%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV069+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 : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 22:54:47 EDT 2023 % Result : Theorem 13.77s 2.75s % Output : Proof 18.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV069+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n001.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 09:11:36 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.58 ________ _____ % 0.19/0.58 ___ __ \_________(_)________________________________ % 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.58 (2023-06-19) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2023 % 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.58 Amanda Stjerna. % 0.19/0.58 Free software under BSD-3-Clause. % 0.19/0.58 % 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.59 Running up to 7 provers in parallel. % 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.44/1.40 Prover 1: Preprocessing ... % 4.44/1.40 Prover 4: Preprocessing ... % 4.44/1.44 Prover 6: Preprocessing ... % 4.44/1.44 Prover 0: Preprocessing ... % 4.44/1.44 Prover 2: Preprocessing ... % 4.44/1.44 Prover 3: Preprocessing ... % 4.44/1.45 Prover 5: Preprocessing ... % 10.48/2.23 Prover 1: Warning: ignoring some quantifiers % 11.59/2.32 Prover 3: Warning: ignoring some quantifiers % 11.70/2.35 Prover 3: Constructing countermodel ... % 11.70/2.35 Prover 4: Warning: ignoring some quantifiers % 11.70/2.36 Prover 6: Proving ... % 11.70/2.36 Prover 1: Constructing countermodel ... % 12.26/2.42 Prover 4: Constructing countermodel ... % 12.74/2.49 Prover 0: Proving ... % 12.74/2.52 Prover 5: Proving ... % 13.37/2.57 Prover 2: Proving ... % 13.77/2.75 Prover 3: proved (2129ms) % 13.77/2.75 % 13.77/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.77/2.75 % 13.77/2.75 Prover 5: stopped % 13.77/2.75 Prover 2: stopped % 13.77/2.76 Prover 0: stopped % 14.16/2.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.16/2.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.16/2.77 Prover 6: stopped % 14.16/2.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.16/2.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.16/2.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.90/2.93 Prover 1: Found proof (size 68) % 15.90/2.93 Prover 1: proved (2336ms) % 15.90/2.94 Prover 4: stopped % 15.90/2.95 Prover 10: Preprocessing ... % 15.90/2.96 Prover 7: Preprocessing ... % 16.28/2.97 Prover 11: Preprocessing ... % 16.28/2.97 Prover 8: Preprocessing ... % 16.28/3.02 Prover 13: Preprocessing ... % 16.28/3.03 Prover 10: stopped % 16.28/3.04 Prover 7: stopped % 16.28/3.04 Prover 11: stopped % 17.17/3.11 Prover 13: stopped % 17.49/3.15 Prover 8: Warning: ignoring some quantifiers % 17.49/3.17 Prover 8: Constructing countermodel ... % 17.49/3.19 Prover 8: stopped % 17.49/3.19 % 17.49/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.49/3.19 % 17.49/3.21 % SZS output start Proof for theBenchmark % 17.81/3.21 Assumptions after simplification: % 17.81/3.21 --------------------------------- % 17.81/3.21 % 17.81/3.21 (cl5_nebula_array_0010) % 17.81/3.24 $i(n135300) & $i(pv10) & $i(n5) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: any] % 17.81/3.24 : ? [v2: $i] : ? [v3: any] : (minus(n135300, n1) = v0 & minus(n5, n1) = v2 & % 17.81/3.24 leq(pv10, v0) = 0 & leq(n0, v2) = v3 & leq(n0, pv10) = 0 & leq(n0, n0) = v1 % 17.81/3.24 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0))) % 17.81/3.24 % 17.81/3.24 (gt_5_0) % 17.81/3.24 gt(n5, n0) = 0 & $i(n5) & $i(n0) % 17.81/3.24 % 17.81/3.24 (leq_succ_gt_equiv) % 17.81/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 17.81/3.24 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 17.81/3.24 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 17.81/3.24 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 17.81/3.24 leq(v0, v1) = 0) % 17.81/3.24 % 17.81/3.24 (pred_minus_1) % 17.81/3.24 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 17.81/3.24 (pred(v0) = v1 & $i(v1))) % 17.81/3.24 % 17.81/3.24 (pred_succ) % 17.81/3.24 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 17.81/3.24 % 17.81/3.24 (reflexivity_leq) % 17.81/3.24 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ~ $i(v0)) % 17.81/3.24 % 17.81/3.24 (successor_1) % 17.81/3.24 succ(n0) = n1 & $i(n1) & $i(n0) % 17.81/3.24 % 17.81/3.24 (successor_2) % 17.81/3.24 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 17.81/3.24 % 17.81/3.24 (successor_3) % 17.81/3.24 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 17.81/3.24 succ(n0) = v0 & $i(v1) & $i(v0)) % 17.81/3.24 % 17.81/3.24 (successor_4) % 17.81/3.25 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 17.81/3.25 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 17.81/3.25 % 17.81/3.25 (successor_5) % 17.81/3.25 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 17.81/3.25 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 17.81/3.25 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.81/3.25 % 17.81/3.25 (function-axioms) % 17.81/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.81/3.26 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 17.81/3.26 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.81/3.26 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 17.81/3.26 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.81/3.26 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 17.81/3.26 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.81/3.26 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 17.81/3.26 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.81/3.26 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 17.81/3.26 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.81/3.26 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 17.81/3.26 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.81/3.26 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 17.81/3.26 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 17.81/3.26 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.81/3.26 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 17.81/3.26 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 17.81/3.26 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 17.81/3.26 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 17.81/3.26 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 17.81/3.26 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 17.81/3.26 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.81/3.26 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 17.81/3.26 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.81/3.26 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 17.81/3.26 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.81/3.26 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 17.81/3.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.81/3.26 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 17.81/3.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.81/3.26 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 17.81/3.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.81/3.26 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 17.81/3.26 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 17.81/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 17.81/3.26 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.81/3.26 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.81/3.26 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 17.81/3.26 % 17.81/3.26 Further assumptions not needed in the proof: % 17.81/3.26 -------------------------------------------- % 17.81/3.26 const_array1_select, const_array2_select, defuse, finite_domain_0, % 17.81/3.26 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 17.81/3.26 finite_domain_5, gt_0_tptp_minus_1, gt_135300_0, gt_135300_1, gt_135300_2, % 17.81/3.26 gt_135300_3, gt_135300_4, gt_135300_5, gt_135300_tptp_minus_1, gt_1_0, % 17.81/3.26 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, % 17.81/3.26 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_1, % 17.81/3.26 gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, % 17.81/3.26 leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_succ, % 17.81/3.26 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 17.81/3.26 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 17.81/3.26 matrix_symm_update_diagonal, sel2_update_1, sel2_update_2, sel2_update_3, % 17.81/3.26 sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, % 17.81/3.26 succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, % 17.81/3.26 succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, % 17.81/3.26 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 17.81/3.26 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 17.81/3.26 % 17.81/3.26 Those formulas are unsatisfiable: % 17.81/3.26 --------------------------------- % 17.81/3.26 % 17.81/3.26 Begin of proof % 18.05/3.26 | % 18.05/3.26 | ALPHA: (leq_succ_gt_equiv) implies: % 18.05/3.26 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 18.05/3.26 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0) % 18.05/3.26 | % 18.05/3.26 | ALPHA: (pred_minus_1) implies: % 18.05/3.26 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 18.05/3.26 | (pred(v0) = v1 & $i(v1))) % 18.05/3.26 | % 18.05/3.26 | ALPHA: (gt_5_0) implies: % 18.05/3.27 | (3) gt(n5, n0) = 0 % 18.05/3.27 | % 18.05/3.27 | ALPHA: (successor_4) implies: % 18.05/3.27 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 18.05/3.27 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 18.05/3.27 | % 18.05/3.27 | ALPHA: (successor_5) implies: % 18.05/3.27 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 18.05/3.27 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 18.05/3.27 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 18.05/3.27 | % 18.05/3.27 | ALPHA: (successor_1) implies: % 18.05/3.27 | (6) succ(n0) = n1 % 18.05/3.27 | % 18.05/3.27 | ALPHA: (successor_2) implies: % 18.05/3.27 | (7) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 18.05/3.27 | % 18.05/3.27 | ALPHA: (successor_3) implies: % 18.05/3.27 | (8) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) = % 18.05/3.27 | v0 & $i(v1) & $i(v0)) % 18.05/3.27 | % 18.05/3.27 | ALPHA: (cl5_nebula_array_0010) implies: % 18.05/3.27 | (9) $i(n0) % 18.05/3.27 | (10) $i(n5) % 18.05/3.27 | (11) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 18.05/3.27 | (minus(n135300, n1) = v0 & minus(n5, n1) = v2 & leq(pv10, v0) = 0 & % 18.05/3.27 | leq(n0, v2) = v3 & leq(n0, pv10) = 0 & leq(n0, n0) = v1 & $i(v2) & % 18.05/3.27 | $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0))) % 18.05/3.27 | % 18.05/3.27 | ALPHA: (function-axioms) implies: % 18.05/3.27 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = % 18.05/3.27 | v1) | ~ (pred(v2) = v0)) % 18.05/3.27 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 18.05/3.27 | v1) | ~ (succ(v2) = v0)) % 18.05/3.27 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.05/3.27 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 18.05/3.27 | v0)) % 18.05/3.27 | % 18.05/3.27 | DELTA: instantiating (7) with fresh symbol all_49_0 gives: % 18.05/3.28 | (15) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0) % 18.05/3.28 | % 18.05/3.28 | ALPHA: (15) implies: % 18.05/3.28 | (16) succ(n0) = all_49_0 % 18.05/3.28 | (17) succ(all_49_0) = n2 % 18.05/3.28 | % 18.05/3.28 | DELTA: instantiating (8) with fresh symbols all_51_0, all_51_1 gives: % 18.05/3.28 | (18) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1 % 18.05/3.28 | & $i(all_51_0) & $i(all_51_1) % 18.05/3.28 | % 18.05/3.28 | ALPHA: (18) implies: % 18.05/3.28 | (19) succ(n0) = all_51_1 % 18.05/3.28 | (20) succ(all_51_1) = all_51_0 % 18.05/3.28 | (21) succ(all_51_0) = n3 % 18.05/3.28 | % 18.05/3.28 | DELTA: instantiating (4) with fresh symbols all_53_0, all_53_1, all_53_2 % 18.05/3.28 | gives: % 18.05/3.28 | (22) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) = % 18.05/3.28 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) & % 18.05/3.28 | $i(all_53_2) % 18.05/3.28 | % 18.05/3.28 | ALPHA: (22) implies: % 18.05/3.28 | (23) succ(n0) = all_53_2 % 18.05/3.28 | (24) succ(all_53_2) = all_53_1 % 18.05/3.28 | (25) succ(all_53_1) = all_53_0 % 18.05/3.28 | (26) succ(all_53_0) = n4 % 18.05/3.28 | % 18.05/3.28 | DELTA: instantiating (5) with fresh symbols all_55_0, all_55_1, all_55_2, % 18.05/3.28 | all_55_3 gives: % 18.05/3.28 | (27) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) = % 18.05/3.28 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 & % 18.05/3.28 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) % 18.05/3.28 | % 18.05/3.28 | ALPHA: (27) implies: % 18.05/3.28 | (28) $i(all_55_0) % 18.05/3.28 | (29) succ(n0) = all_55_3 % 18.05/3.28 | (30) succ(all_55_3) = all_55_2 % 18.05/3.28 | (31) succ(all_55_2) = all_55_1 % 18.05/3.28 | (32) succ(all_55_1) = all_55_0 % 18.05/3.28 | (33) succ(all_55_0) = n5 % 18.05/3.28 | % 18.05/3.28 | DELTA: instantiating (11) with fresh symbols all_57_0, all_57_1, all_57_2, % 18.05/3.28 | all_57_3 gives: % 18.05/3.28 | (34) minus(n135300, n1) = all_57_3 & minus(n5, n1) = all_57_1 & leq(pv10, % 18.05/3.28 | all_57_3) = 0 & leq(n0, all_57_1) = all_57_0 & leq(n0, pv10) = 0 & % 18.05/3.28 | leq(n0, n0) = all_57_2 & $i(all_57_1) & $i(all_57_3) & ( ~ (all_57_0 = % 18.05/3.28 | 0) | ~ (all_57_2 = 0)) % 18.05/3.28 | % 18.05/3.28 | ALPHA: (34) implies: % 18.05/3.28 | (35) leq(n0, n0) = all_57_2 % 18.05/3.28 | (36) leq(n0, all_57_1) = all_57_0 % 18.05/3.28 | (37) minus(n5, n1) = all_57_1 % 18.05/3.28 | (38) ~ (all_57_0 = 0) | ~ (all_57_2 = 0) % 18.05/3.28 | % 18.05/3.28 | GROUND_INST: instantiating (13) with all_51_1, all_53_2, n0, simplifying with % 18.05/3.28 | (19), (23) gives: % 18.05/3.28 | (39) all_53_2 = all_51_1 % 18.05/3.28 | % 18.05/3.28 | GROUND_INST: instantiating (13) with all_49_0, all_53_2, n0, simplifying with % 18.05/3.28 | (16), (23) gives: % 18.05/3.28 | (40) all_53_2 = all_49_0 % 18.05/3.28 | % 18.05/3.29 | GROUND_INST: instantiating (13) with all_51_1, all_55_3, n0, simplifying with % 18.05/3.29 | (19), (29) gives: % 18.05/3.29 | (41) all_55_3 = all_51_1 % 18.05/3.29 | % 18.05/3.29 | GROUND_INST: instantiating (13) with n1, all_55_3, n0, simplifying with (6), % 18.05/3.29 | (29) gives: % 18.05/3.29 | (42) all_55_3 = n1 % 18.05/3.29 | % 18.05/3.29 | COMBINE_EQS: (41), (42) imply: % 18.05/3.29 | (43) all_51_1 = n1 % 18.05/3.29 | % 18.05/3.29 | SIMP: (43) implies: % 18.05/3.29 | (44) all_51_1 = n1 % 18.05/3.29 | % 18.05/3.29 | COMBINE_EQS: (39), (40) imply: % 18.05/3.29 | (45) all_51_1 = all_49_0 % 18.05/3.29 | % 18.05/3.29 | SIMP: (45) implies: % 18.05/3.29 | (46) all_51_1 = all_49_0 % 18.05/3.29 | % 18.05/3.29 | COMBINE_EQS: (44), (46) imply: % 18.05/3.29 | (47) all_49_0 = n1 % 18.05/3.29 | % 18.05/3.29 | COMBINE_EQS: (40), (47) imply: % 18.05/3.29 | (48) all_53_2 = n1 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (30), (42) imply: % 18.05/3.29 | (49) succ(n1) = all_55_2 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (24), (48) imply: % 18.05/3.29 | (50) succ(n1) = all_53_1 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (20), (44) imply: % 18.05/3.29 | (51) succ(n1) = all_51_0 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (17), (47) imply: % 18.05/3.29 | (52) succ(n1) = n2 % 18.05/3.29 | % 18.05/3.29 | GROUND_INST: instantiating (13) with all_51_0, all_53_1, n1, simplifying with % 18.05/3.29 | (50), (51) gives: % 18.05/3.29 | (53) all_53_1 = all_51_0 % 18.05/3.29 | % 18.05/3.29 | GROUND_INST: instantiating (13) with all_53_1, all_55_2, n1, simplifying with % 18.05/3.29 | (49), (50) gives: % 18.05/3.29 | (54) all_55_2 = all_53_1 % 18.05/3.29 | % 18.05/3.29 | GROUND_INST: instantiating (13) with n2, all_55_2, n1, simplifying with (49), % 18.05/3.29 | (52) gives: % 18.05/3.29 | (55) all_55_2 = n2 % 18.05/3.29 | % 18.05/3.29 | COMBINE_EQS: (54), (55) imply: % 18.05/3.29 | (56) all_53_1 = n2 % 18.05/3.29 | % 18.05/3.29 | SIMP: (56) implies: % 18.05/3.29 | (57) all_53_1 = n2 % 18.05/3.29 | % 18.05/3.29 | COMBINE_EQS: (53), (57) imply: % 18.05/3.29 | (58) all_51_0 = n2 % 18.05/3.29 | % 18.05/3.29 | SIMP: (58) implies: % 18.05/3.29 | (59) all_51_0 = n2 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (31), (55) imply: % 18.05/3.29 | (60) succ(n2) = all_55_1 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (25), (57) imply: % 18.05/3.29 | (61) succ(n2) = all_53_0 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (21), (59) imply: % 18.05/3.29 | (62) succ(n2) = n3 % 18.05/3.29 | % 18.05/3.29 | GROUND_INST: instantiating (13) with all_53_0, all_55_1, n2, simplifying with % 18.05/3.29 | (60), (61) gives: % 18.05/3.29 | (63) all_55_1 = all_53_0 % 18.05/3.29 | % 18.05/3.29 | GROUND_INST: instantiating (13) with n3, all_55_1, n2, simplifying with (60), % 18.05/3.29 | (62) gives: % 18.05/3.29 | (64) all_55_1 = n3 % 18.05/3.29 | % 18.05/3.29 | COMBINE_EQS: (63), (64) imply: % 18.05/3.29 | (65) all_53_0 = n3 % 18.05/3.29 | % 18.05/3.29 | SIMP: (65) implies: % 18.05/3.29 | (66) all_53_0 = n3 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (32), (64) imply: % 18.05/3.29 | (67) succ(n3) = all_55_0 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (26), (66) imply: % 18.05/3.29 | (68) succ(n3) = n4 % 18.05/3.29 | % 18.05/3.29 | GROUND_INST: instantiating (13) with n4, all_55_0, n3, simplifying with (67), % 18.05/3.29 | (68) gives: % 18.05/3.29 | (69) all_55_0 = n4 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (33), (69) imply: % 18.05/3.29 | (70) succ(n4) = n5 % 18.05/3.29 | % 18.05/3.29 | REDUCE: (28), (69) imply: % 18.05/3.29 | (71) $i(n4) % 18.05/3.29 | % 18.05/3.29 | GROUND_INST: instantiating (reflexivity_leq) with n0, all_57_2, simplifying % 18.05/3.30 | with (9), (35) gives: % 18.05/3.30 | (72) all_57_2 = 0 % 18.05/3.30 | % 18.05/3.30 | GROUND_INST: instantiating (1) with n0, n4, n5, simplifying with (3), (9), % 18.05/3.30 | (70), (71) gives: % 18.05/3.30 | (73) leq(n0, n4) = 0 % 18.05/3.30 | % 18.05/3.30 | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (70), % 18.05/3.30 | (71) gives: % 18.05/3.30 | (74) pred(n5) = n4 % 18.05/3.30 | % 18.05/3.30 | GROUND_INST: instantiating (2) with n5, all_57_1, simplifying with (10), (37) % 18.05/3.30 | gives: % 18.05/3.30 | (75) pred(n5) = all_57_1 & $i(all_57_1) % 18.05/3.30 | % 18.05/3.30 | ALPHA: (75) implies: % 18.05/3.30 | (76) pred(n5) = all_57_1 % 18.05/3.30 | % 18.05/3.30 | BETA: splitting (38) gives: % 18.05/3.30 | % 18.05/3.30 | Case 1: % 18.05/3.30 | | % 18.05/3.30 | | (77) ~ (all_57_0 = 0) % 18.05/3.30 | | % 18.05/3.30 | | GROUND_INST: instantiating (12) with n4, all_57_1, n5, simplifying with % 18.05/3.30 | | (74), (76) gives: % 18.05/3.30 | | (78) all_57_1 = n4 % 18.05/3.30 | | % 18.05/3.30 | | REDUCE: (36), (78) imply: % 18.05/3.30 | | (79) leq(n0, n4) = all_57_0 % 18.05/3.30 | | % 18.05/3.30 | | GROUND_INST: instantiating (14) with 0, all_57_0, n4, n0, simplifying with % 18.05/3.30 | | (73), (79) gives: % 18.05/3.30 | | (80) all_57_0 = 0 % 18.05/3.30 | | % 18.05/3.30 | | REDUCE: (77), (80) imply: % 18.05/3.30 | | (81) $false % 18.05/3.30 | | % 18.05/3.30 | | CLOSE: (81) is inconsistent. % 18.05/3.30 | | % 18.05/3.30 | Case 2: % 18.05/3.30 | | % 18.05/3.30 | | (82) ~ (all_57_2 = 0) % 18.05/3.30 | | % 18.05/3.30 | | REDUCE: (72), (82) imply: % 18.05/3.30 | | (83) $false % 18.05/3.30 | | % 18.05/3.30 | | CLOSE: (83) is inconsistent. % 18.05/3.30 | | % 18.05/3.30 | End of split % 18.05/3.30 | % 18.05/3.30 End of proof % 18.05/3.30 % SZS output end Proof for theBenchmark % 18.05/3.30 % 18.05/3.30 2720ms %------------------------------------------------------------------------------