%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV162+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 : n007.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 15.17s 2.78s % Output : Proof 18.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SWV162+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n007.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 10:14:58 EDT 2023 % 0.12/0.34 % CPUTime : % 0.61/0.60 ________ _____ % 0.61/0.60 ___ __ \_________(_)________________________________ % 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.60 (2023-06-19) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2023 % 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.60 Amanda Stjerna. % 0.61/0.60 Free software under BSD-3-Clause. % 0.61/0.60 % 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.61 Running up to 7 provers in parallel. % 0.65/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.65/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.65/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.65/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.65/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.65/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.65/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 4.58/1.34 Prover 1: Preprocessing ... % 4.58/1.34 Prover 4: Preprocessing ... % 4.98/1.38 Prover 5: Preprocessing ... % 4.98/1.38 Prover 0: Preprocessing ... % 4.98/1.38 Prover 6: Preprocessing ... % 4.98/1.38 Prover 3: Preprocessing ... % 4.98/1.38 Prover 2: Preprocessing ... % 10.59/2.19 Prover 1: Warning: ignoring some quantifiers % 11.27/2.24 Prover 3: Warning: ignoring some quantifiers % 11.27/2.25 Prover 6: Proving ... % 11.27/2.26 Prover 3: Constructing countermodel ... % 11.27/2.29 Prover 1: Constructing countermodel ... % 11.85/2.30 Prover 4: Warning: ignoring some quantifiers % 11.85/2.37 Prover 0: Proving ... % 11.85/2.38 Prover 4: Constructing countermodel ... % 12.69/2.40 Prover 5: Proving ... % 13.56/2.53 Prover 2: Proving ... % 15.17/2.77 Prover 3: proved (2155ms) % 15.17/2.77 % 15.17/2.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.17/2.78 % 15.17/2.78 Prover 6: stopped % 15.17/2.78 Prover 5: stopped % 15.17/2.78 Prover 2: stopped % 15.17/2.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.17/2.80 Prover 0: stopped % 15.17/2.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.17/2.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.17/2.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.17/2.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.49/2.97 Prover 10: Preprocessing ... % 16.99/2.98 Prover 8: Preprocessing ... % 16.99/2.98 Prover 1: Found proof (size 52) % 16.99/2.98 Prover 1: proved (2367ms) % 16.99/2.98 Prover 4: stopped % 16.99/3.00 Prover 7: Preprocessing ... % 16.99/3.01 Prover 13: Preprocessing ... % 16.99/3.01 Prover 11: Preprocessing ... % 17.74/3.08 Prover 10: stopped % 17.91/3.11 Prover 7: stopped % 18.12/3.12 Prover 11: stopped % 18.15/3.15 Prover 13: stopped % 18.15/3.18 Prover 8: Warning: ignoring some quantifiers % 18.15/3.19 Prover 8: Constructing countermodel ... % 18.55/3.21 Prover 8: stopped % 18.55/3.21 % 18.55/3.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.55/3.21 % 18.55/3.22 % SZS output start Proof for theBenchmark % 18.55/3.23 Assumptions after simplification: % 18.55/3.23 --------------------------------- % 18.55/3.23 % 18.55/3.23 (cl5_nebula_norm_0012) % 18.55/3.26 $i(n135299) & $i(tptp_sum_index) & $i(pv10) & $i(q) & $i(n4) & $i(n1) & $i(n0) % 18.55/3.26 & ? [v0: $i] : ? [v1: $i] : (sum(n0, n4, v0) = n1 & a_select3(q, pv10, % 18.55/3.26 tptp_sum_index) = v0 & pred(pv10) = v1 & leq(pv10, n135299) = 0 & leq(n0, % 18.55/3.26 pv10) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 18.55/3.26 (a_select3(q, v2, tptp_sum_index) = v3) | ~ $i(v2) | ? [v4: any] : ? % 18.55/3.26 [v5: any] : ? [v6: $i] : (sum(n0, n4, v3) = v6 & leq(v2, v1) = v5 & % 18.55/3.26 leq(n0, v2) = v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = n1))) & ? % 18.55/3.26 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = n1) & sum(n0, n4, v3) = v4 % 18.55/3.26 & a_select3(q, v2, tptp_sum_index) = v3 & leq(v2, pv10) = 0 & leq(n0, v2) % 18.55/3.26 = 0 & $i(v4) & $i(v3) & $i(v2))) % 18.55/3.26 % 18.55/3.26 (leq_gt2) % 18.55/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (gt(v1, v0) % 18.55/3.26 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) % 18.55/3.26 = v3)) % 18.55/3.26 % 18.55/3.26 (leq_gt_pred) % 18.55/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 18.55/3.26 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 18.55/3.26 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 18.55/3.26 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 18.55/3.26 | gt(v1, v0) = 0) % 18.55/3.26 % 18.55/3.26 (function-axioms) % 18.55/3.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.55/3.27 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 18.55/3.27 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.55/3.27 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 18.55/3.27 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.55/3.27 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 18.55/3.27 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.55/3.27 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 18.55/3.27 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.55/3.27 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 18.55/3.27 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.55/3.27 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 18.55/3.27 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 18.55/3.27 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 18.55/3.27 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 18.55/3.27 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.55/3.27 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 18.55/3.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 18.55/3.27 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 18.55/3.27 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 18.55/3.27 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 18.55/3.27 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 18.55/3.27 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 18.55/3.27 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 18.55/3.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.55/3.27 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 18.55/3.27 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 18.55/3.27 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 18.55/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.55/3.27 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 18.55/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.55/3.27 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 18.55/3.27 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.55/3.27 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 18.55/3.27 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 18.55/3.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 18.55/3.27 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 18.55/3.27 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.55/3.27 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 18.55/3.27 % 18.55/3.27 Further assumptions not needed in the proof: % 18.55/3.27 -------------------------------------------- % 18.55/3.27 const_array1_select, const_array2_select, defuse, finite_domain_0, % 18.55/3.27 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 18.55/3.27 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, % 18.55/3.27 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, % 18.55/3.27 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, % 18.55/3.27 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, % 18.55/3.27 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 18.55/3.27 leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 18.55/3.27 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 18.55/3.27 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 18.55/3.27 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 18.55/3.27 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 18.55/3.27 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 18.55/3.27 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 18.55/3.27 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2, % 18.55/3.27 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float, % 18.55/3.27 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 18.55/3.27 uniform_int_rand_ranges_lo % 18.55/3.27 % 18.55/3.27 Those formulas are unsatisfiable: % 18.55/3.27 --------------------------------- % 18.55/3.27 % 18.55/3.27 Begin of proof % 18.55/3.27 | % 18.55/3.27 | ALPHA: (leq_gt_pred) implies: % 18.88/3.27 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 18.88/3.27 | (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 18.88/3.27 | [v4: int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) % 18.88/3.27 | % 18.88/3.27 | ALPHA: (cl5_nebula_norm_0012) implies: % 18.88/3.27 | (2) $i(pv10) % 18.88/3.28 | (3) ? [v0: $i] : ? [v1: $i] : (sum(n0, n4, v0) = n1 & a_select3(q, pv10, % 18.88/3.28 | tptp_sum_index) = v0 & pred(pv10) = v1 & leq(pv10, n135299) = 0 & % 18.88/3.28 | leq(n0, pv10) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ % 18.88/3.28 | (a_select3(q, v2, tptp_sum_index) = v3) | ~ $i(v2) | ? [v4: any] % 18.88/3.28 | : ? [v5: any] : ? [v6: $i] : (sum(n0, n4, v3) = v6 & leq(v2, v1) % 18.88/3.28 | = v5 & leq(n0, v2) = v4 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | % 18.88/3.28 | v6 = n1))) & ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 % 18.88/3.28 | = n1) & sum(n0, n4, v3) = v4 & a_select3(q, v2, tptp_sum_index) = % 18.88/3.28 | v3 & leq(v2, pv10) = 0 & leq(n0, v2) = 0 & $i(v4) & $i(v3) & % 18.88/3.28 | $i(v2))) % 18.88/3.28 | % 18.88/3.28 | ALPHA: (function-axioms) implies: % 18.88/3.28 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.88/3.28 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 18.88/3.28 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.88/3.28 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 18.88/3.28 | = v0)) % 18.88/3.28 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.88/3.28 | (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | ~ (sum(v4, v3, v2) = v0)) % 18.88/3.28 | % 18.88/3.28 | DELTA: instantiating (3) with fresh symbols all_61_0, all_61_1 gives: % 18.88/3.28 | (7) sum(n0, n4, all_61_1) = n1 & a_select3(q, pv10, tptp_sum_index) = % 18.88/3.28 | all_61_1 & pred(pv10) = all_61_0 & leq(pv10, n135299) = 0 & leq(n0, % 18.88/3.28 | pv10) = 0 & $i(all_61_0) & $i(all_61_1) & ! [v0: $i] : ! [v1: $i] : % 18.88/3.28 | ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ~ $i(v0) | ? [v2: any] % 18.88/3.28 | : ? [v3: any] : ? [v4: $i] : (sum(n0, n4, v1) = v4 & leq(v0, % 18.88/3.28 | all_61_0) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ % 18.88/3.28 | (v2 = 0) | v4 = n1))) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 18.88/3.28 | ( ~ (v2 = n1) & sum(n0, n4, v1) = v2 & a_select3(q, v0, tptp_sum_index) % 18.88/3.28 | = v1 & leq(v0, pv10) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & % 18.88/3.28 | $i(v0)) % 18.88/3.28 | % 18.88/3.28 | ALPHA: (7) implies: % 18.88/3.28 | (8) pred(pv10) = all_61_0 % 18.88/3.28 | (9) a_select3(q, pv10, tptp_sum_index) = all_61_1 % 18.88/3.28 | (10) sum(n0, n4, all_61_1) = n1 % 18.88/3.28 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (a_select3(q, v0, tptp_sum_index) = % 18.88/3.28 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 18.88/3.28 | (sum(n0, n4, v1) = v4 & leq(v0, all_61_0) = v3 & leq(n0, v0) = v2 & % 18.88/3.28 | $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = n1))) % 18.88/3.29 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = n1) & sum(n0, n4, % 18.88/3.29 | v1) = v2 & a_select3(q, v0, tptp_sum_index) = v1 & leq(v0, pv10) = % 18.88/3.29 | 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 18.88/3.29 | % 18.88/3.29 | DELTA: instantiating (12) with fresh symbols all_79_0, all_79_1, all_79_2 % 18.88/3.29 | gives: % 18.88/3.29 | (13) ~ (all_79_0 = n1) & sum(n0, n4, all_79_1) = all_79_0 & a_select3(q, % 18.88/3.29 | all_79_2, tptp_sum_index) = all_79_1 & leq(all_79_2, pv10) = 0 & % 18.88/3.29 | leq(n0, all_79_2) = 0 & $i(all_79_0) & $i(all_79_1) & $i(all_79_2) % 18.88/3.29 | % 18.88/3.29 | ALPHA: (13) implies: % 18.88/3.29 | (14) ~ (all_79_0 = n1) % 18.88/3.29 | (15) $i(all_79_2) % 18.88/3.29 | (16) leq(n0, all_79_2) = 0 % 18.88/3.29 | (17) leq(all_79_2, pv10) = 0 % 18.88/3.29 | (18) a_select3(q, all_79_2, tptp_sum_index) = all_79_1 % 18.88/3.29 | (19) sum(n0, n4, all_79_1) = all_79_0 % 18.88/3.29 | % 18.88/3.29 | GROUND_INST: instantiating (11) with pv10, all_61_1, simplifying with (2), (9) % 18.88/3.29 | gives: % 18.88/3.29 | (20) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sum(n0, n4, all_61_1) = % 18.88/3.29 | v2 & leq(pv10, all_61_0) = v1 & leq(n0, pv10) = v0 & $i(v2) & ( ~ % 18.88/3.29 | (v1 = 0) | ~ (v0 = 0) | v2 = n1)) % 18.88/3.29 | % 18.88/3.29 | GROUND_INST: instantiating (11) with all_79_2, all_79_1, simplifying with % 18.88/3.29 | (15), (18) gives: % 18.88/3.29 | (21) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sum(n0, n4, all_79_1) = % 18.88/3.29 | v2 & leq(all_79_2, all_61_0) = v1 & leq(n0, all_79_2) = v0 & $i(v2) % 18.88/3.29 | & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = n1)) % 18.88/3.29 | % 18.88/3.29 | DELTA: instantiating (21) with fresh symbols all_103_0, all_103_1, all_103_2 % 18.88/3.29 | gives: % 18.88/3.29 | (22) sum(n0, n4, all_79_1) = all_103_0 & leq(all_79_2, all_61_0) = % 18.88/3.29 | all_103_1 & leq(n0, all_79_2) = all_103_2 & $i(all_103_0) & ( ~ % 18.88/3.29 | (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 = n1) % 18.88/3.29 | % 18.88/3.29 | ALPHA: (22) implies: % 18.88/3.29 | (23) leq(n0, all_79_2) = all_103_2 % 18.88/3.29 | (24) leq(all_79_2, all_61_0) = all_103_1 % 18.88/3.29 | (25) sum(n0, n4, all_79_1) = all_103_0 % 18.88/3.29 | (26) ~ (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 = n1 % 18.88/3.29 | % 18.88/3.29 | DELTA: instantiating (20) with fresh symbols all_105_0, all_105_1, all_105_2 % 18.88/3.29 | gives: % 18.88/3.29 | (27) sum(n0, n4, all_61_1) = all_105_0 & leq(pv10, all_61_0) = all_105_1 & % 18.88/3.29 | leq(n0, pv10) = all_105_2 & $i(all_105_0) & ( ~ (all_105_1 = 0) | ~ % 18.88/3.29 | (all_105_2 = 0) | all_105_0 = n1) % 18.88/3.29 | % 18.88/3.29 | ALPHA: (27) implies: % 18.88/3.29 | (28) sum(n0, n4, all_61_1) = all_105_0 % 18.88/3.29 | % 18.88/3.29 | GROUND_INST: instantiating (4) with 0, all_103_2, all_79_2, n0, simplifying % 18.88/3.29 | with (16), (23) gives: % 18.88/3.29 | (29) all_103_2 = 0 % 18.88/3.29 | % 18.88/3.29 | GROUND_INST: instantiating (6) with n1, all_105_0, all_61_1, n4, n0, % 18.88/3.29 | simplifying with (10), (28) gives: % 18.88/3.29 | (30) all_105_0 = n1 % 18.88/3.29 | % 18.88/3.29 | GROUND_INST: instantiating (6) with all_79_0, all_103_0, all_79_1, n4, n0, % 18.88/3.29 | simplifying with (19), (25) gives: % 18.88/3.29 | (31) all_103_0 = all_79_0 % 18.88/3.29 | % 18.88/3.29 | BETA: splitting (26) gives: % 18.88/3.29 | % 18.88/3.29 | Case 1: % 18.88/3.29 | | % 18.88/3.30 | | (32) ~ (all_103_1 = 0) % 18.88/3.30 | | % 18.88/3.30 | | GROUND_INST: instantiating (1) with all_79_2, pv10, all_61_0, all_103_1, % 18.88/3.30 | | simplifying with (2), (8), (15), (24) gives: % 18.88/3.30 | | (33) all_103_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & gt(pv10, all_79_2) = % 18.88/3.30 | | v0) % 18.88/3.30 | | % 18.88/3.30 | | BETA: splitting (33) gives: % 18.88/3.30 | | % 18.88/3.30 | | Case 1: % 18.88/3.30 | | | % 18.88/3.30 | | | (34) all_103_1 = 0 % 18.88/3.30 | | | % 18.88/3.30 | | | REDUCE: (32), (34) imply: % 18.88/3.30 | | | (35) $false % 18.88/3.30 | | | % 18.88/3.30 | | | CLOSE: (35) is inconsistent. % 18.88/3.30 | | | % 18.88/3.30 | | Case 2: % 18.88/3.30 | | | % 18.88/3.30 | | | (36) ? [v0: int] : ( ~ (v0 = 0) & gt(pv10, all_79_2) = v0) % 18.88/3.30 | | | % 18.88/3.30 | | | DELTA: instantiating (36) with fresh symbol all_125_0 gives: % 18.88/3.30 | | | (37) ~ (all_125_0 = 0) & gt(pv10, all_79_2) = all_125_0 % 18.88/3.30 | | | % 18.88/3.30 | | | ALPHA: (37) implies: % 18.88/3.30 | | | (38) ~ (all_125_0 = 0) % 18.88/3.30 | | | (39) gt(pv10, all_79_2) = all_125_0 % 18.88/3.30 | | | % 18.88/3.30 | | | GROUND_INST: instantiating (leq_gt2) with all_79_2, pv10, all_125_0, % 18.88/3.30 | | | simplifying with (2), (15), (39) gives: % 18.88/3.30 | | | (40) all_125_0 = 0 | all_79_2 = pv10 | ? [v0: int] : ( ~ (v0 = 0) & % 18.88/3.30 | | | leq(all_79_2, pv10) = v0) % 18.88/3.30 | | | % 18.88/3.30 | | | BETA: splitting (40) gives: % 18.88/3.30 | | | % 18.88/3.30 | | | Case 1: % 18.88/3.30 | | | | % 18.88/3.30 | | | | (41) all_125_0 = 0 % 18.88/3.30 | | | | % 18.88/3.30 | | | | REDUCE: (38), (41) imply: % 18.88/3.30 | | | | (42) $false % 18.88/3.30 | | | | % 18.88/3.30 | | | | CLOSE: (42) is inconsistent. % 18.88/3.30 | | | | % 18.88/3.30 | | | Case 2: % 18.88/3.30 | | | | % 18.88/3.30 | | | | (43) all_79_2 = pv10 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_2, % 18.88/3.30 | | | | pv10) = v0) % 18.88/3.30 | | | | % 18.88/3.30 | | | | BETA: splitting (43) gives: % 18.88/3.30 | | | | % 18.88/3.30 | | | | Case 1: % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | (44) all_79_2 = pv10 % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | REDUCE: (18), (44) imply: % 18.88/3.30 | | | | | (45) a_select3(q, pv10, tptp_sum_index) = all_79_1 % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | GROUND_INST: instantiating (5) with all_61_1, all_79_1, % 18.88/3.30 | | | | | tptp_sum_index, pv10, q, simplifying with (9), (45) % 18.88/3.30 | | | | | gives: % 18.88/3.30 | | | | | (46) all_79_1 = all_61_1 % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | REDUCE: (19), (46) imply: % 18.88/3.30 | | | | | (47) sum(n0, n4, all_61_1) = all_79_0 % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | GROUND_INST: instantiating (6) with n1, all_79_0, all_61_1, n4, n0, % 18.88/3.30 | | | | | simplifying with (10), (47) gives: % 18.88/3.30 | | | | | (48) all_79_0 = n1 % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | REDUCE: (14), (48) imply: % 18.88/3.30 | | | | | (49) $false % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | CLOSE: (49) is inconsistent. % 18.88/3.30 | | | | | % 18.88/3.30 | | | | Case 2: % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | (50) ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_2, pv10) = v0) % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | DELTA: instantiating (50) with fresh symbol all_151_0 gives: % 18.88/3.30 | | | | | (51) ~ (all_151_0 = 0) & leq(all_79_2, pv10) = all_151_0 % 18.88/3.30 | | | | | % 18.88/3.30 | | | | | ALPHA: (51) implies: % 18.88/3.30 | | | | | (52) ~ (all_151_0 = 0) % 18.88/3.30 | | | | | (53) leq(all_79_2, pv10) = all_151_0 % 18.88/3.31 | | | | | % 18.88/3.31 | | | | | GROUND_INST: instantiating (4) with 0, all_151_0, pv10, all_79_2, % 18.88/3.31 | | | | | simplifying with (17), (53) gives: % 18.88/3.31 | | | | | (54) all_151_0 = 0 % 18.88/3.31 | | | | | % 18.88/3.31 | | | | | REDUCE: (52), (54) imply: % 18.88/3.31 | | | | | (55) $false % 18.88/3.31 | | | | | % 18.88/3.31 | | | | | CLOSE: (55) is inconsistent. % 18.88/3.31 | | | | | % 18.88/3.31 | | | | End of split % 18.88/3.31 | | | | % 18.88/3.31 | | | End of split % 18.88/3.31 | | | % 18.88/3.31 | | End of split % 18.88/3.31 | | % 18.88/3.31 | Case 2: % 18.88/3.31 | | % 18.88/3.31 | | (56) ~ (all_103_2 = 0) | all_103_0 = n1 % 18.88/3.31 | | % 18.88/3.31 | | BETA: splitting (56) gives: % 18.88/3.31 | | % 18.88/3.31 | | Case 1: % 18.88/3.31 | | | % 18.88/3.31 | | | (57) ~ (all_103_2 = 0) % 18.88/3.31 | | | % 18.88/3.31 | | | REDUCE: (29), (57) imply: % 18.88/3.31 | | | (58) $false % 18.88/3.31 | | | % 18.88/3.31 | | | CLOSE: (58) is inconsistent. % 18.88/3.31 | | | % 18.88/3.31 | | Case 2: % 18.88/3.31 | | | % 18.88/3.31 | | | (59) all_103_0 = n1 % 18.88/3.31 | | | % 18.88/3.31 | | | COMBINE_EQS: (31), (59) imply: % 18.88/3.31 | | | (60) all_79_0 = n1 % 18.88/3.31 | | | % 18.88/3.31 | | | SIMP: (60) implies: % 18.88/3.31 | | | (61) all_79_0 = n1 % 18.88/3.31 | | | % 18.88/3.31 | | | REDUCE: (14), (61) imply: % 18.88/3.31 | | | (62) $false % 18.88/3.31 | | | % 18.88/3.31 | | | CLOSE: (62) is inconsistent. % 18.88/3.31 | | | % 18.88/3.31 | | End of split % 18.88/3.31 | | % 18.88/3.31 | End of split % 18.88/3.31 | % 18.88/3.31 End of proof % 18.88/3.31 % SZS output end Proof for theBenchmark % 18.88/3.31 % 18.88/3.31 2710ms %------------------------------------------------------------------------------