%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV163+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 : n014.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 22:55:10 EDT 2023 % Result : Theorem 15.03s 2.80s % Output : Proof 19.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWV163+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n014.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 03:33:45 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.60/1.38 Prover 1: Preprocessing ... % 4.60/1.39 Prover 4: Preprocessing ... % 5.13/1.41 Prover 2: Preprocessing ... % 5.13/1.41 Prover 5: Preprocessing ... % 5.13/1.41 Prover 0: Preprocessing ... % 5.13/1.41 Prover 6: Preprocessing ... % 5.13/1.41 Prover 3: Preprocessing ... % 10.41/2.21 Prover 1: Warning: ignoring some quantifiers % 10.41/2.24 Prover 3: Warning: ignoring some quantifiers % 10.41/2.28 Prover 6: Proving ... % 10.41/2.28 Prover 3: Constructing countermodel ... % 10.41/2.28 Prover 4: Warning: ignoring some quantifiers % 10.41/2.28 Prover 1: Constructing countermodel ... % 11.92/2.34 Prover 4: Constructing countermodel ... % 12.67/2.42 Prover 5: Proving ... % 12.67/2.46 Prover 0: Proving ... % 12.67/2.49 Prover 2: Proving ... % 15.03/2.79 Prover 3: proved (2153ms) % 15.03/2.79 % 15.03/2.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.03/2.80 % 15.03/2.80 Prover 2: stopped % 15.03/2.80 Prover 6: stopped % 15.03/2.80 Prover 5: stopped % 15.66/2.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.66/2.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.66/2.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.66/2.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.66/2.81 Prover 0: stopped % 15.66/2.82 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.60/3.02 Prover 1: Found proof (size 23) % 16.60/3.02 Prover 1: proved (2381ms) % 16.60/3.02 Prover 4: stopped % 16.60/3.10 Prover 8: Preprocessing ... % 17.99/3.13 Prover 13: Preprocessing ... % 17.99/3.14 Prover 11: Preprocessing ... % 17.99/3.14 Prover 10: Preprocessing ... % 17.99/3.15 Prover 7: Preprocessing ... % 17.99/3.19 Prover 10: stopped % 17.99/3.21 Prover 11: stopped % 17.99/3.21 Prover 13: stopped % 18.74/3.22 Prover 7: stopped % 18.74/3.27 Prover 8: Warning: ignoring some quantifiers % 18.74/3.28 Prover 8: Constructing countermodel ... % 19.12/3.30 Prover 8: stopped % 19.12/3.30 % 19.12/3.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.12/3.30 % 19.12/3.30 % SZS output start Proof for theBenchmark % 19.12/3.31 Assumptions after simplification: % 19.12/3.31 --------------------------------- % 19.12/3.31 % 19.12/3.31 (cl5_nebula_norm_0013) % 19.12/3.34 $i(x) & $i(center) & $i(tptp_sum_index) & $i(q) & $i(n135299) & $i(pv10) & % 19.12/3.34 $i(n4) & $i(n1) & $i(tptp_minus_1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? % 19.12/3.34 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (times(v3, % 19.12/3.34 v3) = v4 & sqrt(v4) = v5 & minus(v2, v1) = v3 & sum(n0, n4, v5) = v6 & % 19.12/3.34 a_select3(center, tptp_sum_index, n0) = v2 & a_select2(x, pv10) = v1 & % 19.12/3.34 pred(pv10) = v0 & leq(pv10, n135299) = 0 & leq(n0, pv10) = 0 & $i(v6) & % 19.12/3.34 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: % 19.12/3.34 $i] : ( ~ (a_select3(q, v7, tptp_sum_index) = v8) | ~ $i(v7) | ? [v9: % 19.12/3.34 any] : ? [v10: any] : ? [v11: $i] : (sum(n0, n4, v8) = v11 & leq(v7, % 19.12/3.34 v0) = v10 & leq(n0, v7) = v9 & $i(v11) & ( ~ (v10 = 0) | ~ (v9 = 0) | % 19.12/3.34 v11 = n1))) & ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 19.12/3.34 ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ( ~ (v13 = v8) & times(v10, % 19.12/3.34 v10) = v11 & sqrt(v11) = v12 & divide(v12, v6) = v13 & minus(v9, v1) = % 19.12/3.34 v10 & a_select3(center, v7, n0) = v9 & a_select3(q, pv10, v7) = v8 & % 19.12/3.34 leq(v7, tptp_minus_1) = 0 & leq(n0, v7) = 0 & $i(v13) & $i(v12) & $i(v11) % 19.12/3.34 & $i(v10) & $i(v9) & $i(v8) & $i(v7))) % 19.12/3.34 % 19.12/3.34 (finite_domain_0) % 19.12/3.34 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.12/3.34 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.12/3.34 % 19.12/3.34 (irreflexivity_gt) % 19.12/3.34 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 19.12/3.34 % 19.12/3.34 (leq_gt1) % 19.12/3.34 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 19.12/3.34 leq(v0, v1) = 0) % 19.12/3.34 % 19.12/3.34 (leq_gt_pred) % 19.12/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.12/3.35 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 19.12/3.35 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 19.12/3.35 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 19.12/3.35 | gt(v1, v0) = 0) % 19.12/3.35 % 19.12/3.35 (pred_succ) % 19.12/3.35 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 19.12/3.35 % 19.12/3.35 (succ_tptp_minus_1) % 19.12/3.35 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 19.12/3.35 % 19.12/3.35 (function-axioms) % 19.12/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.12/3.35 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.12/3.35 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.12/3.35 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.12/3.35 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.12/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.12/3.35 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.12/3.35 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.12/3.35 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.12/3.35 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.12/3.35 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.12/3.35 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3, % 19.12/3.35 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.12/3.35 = v0 | ~ (divide(v3, v2) = v1) | ~ (divide(v3, v2) = v0)) & ! [v0: $i] : % 19.12/3.35 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | % 19.12/3.35 ~ (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 19.12/3.35 $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: % 19.12/3.35 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, % 19.12/3.35 v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 19.12/3.35 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ % 19.12/3.35 (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.12/3.35 [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = % 19.12/3.35 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.12/3.35 ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 19.12/3.35 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ % 19.12/3.35 (tptp_const_array1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 19.12/3.35 : ! [v3: $i] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) % 19.12/3.35 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 19.12/3.35 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & % 19.12/3.35 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.12/3.35 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.12/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.12/3.35 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.12/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.12/3.35 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.12/3.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.12/3.35 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.12/3.35 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) & % 19.12/3.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ % 19.12/3.35 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.12/3.35 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.12/3.35 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : % 19.12/3.36 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = % 19.12/3.36 v0)) % 19.12/3.36 % 19.12/3.36 Further assumptions not needed in the proof: % 19.12/3.36 -------------------------------------------- % 19.12/3.36 const_array1_select, const_array2_select, defuse, finite_domain_1, % 19.12/3.36 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 19.12/3.36 gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, gt_135299_3, % 19.12/3.36 gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, % 19.12/3.36 gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, % 19.12/3.36 gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, % 19.12/3.36 gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, leq_geq, leq_gt2, leq_minus, % 19.12/3.36 leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, lt_gt, % 19.12/3.36 matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 19.12/3.36 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.12/3.36 matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1, % 19.12/3.36 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, % 19.12/3.36 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, % 19.12/3.36 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, % 19.12/3.36 succ_pred, successor_1, successor_2, successor_3, successor_4, successor_5, % 19.12/3.36 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 19.12/3.36 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 19.12/3.36 % 19.12/3.36 Those formulas are unsatisfiable: % 19.12/3.36 --------------------------------- % 19.12/3.36 % 19.12/3.36 Begin of proof % 19.12/3.36 | % 19.12/3.36 | ALPHA: (leq_gt_pred) implies: % 19.12/3.36 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 19.12/3.36 | (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 19.12/3.36 | % 19.12/3.36 | ALPHA: (succ_tptp_minus_1) implies: % 19.12/3.36 | (2) succ(tptp_minus_1) = n0 % 19.12/3.36 | % 19.12/3.36 | ALPHA: (finite_domain_0) implies: % 19.12/3.36 | (3) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 19.12/3.36 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 19.12/3.36 | % 19.12/3.36 | ALPHA: (cl5_nebula_norm_0013) implies: % 19.12/3.36 | (4) $i(n0) % 19.12/3.36 | (5) $i(tptp_minus_1) % 19.12/3.36 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.12/3.36 | ? [v5: $i] : ? [v6: $i] : (times(v3, v3) = v4 & sqrt(v4) = v5 & % 19.12/3.36 | minus(v2, v1) = v3 & sum(n0, n4, v5) = v6 & a_select3(center, % 19.12/3.36 | tptp_sum_index, n0) = v2 & a_select2(x, pv10) = v1 & pred(pv10) = % 19.12/3.36 | v0 & leq(pv10, n135299) = 0 & leq(n0, pv10) = 0 & $i(v6) & $i(v5) & % 19.12/3.36 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: % 19.12/3.36 | $i] : ( ~ (a_select3(q, v7, tptp_sum_index) = v8) | ~ $i(v7) | ? % 19.12/3.36 | [v9: any] : ? [v10: any] : ? [v11: $i] : (sum(n0, n4, v8) = v11 & % 19.12/3.36 | leq(v7, v0) = v10 & leq(n0, v7) = v9 & $i(v11) & ( ~ (v10 = 0) | % 19.12/3.36 | ~ (v9 = 0) | v11 = n1))) & ? [v7: $i] : ? [v8: $i] : ? [v9: % 19.12/3.36 | $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ( % 19.12/3.36 | ~ (v13 = v8) & times(v10, v10) = v11 & sqrt(v11) = v12 & % 19.12/3.36 | divide(v12, v6) = v13 & minus(v9, v1) = v10 & a_select3(center, v7, % 19.12/3.36 | n0) = v9 & a_select3(q, pv10, v7) = v8 & leq(v7, tptp_minus_1) = % 19.12/3.36 | 0 & leq(n0, v7) = 0 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 19.12/3.36 | $i(v9) & $i(v8) & $i(v7))) % 19.12/3.36 | % 19.12/3.36 | ALPHA: (function-axioms) implies: % 19.12/3.36 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.12/3.36 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 19.12/3.37 | % 19.12/3.37 | DELTA: instantiating (6) with fresh symbols all_74_0, all_74_1, all_74_2, % 19.12/3.37 | all_74_3, all_74_4, all_74_5, all_74_6 gives: % 19.12/3.37 | (8) times(all_74_3, all_74_3) = all_74_2 & sqrt(all_74_2) = all_74_1 & % 19.12/3.37 | minus(all_74_4, all_74_5) = all_74_3 & sum(n0, n4, all_74_1) = all_74_0 % 19.12/3.37 | & a_select3(center, tptp_sum_index, n0) = all_74_4 & a_select2(x, pv10) % 19.12/3.37 | = all_74_5 & pred(pv10) = all_74_6 & leq(pv10, n135299) = 0 & leq(n0, % 19.12/3.37 | pv10) = 0 & $i(all_74_0) & $i(all_74_1) & $i(all_74_2) & $i(all_74_3) % 19.12/3.37 | & $i(all_74_4) & $i(all_74_5) & $i(all_74_6) & ! [v0: $i] : ! [v1: % 19.12/3.37 | $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ~ $i(v0) | ? % 19.12/3.37 | [v2: any] : ? [v3: any] : ? [v4: $i] : (sum(n0, n4, v1) = v4 & % 19.12/3.37 | leq(v0, all_74_6) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | % 19.12/3.37 | ~ (v2 = 0) | v4 = n1))) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 19.12/3.37 | $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 % 19.12/3.37 | = v1) & times(v3, v3) = v4 & sqrt(v4) = v5 & divide(v5, all_74_0) = % 19.12/3.37 | v6 & minus(v2, all_74_5) = v3 & a_select3(center, v0, n0) = v2 & % 19.12/3.37 | a_select3(q, pv10, v0) = v1 & leq(v0, tptp_minus_1) = 0 & leq(n0, v0) % 19.12/3.37 | = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 19.12/3.37 | % 19.12/3.37 | ALPHA: (8) implies: % 19.12/3.37 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.12/3.37 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v1) & times(v3, v3) = v4 & % 19.12/3.37 | sqrt(v4) = v5 & divide(v5, all_74_0) = v6 & minus(v2, all_74_5) = v3 % 19.12/3.37 | & a_select3(center, v0, n0) = v2 & a_select3(q, pv10, v0) = v1 & % 19.12/3.37 | leq(v0, tptp_minus_1) = 0 & leq(n0, v0) = 0 & $i(v6) & $i(v5) & % 19.12/3.37 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 19.12/3.37 | % 19.12/3.37 | DELTA: instantiating (9) with fresh symbols all_79_0, all_79_1, all_79_2, % 19.12/3.37 | all_79_3, all_79_4, all_79_5, all_79_6 gives: % 19.12/3.37 | (10) ~ (all_79_0 = all_79_5) & times(all_79_3, all_79_3) = all_79_2 & % 19.12/3.37 | sqrt(all_79_2) = all_79_1 & divide(all_79_1, all_74_0) = all_79_0 & % 19.12/3.37 | minus(all_79_4, all_74_5) = all_79_3 & a_select3(center, all_79_6, n0) % 19.12/3.37 | = all_79_4 & a_select3(q, pv10, all_79_6) = all_79_5 & leq(all_79_6, % 19.12/3.37 | tptp_minus_1) = 0 & leq(n0, all_79_6) = 0 & $i(all_79_0) & % 19.12/3.37 | $i(all_79_1) & $i(all_79_2) & $i(all_79_3) & $i(all_79_4) & % 19.12/3.37 | $i(all_79_5) & $i(all_79_6) % 19.12/3.37 | % 19.12/3.37 | ALPHA: (10) implies: % 19.12/3.37 | (11) $i(all_79_6) % 19.12/3.37 | (12) leq(n0, all_79_6) = 0 % 19.12/3.37 | (13) leq(all_79_6, tptp_minus_1) = 0 % 19.12/3.37 | % 19.12/3.37 | GROUND_INST: instantiating (3) with all_79_6, simplifying with (11), (12) % 19.12/3.37 | gives: % 19.51/3.37 | (14) all_79_6 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_6, n0) = v0) % 19.51/3.37 | % 19.51/3.37 | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with % 19.51/3.37 | (2), (5) gives: % 19.51/3.37 | (15) pred(n0) = tptp_minus_1 % 19.51/3.37 | % 19.51/3.37 | GROUND_INST: instantiating (1) with all_79_6, n0, tptp_minus_1, simplifying % 19.51/3.37 | with (4), (11), (13), (15) gives: % 19.51/3.38 | (16) gt(n0, all_79_6) = 0 % 19.51/3.38 | % 19.51/3.38 | GROUND_INST: instantiating (leq_gt1) with all_79_6, n0, simplifying with (4), % 19.51/3.38 | (11), (16) gives: % 19.51/3.38 | (17) leq(all_79_6, n0) = 0 % 19.51/3.38 | % 19.51/3.38 | BETA: splitting (14) gives: % 19.51/3.38 | % 19.51/3.38 | Case 1: % 19.51/3.38 | | % 19.51/3.38 | | (18) all_79_6 = n0 % 19.51/3.38 | | % 19.51/3.38 | | REDUCE: (16), (18) imply: % 19.51/3.38 | | (19) gt(n0, n0) = 0 % 19.51/3.38 | | % 19.51/3.38 | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with (4), % 19.51/3.38 | | (19) gives: % 19.52/3.38 | | (20) $false % 19.52/3.38 | | % 19.52/3.38 | | CLOSE: (20) is inconsistent. % 19.52/3.38 | | % 19.52/3.38 | Case 2: % 19.52/3.38 | | % 19.52/3.38 | | (21) ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_6, n0) = v0) % 19.52/3.38 | | % 19.52/3.38 | | DELTA: instantiating (21) with fresh symbol all_119_0 gives: % 19.52/3.38 | | (22) ~ (all_119_0 = 0) & leq(all_79_6, n0) = all_119_0 % 19.52/3.38 | | % 19.52/3.38 | | ALPHA: (22) implies: % 19.52/3.38 | | (23) ~ (all_119_0 = 0) % 19.52/3.38 | | (24) leq(all_79_6, n0) = all_119_0 % 19.52/3.38 | | % 19.52/3.38 | | GROUND_INST: instantiating (7) with 0, all_119_0, n0, all_79_6, simplifying % 19.52/3.38 | | with (17), (24) gives: % 19.52/3.38 | | (25) all_119_0 = 0 % 19.52/3.38 | | % 19.52/3.38 | | REDUCE: (23), (25) imply: % 19.52/3.38 | | (26) $false % 19.52/3.38 | | % 19.52/3.38 | | CLOSE: (26) is inconsistent. % 19.52/3.38 | | % 19.52/3.38 | End of split % 19.52/3.38 | % 19.52/3.38 End of proof % 19.52/3.38 % SZS output end Proof for theBenchmark % 19.52/3.38 % 19.52/3.38 2761ms %------------------------------------------------------------------------------