40 Prover 5: Preprocessing ... % 4.52/1.42 Prover 0: Preprocessing ... % 13.16/2.50 Prover 1: Warning: ignoring some quantifiers % 13.43/2.55 Prover 3: Warning: ignoring some quantifiers % 13.43/2.59 Prover 4: Warning: ignoring some quantifiers % 13.88/2.62 Prover 3: Constructing countermodel ... % 13.88/2.62 Prover 1: Constructing countermodel ... % 13.88/2.63 Prover 6: Proving ... % 14.35/2.71 Prover 4: Constructing countermodel ... % 15.05/2.77 Prover 0: Proving ... % 15.05/2.77 Prover 5: Proving ... % 15.34/2.83 Prover 2: Proving ... % 18.43/3.24 Prover 3: proved (2617ms) % 18.43/3.24 % 18.43/3.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.43/3.25 % 18.43/3.25 Prover 2: stopped % 18.43/3.25 Prover 6: stopped % 18.43/3.25 Prover 5: stopped % 18.43/3.26 Prover 0: stopped % 18.99/3.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 18.99/3.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.99/3.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.99/3.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.99/3.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.26/3.44 Prover 10: Preprocessing ... % 20.26/3.46 Prover 8: Preprocessing ... % 20.86/3.53 Prover 11: Preprocessing ... % 20.86/3.53 Prover 13: Preprocessing ... % 20.86/3.56 Prover 7: Preprocessing ... % 21.44/3.64 Prover 1: Found proof (size 57) % 21.44/3.64 Prover 1: proved (3021ms) % 21.44/3.64 Prover 4: stopped % 21.44/3.65 Prover 10: stopped % 22.13/3.71 Prover 11: stopped % 22.13/3.71 Prover 7: stopped % 22.42/3.74 Prover 13: stopped % 22.42/3.79 Prover 8: Warning: ignoring some quantifiers % 22.42/3.80 Prover 8: Constructing countermodel ... % 22.85/3.82 Prover 8: stopped % 22.85/3.82 % 22.85/3.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.85/3.82 % 22.85/3.84 % SZS output start Proof for theBenchmark % 22.85/3.85 Assumptions after simplification: % 22.85/3.85 --------------------------------- % 22.85/3.85 % 22.85/3.85 (gauss_array_0007) % 22.85/3.87 $i(s_values7) & $i(pv1325) & $i(s_worst7) & $i(s_sworst7) & $i(s_best7) & % 22.85/3.87 $i(n3) & $i(n2) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 22.85/3.87 int] : ( ~ (v3 = 0) & a_select2(s_values7, pv1325) = v0 & % 22.85/3.87 a_select2(s_values7, s_worst7) = v2 & a_select2(s_values7, s_best7) = v1 & % 22.85/3.87 leq(v0, v2) = 0 & leq(v0, v1) = 0 & leq(pv1325, n3) = 0 & leq(s_worst7, n3) % 22.85/3.87 = 0 & leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = 0 & leq(n2, pv1325) = 0 & % 22.85/3.88 leq(n0, pv1325) = v3 & leq(n0, s_worst7) = 0 & leq(n0, s_sworst7) = 0 & % 22.85/3.88 leq(n0, s_best7) = 0 & $i(v2) & $i(v1) & $i(v0)) % 22.85/3.88 % 22.85/3.88 (gt_2_0) % 22.85/3.88 gt(n2, n0) = 0 & $i(n2) & $i(n0) % 22.85/3.88 % 22.85/3.88 (leq_gt1) % 22.85/3.88 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 22.85/3.88 leq(v0, v1) = 0) % 22.85/3.88 % 22.85/3.88 (leq_succ_gt) % 22.85/3.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2, % 22.85/3.88 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 22.85/3.88 % 22.85/3.88 (leq_succ_gt_equiv) % 22.85/3.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 22.85/3.88 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 22.85/3.88 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 22.85/3.88 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 22.85/3.88 leq(v0, v1) = 0) % 22.85/3.88 % 22.85/3.88 (successor_1) % 23.21/3.88 succ(n0) = n1 & $i(n1) & $i(n0) % 23.21/3.88 % 23.21/3.88 (successor_2) % 23.21/3.88 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 23.21/3.88 % 23.21/3.88 (successor_3) % 23.21/3.88 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 23.21/3.88 succ(n0) = v0 & $i(v1) & $i(v0)) % 23.21/3.88 % 23.21/3.88 (successor_4) % 23.21/3.89 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 23.21/3.89 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 23.21/3.89 % 23.21/3.89 (successor_5) % 23.21/3.89 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 23.21/3.89 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 23.21/3.89 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 23.21/3.89 % 23.21/3.89 (transitivity_leq) % 23.21/3.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (leq(v0, % 23.21/3.89 v2) = v3) | ~ (leq(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 23.21/3.89 ? [v4: int] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) % 23.21/3.89 % 23.21/3.89 (function-axioms) % 23.21/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 23.21/3.90 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 23.21/3.90 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.21/3.90 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 23.21/3.90 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.21/3.90 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 23.21/3.90 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 23.21/3.90 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 23.21/3.90 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.21/3.90 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 23.21/3.90 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.21/3.90 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 23.21/3.90 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 23.21/3.90 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 23.21/3.90 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 23.21/3.90 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.21/3.90 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 23.21/3.90 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.21/3.90 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 23.21/3.90 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 23.21/3.90 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 23.21/3.90 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 23.21/3.90 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 23.21/3.90 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 23.21/3.90 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.21/3.90 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 23.21/3.90 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 23.21/3.90 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 23.21/3.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.21/3.90 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 23.21/3.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.21/3.90 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 23.21/3.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.21/3.90 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 23.21/3.90 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 23.21/3.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 23.21/3.90 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.21/3.90 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.21/3.90 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 23.21/3.90 % 23.21/3.90 Further assumptions not needed in the proof: % 23.21/3.90 -------------------------------------------- % 23.21/3.90 const_array1_select, const_array2_select, defuse, finite_domain_0, % 23.21/3.90 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 23.21/3.90 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_1, % 23.21/3.90 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, % 23.21/3.90 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, % 23.21/3.90 gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt2, leq_gt_pred, % 23.21/3.90 leq_minus, leq_succ, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 23.21/3.90 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 23.21/3.90 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 23.21/3.90 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 23.21/3.90 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 23.21/3.90 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 23.21/3.90 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, sum_plus_base, % 23.21/3.90 sum_plus_base_float, totality, transitivity_gt, ttrue, % 23.21/3.90 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 23.21/3.90 % 23.21/3.90 Those formulas are unsatisfiable: % 23.21/3.90 --------------------------------- % 23.21/3.90 % 23.21/3.90 Begin of proof % 23.21/3.90 | % 23.21/3.90 | ALPHA: (leq_succ_gt_equiv) implies: % 23.21/3.91 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 23.21/3.91 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0) % 23.21/3.91 | % 23.21/3.91 | ALPHA: (gt_2_0) implies: % 23.21/3.91 | (2) gt(n2, n0) = 0 % 23.21/3.91 | % 23.21/3.91 | ALPHA: (successor_4) implies: % 23.21/3.91 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 23.21/3.91 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 23.21/3.91 | % 23.21/3.91 | ALPHA: (successor_5) implies: % 23.21/3.91 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 23.21/3.91 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 23.21/3.91 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 23.21/3.91 | % 23.21/3.91 | ALPHA: (successor_1) implies: % 23.21/3.91 | (5) succ(n0) = n1 % 23.21/3.91 | % 23.21/3.91 | ALPHA: (successor_2) implies: % 23.21/3.91 | (6) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 23.21/3.91 | % 23.21/3.91 | ALPHA: (successor_3) implies: % 23.21/3.91 | (7) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) = % 23.21/3.91 | v0 & $i(v1) & $i(v0)) % 23.21/3.91 | % 23.21/3.91 | ALPHA: (gauss_array_0007) implies: % 23.21/3.91 | (8) $i(n0) % 23.21/3.91 | (9) $i(pv1325) % 23.21/3.91 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 23.21/3.91 | & a_select2(s_values7, pv1325) = v0 & a_select2(s_values7, s_worst7) % 23.21/3.91 | = v2 & a_select2(s_values7, s_best7) = v1 & leq(v0, v2) = 0 & % 23.21/3.91 | leq(v0, v1) = 0 & leq(pv1325, n3) = 0 & leq(s_worst7, n3) = 0 & % 23.21/3.91 | leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = 0 & leq(n2, pv1325) = 0 % 23.21/3.91 | & leq(n0, pv1325) = v3 & leq(n0, s_worst7) = 0 & leq(n0, s_sworst7) % 23.21/3.91 | = 0 & leq(n0, s_best7) = 0 & $i(v2) & $i(v1) & $i(v0)) % 23.21/3.91 | % 23.21/3.91 | ALPHA: (function-axioms) implies: % 23.21/3.92 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 23.21/3.92 | v1) | ~ (succ(v2) = v0)) % 23.21/3.92 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.21/3.92 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 23.21/3.92 | v0)) % 23.21/3.92 | % 23.21/3.92 | DELTA: instantiating (6) with fresh symbol all_49_0 gives: % 23.21/3.92 | (13) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0) % 23.21/3.92 | % 23.21/3.92 | ALPHA: (13) implies: % 23.21/3.92 | (14) $i(all_49_0) % 23.21/3.92 | (15) succ(n0) = all_49_0 % 23.21/3.92 | (16) succ(all_49_0) = n2 % 23.21/3.92 | % 23.21/3.92 | DELTA: instantiating (7) with fresh symbols all_51_0, all_51_1 gives: % 23.21/3.92 | (17) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1 % 23.21/3.92 | & $i(all_51_0) & $i(all_51_1) % 23.21/3.92 | % 23.21/3.92 | ALPHA: (17) implies: % 23.21/3.92 | (18) succ(n0) = all_51_1 % 23.21/3.92 | (19) succ(all_51_1) = all_51_0 % 23.21/3.92 | % 23.21/3.92 | DELTA: instantiating (3) with fresh symbols all_53_0, all_53_1, all_53_2 % 23.21/3.92 | gives: % 23.21/3.92 | (20) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) = % 23.21/3.92 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) & % 23.21/3.92 | $i(all_53_2) % 23.21/3.92 | % 23.21/3.92 | ALPHA: (20) implies: % 23.21/3.92 | (21) succ(n0) = all_53_2 % 23.21/3.92 | (22) succ(all_53_2) = all_53_1 % 23.21/3.92 | % 23.21/3.92 | DELTA: instantiating (4) with fresh symbols all_55_0, all_55_1, all_55_2, % 23.21/3.92 | all_55_3 gives: % 23.21/3.92 | (23) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) = % 23.21/3.92 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 & % 23.21/3.92 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) % 23.21/3.92 | % 23.21/3.92 | ALPHA: (23) implies: % 23.21/3.92 | (24) succ(n0) = all_55_3 % 23.21/3.92 | (25) succ(all_55_3) = all_55_2 % 23.21/3.92 | % 23.21/3.92 | DELTA: instantiating (10) with fresh symbols all_61_0, all_61_1, all_61_2, % 23.21/3.92 | all_61_3 gives: % 23.21/3.92 | (26) ~ (all_61_0 = 0) & a_select2(s_values7, pv1325) = all_61_3 & % 23.21/3.92 | a_select2(s_values7, s_worst7) = all_61_1 & a_select2(s_values7, % 23.21/3.92 | s_best7) = all_61_2 & leq(all_61_3, all_61_1) = 0 & leq(all_61_3, % 23.21/3.92 | all_61_2) = 0 & leq(pv1325, n3) = 0 & leq(s_worst7, n3) = 0 & % 23.21/3.92 | leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = 0 & leq(n2, pv1325) = 0 & % 23.21/3.92 | leq(n0, pv1325) = all_61_0 & leq(n0, s_worst7) = 0 & leq(n0, % 23.21/3.92 | s_sworst7) = 0 & leq(n0, s_best7) = 0 & $i(all_61_1) & $i(all_61_2) % 23.21/3.92 | & $i(all_61_3) % 23.21/3.92 | % 23.21/3.92 | ALPHA: (26) implies: % 23.21/3.93 | (27) ~ (all_61_0 = 0) % 23.21/3.93 | (28) leq(n0, pv1325) = all_61_0 % 23.21/3.93 | (29) leq(n2, pv1325) = 0 % 23.21/3.93 | % 23.21/3.93 | GROUND_INST: instantiating (11) with all_51_1, all_53_2, n0, simplifying with % 23.21/3.93 | (18), (21) gives: % 23.21/3.93 | (30) all_53_2 = all_51_1 % 23.21/3.93 | % 23.21/3.93 | GROUND_INST: instantiating (11) with all_49_0, all_53_2, n0, simplifying with % 23.21/3.93 | (15), (21) gives: % 23.21/3.93 | (31) all_53_2 = all_49_0 % 23.21/3.93 | % 23.21/3.93 | GROUND_INST: instantiating (11) with all_51_1, all_55_3, n0, simplifying with % 23.21/3.93 | (18), (24) gives: % 23.21/3.93 | (32) all_55_3 = all_51_1 % 23.21/3.93 | % 23.21/3.93 | GROUND_INST: instantiating (11) with n1, all_55_3, n0, simplifying with (5), % 23.21/3.93 | (24) gives: % 23.21/3.93 | (33) all_55_3 = n1 % 23.21/3.93 | % 23.21/3.93 | COMBINE_EQS: (32), (33) imply: % 23.21/3.93 | (34) all_51_1 = n1 % 23.21/3.93 | % 23.21/3.93 | SIMP: (34) implies: % 23.21/3.93 | (35) all_51_1 = n1 % 23.21/3.93 | % 23.21/3.93 | COMBINE_EQS: (30), (31) imply: % 23.21/3.93 | (36) all_51_1 = all_49_0 % 23.21/3.93 | % 23.21/3.93 | SIMP: (36) implies: % 23.21/3.93 | (37) all_51_1 = all_49_0 % 23.21/3.93 | % 23.21/3.93 | COMBINE_EQS: (35), (37) imply: % 23.21/3.93 | (38) all_49_0 = n1 % 23.21/3.93 | % 23.21/3.93 | COMBINE_EQS: (31), (38) imply: % 23.21/3.93 | (39) all_53_2 = n1 % 23.21/3.93 | % 23.21/3.93 | REDUCE: (25), (33) imply: % 23.21/3.93 | (40) succ(n1) = all_55_2 % 23.21/3.93 | % 23.21/3.93 | REDUCE: (22), (39) imply: % 23.21/3.93 | (41) succ(n1) = all_53_1 % 23.21/3.93 | % 23.21/3.93 | REDUCE: (19), (35) imply: % 23.21/3.93 | (42) succ(n1) = all_51_0 % 23.21/3.93 | % 23.21/3.93 | REDUCE: (16), (38) imply: % 23.21/3.93 | (43) succ(n1) = n2 % 23.21/3.93 | % 23.21/3.93 | REDUCE: (14), (38) imply: % 23.21/3.93 | (44) $i(n1) % 23.21/3.93 | % 23.21/3.93 | GROUND_INST: instantiating (11) with all_51_0, all_53_1, n1, simplifying with % 23.21/3.93 | (41), (42) gives: % 23.21/3.93 | (45) all_53_1 = all_51_0 % 23.21/3.93 | % 23.21/3.93 | GROUND_INST: instantiating (11) with all_53_1, all_55_2, n1, simplifying with % 23.21/3.93 | (40), (41) gives: % 23.21/3.93 | (46) all_55_2 = all_53_1 % 23.21/3.93 | % 23.21/3.93 | GROUND_INST: instantiating (11) with n2, all_55_2, n1, simplifying with (40), % 23.21/3.93 | (43) gives: % 23.21/3.93 | (47) all_55_2 = n2 % 23.21/3.93 | % 23.21/3.93 | COMBINE_EQS: (46), (47) imply: % 23.21/3.94 | (48) all_53_1 = n2 % 23.21/3.94 | % 23.21/3.94 | SIMP: (48) implies: % 23.21/3.94 | (49) all_53_1 = n2 % 23.21/3.94 | % 23.21/3.94 | COMBINE_EQS: (45), (49) imply: % 23.21/3.94 | (50) all_51_0 = n2 % 23.21/3.94 | % 23.21/3.94 | SIMP: (50) implies: % 23.21/3.94 | (51) all_51_0 = n2 % 23.21/3.94 | % 23.21/3.94 | GROUND_INST: instantiating (leq_succ_gt) with n1, pv1325, n2, simplifying with % 23.21/3.94 | (9), (29), (43), (44) gives: % 23.21/3.94 | (52) gt(pv1325, n1) = 0 % 23.21/3.94 | % 23.21/3.94 | GROUND_INST: instantiating (1) with n0, n1, n2, simplifying with (2), (8), % 23.21/3.94 | (43), (44) gives: % 23.21/3.94 | (53) leq(n0, n1) = 0 % 23.21/3.94 | % 23.21/3.94 | GROUND_INST: instantiating (leq_gt1) with n1, pv1325, simplifying with (9), % 23.21/3.94 | (44), (52) gives: % 23.21/3.94 | (54) leq(n1, pv1325) = 0 % 23.21/3.94 | % 23.21/3.94 | GROUND_INST: instantiating (transitivity_leq) with n0, n1, pv1325, all_61_0, % 23.21/3.94 | simplifying with (8), (9), (28), (44), (53) gives: % 23.21/3.94 | (55) all_61_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & leq(n1, pv1325) = v0) % 23.21/3.94 | % 23.21/3.94 | BETA: splitting (55) gives: % 23.21/3.94 | % 23.21/3.94 | Case 1: % 23.21/3.94 | | % 23.21/3.94 | | (56) all_61_0 = 0 % 23.21/3.94 | | % 23.21/3.94 | | REDUCE: (27), (56) imply: % 23.21/3.94 | | (57) $false % 23.21/3.94 | | % 23.21/3.94 | | CLOSE: (57) is inconsistent. % 23.21/3.94 | | % 23.21/3.94 | Case 2: % 23.21/3.94 | | % 23.21/3.94 | | (58) ? [v0: int] : ( ~ (v0 = 0) & leq(n1, pv1325) = v0) % 23.21/3.94 | | % 23.21/3.94 | | DELTA: instantiating (58) with fresh symbol all_126_0 gives: % 23.21/3.94 | | (59) ~ (all_126_0 = 0) & leq(n1, pv1325) = all_126_0 % 23.21/3.94 | | % 23.21/3.94 | | ALPHA: (59) implies: % 23.21/3.94 | | (60) ~ (all_126_0 = 0) % 23.21/3.94 | | (61) leq(n1, pv1325) = all_126_0 % 23.21/3.94 | | % 23.21/3.95 | | GROUND_INST: instantiating (12) with 0, all_126_0, pv1325, n1, simplifying % 23.21/3.95 | | with (54), (61) gives: % 23.21/3.95 | | (62) all_126_0 = 0 % 23.21/3.95 | | % 23.21/3.95 | | REDUCE: (60), (62) imply: % 23.21/3.95 | | (63) $false % 23.21/3.95 | | % 23.21/3.95 | | CLOSE: (63) is inconsistent. % 23.21/3.95 | | % 23.21/3.95 | End of split % 23.21/3.95 | % 23.21/3.95 End of proof % 23.21/3.95 % SZS output end Proof for theBenchmark % 23.21/3.95 % 23.21/3.95 3357ms %------------------------------------------------------------------------------