%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV067+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 : n016.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 22:54:46 EDT 2023 % Result : Theorem 16.22s 2.91s % Output : Proof 19.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV067+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n016.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 04:41:15 EDT 2023 % 0.12/0.35 % CPUTime : % 0.69/0.67 ________ _____ % 0.69/0.67 ___ __ \_________(_)________________________________ % 0.69/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.69/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.69/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.69/0.67 % 0.69/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.69/0.67 (2023-06-19) % 0.69/0.67 % 0.69/0.67 (c) Philipp Rümmer, 2009-2023 % 0.69/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.69/0.67 Amanda Stjerna. % 0.69/0.67 Free software under BSD-3-Clause. % 0.69/0.67 % 0.69/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.69/0.67 % 0.69/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.68 Running up to 7 provers in parallel. % 0.69/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.69/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.69/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.69/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.69/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.69/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.69/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.75/1.41 Prover 4: Preprocessing ... % 4.75/1.41 Prover 1: Preprocessing ... % 4.75/1.45 Prover 6: Preprocessing ... % 4.75/1.45 Prover 5: Preprocessing ... % 4.75/1.45 Prover 0: Preprocessing ... % 4.75/1.45 Prover 2: Preprocessing ... % 4.75/1.45 Prover 3: Preprocessing ... % 10.41/2.17 Prover 1: Warning: ignoring some quantifiers % 11.06/2.27 Prover 1: Constructing countermodel ... % 11.06/2.28 Prover 3: Warning: ignoring some quantifiers % 11.65/2.31 Prover 3: Constructing countermodel ... % 11.65/2.32 Prover 4: Warning: ignoring some quantifiers % 11.65/2.34 Prover 6: Proving ... % 12.60/2.43 Prover 4: Constructing countermodel ... % 12.60/2.49 Prover 0: Proving ... % 13.30/2.51 Prover 2: Proving ... % 13.30/2.51 Prover 5: Proving ... % 16.22/2.91 Prover 3: proved (2220ms) % 16.22/2.91 % 16.22/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.22/2.91 % 16.22/2.91 Prover 0: stopped % 16.22/2.91 Prover 6: stopped % 16.22/2.91 Prover 2: stopped % 16.22/2.91 Prover 5: stopped % 16.22/2.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.22/2.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.22/2.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.22/2.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.22/2.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.78/2.98 Prover 1: Found proof (size 33) % 16.78/2.98 Prover 1: proved (2294ms) % 16.78/2.98 Prover 4: stopped % 17.24/3.07 Prover 7: Preprocessing ... % 17.24/3.10 Prover 10: Preprocessing ... % 17.97/3.13 Prover 13: Preprocessing ... % 17.97/3.13 Prover 8: Preprocessing ... % 17.97/3.14 Prover 11: Preprocessing ... % 17.97/3.17 Prover 7: stopped % 17.97/3.18 Prover 10: stopped % 18.47/3.23 Prover 13: stopped % 18.47/3.24 Prover 11: stopped % 19.11/3.32 Prover 8: Warning: ignoring some quantifiers % 19.11/3.34 Prover 8: Constructing countermodel ... % 19.25/3.36 Prover 8: stopped % 19.25/3.36 % 19.25/3.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.25/3.36 % 19.25/3.37 % SZS output start Proof for theBenchmark % 19.25/3.37 Assumptions after simplification: % 19.25/3.37 --------------------------------- % 19.25/3.37 % 19.25/3.37 (cl5_nebula_array_0008) % 19.25/3.40 $i(pv78) & $i(q) & $i(n135300) & $i(pv63) & $i(pv10) & $i(n5) & $i(n1) & % 19.25/3.40 $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: % 19.25/3.40 MultipleValueBool] : ( ~ (v2 = 0) & minus(n135300, n1) = v0 & minus(n5, n1) % 19.25/3.40 = v1 & a_select3(q, pv10, pv63) = v3 & leq(pv63, v1) = 0 & leq(pv10, v0) = 0 % 19.25/3.40 & leq(n1, pv63) = 0 & leq(n0, pv63) = v2 & leq(n0, pv10) = 0 & gt(v3, pv78) % 19.25/3.40 = v4 & $i(v3) & $i(v1) & $i(v0)) % 19.25/3.40 % 19.25/3.40 (leq_gt1) % 19.25/3.40 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 19.25/3.40 leq(v0, v1) = 0) % 19.25/3.40 % 19.25/3.40 (leq_succ_gt) % 19.25/3.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2, % 19.25/3.40 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 19.25/3.40 % 19.25/3.40 (successor_1) % 19.25/3.40 succ(n0) = n1 & $i(n1) & $i(n0) % 19.25/3.40 % 19.25/3.40 (successor_2) % 19.25/3.40 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 19.25/3.40 % 19.25/3.40 (successor_3) % 19.25/3.40 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 19.25/3.40 succ(n0) = v0 & $i(v1) & $i(v0)) % 19.25/3.40 % 19.25/3.40 (successor_4) % 19.25/3.40 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 19.25/3.40 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 19.25/3.40 % 19.25/3.40 (successor_5) % 19.25/3.40 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 19.25/3.40 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 19.25/3.40 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 19.25/3.40 % 19.25/3.40 (function-axioms) % 19.25/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.25/3.41 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 19.25/3.41 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.25/3.41 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 19.25/3.41 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.25/3.41 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 19.25/3.41 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.25/3.41 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 19.25/3.41 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.25/3.41 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 19.25/3.41 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.25/3.41 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 19.25/3.41 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.25/3.41 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 19.25/3.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 19.25/3.41 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.25/3.41 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 19.25/3.41 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 19.25/3.41 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 19.25/3.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 19.25/3.41 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.25/3.41 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 19.25/3.41 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 19.25/3.41 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 19.25/3.41 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.25/3.41 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 19.25/3.41 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.25/3.41 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 19.25/3.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.25/3.41 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 19.25/3.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.25/3.41 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 19.25/3.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.25/3.41 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 19.25/3.41 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 19.25/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 19.25/3.41 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 19.25/3.41 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 19.25/3.41 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 19.25/3.41 % 19.25/3.41 Further assumptions not needed in the proof: % 19.25/3.41 -------------------------------------------- % 19.25/3.41 const_array1_select, const_array2_select, defuse, finite_domain_0, % 19.25/3.41 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 19.25/3.41 finite_domain_5, gt_0_tptp_minus_1, gt_135300_0, gt_135300_1, gt_135300_2, % 19.25/3.41 gt_135300_3, gt_135300_4, gt_135300_5, gt_135300_tptp_minus_1, gt_1_0, % 19.25/3.41 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, % 19.25/3.41 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, % 19.25/3.41 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 19.25/3.41 leq_geq, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt_equiv, % 19.25/3.41 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 19.25/3.41 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 19.25/3.41 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 19.25/3.41 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 19.25/3.41 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 19.25/3.41 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 19.25/3.41 succ_plus_5_r, succ_pred, succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, % 19.25/3.41 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 19.25/3.41 uniform_int_rand_ranges_lo % 19.25/3.41 % 19.25/3.41 Those formulas are unsatisfiable: % 19.25/3.41 --------------------------------- % 19.25/3.41 % 19.25/3.41 Begin of proof % 19.25/3.41 | % 19.25/3.42 | ALPHA: (successor_4) implies: % 19.25/3.42 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 19.25/3.42 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 19.25/3.42 | % 19.25/3.42 | ALPHA: (successor_5) implies: % 19.25/3.42 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 19.25/3.42 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 19.25/3.42 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 19.25/3.42 | % 19.25/3.42 | ALPHA: (successor_1) implies: % 19.25/3.42 | (3) succ(n0) = n1 % 19.25/3.42 | % 19.25/3.42 | ALPHA: (successor_2) implies: % 19.25/3.42 | (4) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 19.25/3.42 | % 19.25/3.42 | ALPHA: (successor_3) implies: % 19.25/3.42 | (5) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) = % 19.25/3.42 | v0 & $i(v1) & $i(v0)) % 19.25/3.42 | % 19.25/3.42 | ALPHA: (cl5_nebula_array_0008) implies: % 19.25/3.42 | (6) $i(n0) % 19.25/3.42 | (7) $i(pv63) % 19.25/3.42 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: % 19.25/3.42 | MultipleValueBool] : ( ~ (v2 = 0) & minus(n135300, n1) = v0 & % 19.25/3.42 | minus(n5, n1) = v1 & a_select3(q, pv10, pv63) = v3 & leq(pv63, v1) = % 19.25/3.42 | 0 & leq(pv10, v0) = 0 & leq(n1, pv63) = 0 & leq(n0, pv63) = v2 & % 19.25/3.42 | leq(n0, pv10) = 0 & gt(v3, pv78) = v4 & $i(v3) & $i(v1) & $i(v0)) % 19.25/3.42 | % 19.25/3.42 | ALPHA: (function-axioms) implies: % 19.25/3.42 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) % 19.25/3.42 | | ~ (succ(v2) = v0)) % 19.25/3.42 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 19.25/3.42 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 19.25/3.42 | v0)) % 19.25/3.42 | % 19.25/3.42 | DELTA: instantiating (4) with fresh symbol all_49_0 gives: % 19.25/3.42 | (11) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0) % 19.25/3.42 | % 19.25/3.42 | ALPHA: (11) implies: % 19.25/3.42 | (12) succ(n0) = all_49_0 % 19.25/3.42 | % 19.25/3.42 | DELTA: instantiating (5) with fresh symbols all_51_0, all_51_1 gives: % 19.25/3.42 | (13) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1 % 19.25/3.42 | & $i(all_51_0) & $i(all_51_1) % 19.25/3.42 | % 19.25/3.42 | ALPHA: (13) implies: % 19.25/3.42 | (14) succ(n0) = all_51_1 % 19.25/3.42 | % 19.25/3.42 | DELTA: instantiating (1) with fresh symbols all_53_0, all_53_1, all_53_2 % 19.25/3.42 | gives: % 19.25/3.42 | (15) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) = % 19.25/3.42 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) & % 19.25/3.42 | $i(all_53_2) % 19.25/3.42 | % 19.25/3.42 | ALPHA: (15) implies: % 19.25/3.42 | (16) succ(n0) = all_53_2 % 19.64/3.42 | % 19.64/3.42 | DELTA: instantiating (2) with fresh symbols all_55_0, all_55_1, all_55_2, % 19.64/3.42 | all_55_3 gives: % 19.64/3.42 | (17) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) = % 19.64/3.42 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 & % 19.64/3.42 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) % 19.64/3.42 | % 19.64/3.42 | ALPHA: (17) implies: % 19.64/3.42 | (18) succ(n0) = all_55_3 % 19.64/3.42 | % 19.64/3.42 | DELTA: instantiating (8) with fresh symbols all_59_0, all_59_1, all_59_2, % 19.64/3.43 | all_59_3, all_59_4 gives: % 19.64/3.43 | (19) ~ (all_59_2 = 0) & minus(n135300, n1) = all_59_4 & minus(n5, n1) = % 19.64/3.43 | all_59_3 & a_select3(q, pv10, pv63) = all_59_1 & leq(pv63, all_59_3) = % 19.64/3.43 | 0 & leq(pv10, all_59_4) = 0 & leq(n1, pv63) = 0 & leq(n0, pv63) = % 19.64/3.43 | all_59_2 & leq(n0, pv10) = 0 & gt(all_59_1, pv78) = all_59_0 & % 19.64/3.43 | $i(all_59_1) & $i(all_59_3) & $i(all_59_4) % 19.64/3.43 | % 19.64/3.43 | ALPHA: (19) implies: % 19.64/3.43 | (20) ~ (all_59_2 = 0) % 19.64/3.43 | (21) leq(n0, pv63) = all_59_2 % 19.64/3.43 | (22) leq(n1, pv63) = 0 % 19.64/3.43 | % 19.64/3.43 | GROUND_INST: instantiating (9) with all_51_1, all_53_2, n0, simplifying with % 19.64/3.43 | (14), (16) gives: % 19.64/3.43 | (23) all_53_2 = all_51_1 % 19.64/3.43 | % 19.64/3.43 | GROUND_INST: instantiating (9) with all_49_0, all_53_2, n0, simplifying with % 19.64/3.43 | (12), (16) gives: % 19.64/3.43 | (24) all_53_2 = all_49_0 % 19.64/3.43 | % 19.64/3.43 | GROUND_INST: instantiating (9) with all_51_1, all_55_3, n0, simplifying with % 19.64/3.43 | (14), (18) gives: % 19.64/3.43 | (25) all_55_3 = all_51_1 % 19.64/3.43 | % 19.64/3.43 | GROUND_INST: instantiating (9) with n1, all_55_3, n0, simplifying with (3), % 19.64/3.43 | (18) gives: % 19.64/3.43 | (26) all_55_3 = n1 % 19.64/3.43 | % 19.64/3.43 | COMBINE_EQS: (25), (26) imply: % 19.64/3.43 | (27) all_51_1 = n1 % 19.64/3.43 | % 19.64/3.43 | SIMP: (27) implies: % 19.64/3.43 | (28) all_51_1 = n1 % 19.64/3.43 | % 19.64/3.43 | COMBINE_EQS: (23), (24) imply: % 19.64/3.43 | (29) all_51_1 = all_49_0 % 19.64/3.43 | % 19.64/3.43 | SIMP: (29) implies: % 19.64/3.43 | (30) all_51_1 = all_49_0 % 19.64/3.43 | % 19.64/3.43 | COMBINE_EQS: (28), (30) imply: % 19.64/3.43 | (31) all_49_0 = n1 % 19.64/3.43 | % 19.64/3.43 | GROUND_INST: instantiating (leq_succ_gt) with n0, pv63, n1, simplifying with % 19.64/3.43 | (3), (6), (7), (22) gives: % 19.64/3.43 | (32) gt(pv63, n0) = 0 % 19.64/3.43 | % 19.64/3.43 | GROUND_INST: instantiating (leq_gt1) with n0, pv63, simplifying with (6), (7), % 19.64/3.43 | (32) gives: % 19.64/3.43 | (33) leq(n0, pv63) = 0 % 19.64/3.43 | % 19.64/3.43 | GROUND_INST: instantiating (10) with all_59_2, 0, pv63, n0, simplifying with % 19.64/3.43 | (21), (33) gives: % 19.64/3.43 | (34) all_59_2 = 0 % 19.64/3.43 | % 19.64/3.43 | REDUCE: (20), (34) imply: % 19.64/3.43 | (35) $false % 19.64/3.43 | % 19.64/3.43 | CLOSE: (35) is inconsistent. % 19.64/3.43 | % 19.64/3.43 End of proof % 19.64/3.43 % SZS output end Proof for theBenchmark % 19.64/3.43 % 19.64/3.43 2764ms %------------------------------------------------------------------------------