%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV046+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 : n015.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 22:54:42 EDT 2023 % Result : Theorem 15.85s 2.89s % Output : Proof 20.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV046+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n015.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Aug 29 03:24:10 EDT 2023 % 0.17/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.16/1.28 Prover 4: Preprocessing ... % 4.16/1.28 Prover 1: Preprocessing ... % 4.16/1.31 Prover 5: Preprocessing ... % 4.16/1.31 Prover 0: Preprocessing ... % 4.16/1.31 Prover 2: Preprocessing ... % 4.16/1.31 Prover 6: Preprocessing ... % 4.16/1.31 Prover 3: Preprocessing ... % 10.71/2.17 Prover 1: Warning: ignoring some quantifiers % 11.02/2.26 Prover 1: Constructing countermodel ... % 11.02/2.27 Prover 6: Proving ... % 11.02/2.28 Prover 3: Warning: ignoring some quantifiers % 11.02/2.33 Prover 3: Constructing countermodel ... % 12.37/2.39 Prover 4: Warning: ignoring some quantifiers % 13.05/2.49 Prover 4: Constructing countermodel ... % 13.56/2.53 Prover 0: Proving ... % 13.82/2.60 Prover 5: Proving ... % 13.82/2.62 Prover 2: Proving ... % 15.85/2.89 Prover 3: proved (2260ms) % 15.85/2.89 % 15.85/2.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.85/2.89 % 15.85/2.89 Prover 0: stopped % 15.85/2.89 Prover 6: stopped % 15.85/2.89 Prover 5: stopped % 15.85/2.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.85/2.91 Prover 2: stopped % 15.85/2.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.85/2.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.85/2.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.85/2.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.02/3.05 Prover 7: Preprocessing ... % 17.02/3.05 Prover 11: Preprocessing ... % 17.87/3.11 Prover 1: Found proof (size 21) % 17.87/3.11 Prover 13: Preprocessing ... % 17.87/3.11 Prover 1: proved (2497ms) % 17.87/3.11 Prover 4: stopped % 17.87/3.12 Prover 8: Preprocessing ... % 17.87/3.12 Prover 10: Preprocessing ... % 18.09/3.17 Prover 7: stopped % 18.09/3.21 Prover 11: stopped % 18.09/3.22 Prover 10: stopped % 18.76/3.26 Prover 13: stopped % 19.42/3.38 Prover 8: Warning: ignoring some quantifiers % 19.42/3.40 Prover 8: Constructing countermodel ... % 19.64/3.42 Prover 8: stopped % 19.64/3.42 % 19.64/3.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.64/3.42 % 19.64/3.43 % SZS output start Proof for theBenchmark % 19.64/3.44 Assumptions after simplification: % 19.64/3.44 --------------------------------- % 19.64/3.44 % 19.64/3.44 (cl5_nebula_norm_0010) % 19.78/3.48 $i(mu) & $i(pv83) & $i(pv44) & $i(pv80) & $i(x) & $i(pv81) & $i(pv78) & % 19.78/3.48 $i(pv35) & $i(pv79) & $i(q) & $i(n135300) & $i(n5) & $i(n1) & $i(n0) & ? [v0: % 19.78/3.49 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 19.78/3.49 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 19.78/3.49 $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : % 19.78/3.49 (divide(pv80, pv44) = v8 & times(v11, v13) = v14 & times(v11, v12) = v13 & % 19.78/3.49 times(v2, v3) = v4 & tptp_update2(mu, pv35, v8) = v9 & minus(v7, v10) = v11 % 19.78/3.49 & minus(n135300, n1) = v0 & minus(n5, n1) = v5 & minus(n0, n1) = v6 & % 19.78/3.49 sum(n0, v6, v14) = v15 & sum(n0, v0, v4) = pv80 & sum(n0, v0, v1) = pv78 & % 19.78/3.49 a_select3(q, pv83, pv35) = v12 & a_select3(q, pv81, pv35) = v2 & % 19.78/3.49 a_select3(q, pv79, pv35) = v1 & a_select2(v9, pv35) = v10 & a_select2(x, % 19.78/3.49 pv83) = v7 & a_select2(x, pv81) = v3 & leq(pv35, v5) = 0 & leq(n0, pv35) = % 19.78/3.49 0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & % 19.78/3.49 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 19.78/3.49 $i(v0) & ((pv44 = n0 & ~ true) | ( ~ (v15 = n0) & ~ (pv44 = n0)))) % 19.78/3.49 % 19.78/3.49 (gt_3_tptp_minus_1) % 19.78/3.49 gt(n3, tptp_minus_1) = 0 & $i(n3) & $i(tptp_minus_1) % 19.78/3.49 % 19.78/3.49 (pred_minus_1) % 19.78/3.49 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 19.78/3.49 (pred(v0) = v1 & $i(v1))) % 19.78/3.49 % 19.78/3.49 (pred_succ) % 19.78/3.49 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 19.78/3.49 % 19.78/3.49 (succ_tptp_minus_1) % 19.78/3.49 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 19.78/3.49 % 19.78/3.49 (sum_plus_base) % 19.78/3.49 $i(tptp_minus_1) & $i(n0) & ! [v0: $i] : ! [v1: $i] : (v1 = n0 | ~ (sum(n0, % 19.78/3.49 tptp_minus_1, v0) = v1) | ~ $i(v0)) % 19.78/3.49 % 19.78/3.49 (ttrue) % 19.78/3.49 true % 19.78/3.49 % 19.78/3.49 (function-axioms) % 19.78/3.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.78/3.51 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.78/3.51 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.78/3.51 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.78/3.51 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.78/3.51 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.78/3.51 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.78/3.51 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.78/3.51 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.78/3.51 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.78/3.51 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.78/3.51 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (divide(v3, v2) = v1) | ~ (divide(v3, % 19.78/3.51 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.78/3.51 = v0 | ~ (times(v3, v2) = v1) | ~ (times(v3, v2) = v0)) & ! [v0: $i] : ! % 19.78/3.51 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ % 19.78/3.51 (minus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 19.78/3.51 $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: % 19.78/3.51 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, % 19.78/3.51 v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 19.78/3.51 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ % 19.78/3.51 (tptp_msub(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.78/3.51 [v3: $i] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = % 19.78/3.51 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.78/3.51 ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 19.78/3.51 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ % 19.78/3.51 (tptp_const_array1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 19.78/3.51 : ! [v3: $i] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) % 19.78/3.51 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 19.78/3.51 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & % 19.78/3.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.78/3.51 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.78/3.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.78/3.51 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.78/3.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.78/3.51 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.78/3.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.78/3.51 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.78/3.51 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 19.78/3.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 19.78/3.51 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.78/3.51 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.78/3.51 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 19.78/3.51 % 19.78/3.51 Further assumptions not needed in the proof: % 19.78/3.51 -------------------------------------------- % 19.78/3.51 const_array1_select, const_array2_select, defuse, finite_domain_0, % 19.78/3.51 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 19.78/3.51 finite_domain_5, gt_0_tptp_minus_1, gt_135300_0, gt_135300_1, gt_135300_2, % 19.78/3.51 gt_135300_3, gt_135300_4, gt_135300_5, gt_135300_tptp_minus_1, gt_1_0, % 19.78/3.51 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, % 19.78/3.51 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, % 19.78/3.51 gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1, % 19.78/3.51 leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 19.78/3.51 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 19.78/3.51 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.78/3.51 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 19.78/3.51 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, % 19.78/3.51 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, % 19.78/3.51 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, % 19.78/3.51 successor_1, successor_2, successor_3, successor_4, successor_5, % 19.78/3.51 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 19.78/3.51 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 19.78/3.51 % 19.78/3.51 Those formulas are unsatisfiable: % 19.78/3.51 --------------------------------- % 19.78/3.51 % 19.78/3.51 Begin of proof % 19.78/3.51 | % 19.78/3.51 | ALPHA: (sum_plus_base) implies: % 19.78/3.51 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = n0 | ~ (sum(n0, tptp_minus_1, v0) = % 19.78/3.51 | v1) | ~ $i(v0)) % 19.78/3.51 | % 19.78/3.51 | ALPHA: (succ_tptp_minus_1) implies: % 19.78/3.51 | (2) succ(tptp_minus_1) = n0 % 19.78/3.51 | % 19.78/3.51 | ALPHA: (pred_minus_1) implies: % 19.78/3.51 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 19.78/3.51 | (pred(v0) = v1 & $i(v1))) % 19.78/3.51 | % 19.78/3.51 | ALPHA: (gt_3_tptp_minus_1) implies: % 19.78/3.51 | (4) $i(tptp_minus_1) % 19.78/3.51 | % 19.78/3.51 | ALPHA: (cl5_nebula_norm_0010) implies: % 19.78/3.51 | (5) $i(n0) % 19.78/3.52 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.78/3.52 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 19.78/3.52 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 19.78/3.52 | ? [v15: $i] : (divide(pv80, pv44) = v8 & times(v11, v13) = v14 & % 19.78/3.52 | times(v11, v12) = v13 & times(v2, v3) = v4 & tptp_update2(mu, pv35, % 19.78/3.52 | v8) = v9 & minus(v7, v10) = v11 & minus(n135300, n1) = v0 & % 19.78/3.52 | minus(n5, n1) = v5 & minus(n0, n1) = v6 & sum(n0, v6, v14) = v15 & % 19.78/3.52 | sum(n0, v0, v4) = pv80 & sum(n0, v0, v1) = pv78 & a_select3(q, pv83, % 19.78/3.52 | pv35) = v12 & a_select3(q, pv81, pv35) = v2 & a_select3(q, pv79, % 19.78/3.52 | pv35) = v1 & a_select2(v9, pv35) = v10 & a_select2(x, pv83) = v7 & % 19.78/3.52 | a_select2(x, pv81) = v3 & leq(pv35, v5) = 0 & leq(n0, pv35) = 0 & % 19.78/3.52 | $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & % 19.78/3.52 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 19.78/3.52 | & $i(v0) & ((pv44 = n0 & ~ true) | ( ~ (v15 = n0) & ~ (pv44 = % 19.78/3.52 | n0)))) % 19.78/3.52 | % 19.78/3.52 | ALPHA: (function-axioms) implies: % 19.78/3.52 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) % 19.78/3.52 | | ~ (pred(v2) = v0)) % 19.78/3.52 | % 19.78/3.52 | DELTA: instantiating (6) with fresh symbols all_70_0, all_70_1, all_70_2, % 19.78/3.52 | all_70_3, all_70_4, all_70_5, all_70_6, all_70_7, all_70_8, all_70_9, % 19.78/3.52 | all_70_10, all_70_11, all_70_12, all_70_13, all_70_14, all_70_15 gives: % 19.78/3.52 | (8) divide(pv80, pv44) = all_70_7 & times(all_70_4, all_70_2) = all_70_1 & % 19.78/3.52 | times(all_70_4, all_70_3) = all_70_2 & times(all_70_13, all_70_12) = % 19.78/3.52 | all_70_11 & tptp_update2(mu, pv35, all_70_7) = all_70_6 & % 19.78/3.52 | minus(all_70_8, all_70_5) = all_70_4 & minus(n135300, n1) = all_70_15 & % 19.78/3.52 | minus(n5, n1) = all_70_10 & minus(n0, n1) = all_70_9 & sum(n0, % 19.78/3.52 | all_70_9, all_70_1) = all_70_0 & sum(n0, all_70_15, all_70_11) = pv80 % 19.78/3.52 | & sum(n0, all_70_15, all_70_14) = pv78 & a_select3(q, pv83, pv35) = % 19.78/3.52 | all_70_3 & a_select3(q, pv81, pv35) = all_70_13 & a_select3(q, pv79, % 19.78/3.52 | pv35) = all_70_14 & a_select2(all_70_6, pv35) = all_70_5 & % 19.78/3.52 | a_select2(x, pv83) = all_70_8 & a_select2(x, pv81) = all_70_12 & % 19.78/3.52 | leq(pv35, all_70_10) = 0 & leq(n0, pv35) = 0 & $i(all_70_0) & % 19.78/3.52 | $i(all_70_1) & $i(all_70_2) & $i(all_70_3) & $i(all_70_4) & % 19.78/3.52 | $i(all_70_5) & $i(all_70_6) & $i(all_70_7) & $i(all_70_8) & % 19.78/3.52 | $i(all_70_9) & $i(all_70_10) & $i(all_70_11) & $i(all_70_12) & % 19.78/3.52 | $i(all_70_13) & $i(all_70_14) & $i(all_70_15) & ((pv44 = n0 & ~ true) % 19.78/3.52 | | ( ~ (all_70_0 = n0) & ~ (pv44 = n0))) % 19.78/3.52 | % 19.78/3.52 | ALPHA: (8) implies: % 19.78/3.52 | (9) $i(all_70_1) % 19.78/3.52 | (10) sum(n0, all_70_9, all_70_1) = all_70_0 % 19.78/3.52 | (11) minus(n0, n1) = all_70_9 % 19.78/3.52 | (12) (pv44 = n0 & ~ true) | ( ~ (all_70_0 = n0) & ~ (pv44 = n0)) % 19.78/3.52 | % 19.78/3.52 | BETA: splitting (12) gives: % 19.78/3.52 | % 19.78/3.52 | Case 1: % 19.78/3.52 | | % 19.78/3.52 | | (13) pv44 = n0 & ~ true % 19.78/3.52 | | % 19.78/3.52 | | ALPHA: (13) implies: % 19.78/3.52 | | (14) ~ true % 19.78/3.52 | | % 19.78/3.52 | | PRED_UNIFY: (14), (ttrue) imply: % 19.78/3.52 | | (15) $false % 19.78/3.53 | | % 19.78/3.53 | | CLOSE: (15) is inconsistent. % 19.78/3.53 | | % 19.78/3.53 | Case 2: % 19.78/3.53 | | % 19.78/3.53 | | (16) ~ (all_70_0 = n0) & ~ (pv44 = n0) % 19.78/3.53 | | % 19.78/3.53 | | ALPHA: (16) implies: % 19.78/3.53 | | (17) ~ (all_70_0 = n0) % 19.78/3.53 | | % 19.78/3.53 | | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying % 19.78/3.53 | | with (2), (4) gives: % 19.78/3.53 | | (18) pred(n0) = tptp_minus_1 % 19.78/3.53 | | % 19.78/3.53 | | GROUND_INST: instantiating (3) with n0, all_70_9, simplifying with (5), (11) % 19.78/3.53 | | gives: % 19.78/3.53 | | (19) pred(n0) = all_70_9 & $i(all_70_9) % 19.78/3.53 | | % 20.19/3.53 | | ALPHA: (19) implies: % 20.19/3.53 | | (20) pred(n0) = all_70_9 % 20.19/3.53 | | % 20.19/3.53 | | GROUND_INST: instantiating (7) with tptp_minus_1, all_70_9, n0, simplifying % 20.19/3.53 | | with (18), (20) gives: % 20.19/3.53 | | (21) all_70_9 = tptp_minus_1 % 20.19/3.53 | | % 20.19/3.53 | | REDUCE: (10), (21) imply: % 20.19/3.53 | | (22) sum(n0, tptp_minus_1, all_70_1) = all_70_0 % 20.19/3.53 | | % 20.19/3.53 | | GROUND_INST: instantiating (1) with all_70_1, all_70_0, simplifying with % 20.19/3.53 | | (9), (22) gives: % 20.19/3.53 | | (23) all_70_0 = n0 % 20.19/3.53 | | % 20.19/3.53 | | REDUCE: (17), (23) imply: % 20.19/3.53 | | (24) $false % 20.19/3.53 | | % 20.19/3.53 | | CLOSE: (24) is inconsistent. % 20.19/3.53 | | % 20.19/3.53 | End of split % 20.19/3.53 | % 20.19/3.53 End of proof % 20.19/3.53 % SZS output end Proof for theBenchmark % 20.19/3.53 % 20.19/3.53 2932ms %------------------------------------------------------------------------------