%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV042+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 : n004.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 22:54:41 EDT 2023 % Result : Theorem 17.51s 3.06s % Output : Proof 30.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWV042+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n004.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 07:18:37 EDT 2023 % 0.14/0.35 % 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. % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 4.72/1.40 Prover 4: Preprocessing ... % 5.24/1.41 Prover 1: Preprocessing ... % 5.24/1.44 Prover 5: Preprocessing ... % 5.24/1.44 Prover 3: Preprocessing ... % 5.24/1.44 Prover 0: Preprocessing ... % 5.24/1.44 Prover 6: Preprocessing ... % 5.24/1.44 Prover 2: Preprocessing ... % 10.52/2.13 Prover 1: Warning: ignoring some quantifiers % 11.14/2.23 Prover 1: Constructing countermodel ... % 11.14/2.25 Prover 3: Warning: ignoring some quantifiers % 11.14/2.28 Prover 3: Constructing countermodel ... % 11.82/2.28 Prover 4: Warning: ignoring some quantifiers % 11.94/2.30 Prover 6: Proving ... % 12.04/2.40 Prover 4: Constructing countermodel ... % 12.04/2.46 Prover 0: Proving ... % 13.09/2.54 Prover 2: Proving ... % 13.09/2.55 Prover 5: Proving ... % 17.51/3.06 Prover 3: proved (2404ms) % 17.51/3.06 % 17.51/3.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.51/3.06 % 17.51/3.06 Prover 0: stopped % 17.51/3.07 Prover 2: stopped % 17.51/3.07 Prover 5: stopped % 17.51/3.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.51/3.08 Prover 6: stopped % 17.51/3.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.51/3.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.51/3.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.51/3.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.94/3.25 Prover 7: Preprocessing ... % 18.94/3.27 Prover 8: Preprocessing ... % 18.94/3.31 Prover 13: Preprocessing ... % 19.49/3.31 Prover 10: Preprocessing ... % 19.49/3.32 Prover 11: Preprocessing ... % 20.82/3.52 Prover 10: Warning: ignoring some quantifiers % 21.29/3.58 Prover 10: Constructing countermodel ... % 21.29/3.58 Prover 8: Warning: ignoring some quantifiers % 21.29/3.58 Prover 7: Warning: ignoring some quantifiers % 21.29/3.60 Prover 7: Constructing countermodel ... % 21.29/3.61 Prover 8: Constructing countermodel ... % 21.84/3.65 Prover 13: Warning: ignoring some quantifiers % 21.84/3.67 Prover 13: Constructing countermodel ... % 21.84/3.74 Prover 11: Warning: ignoring some quantifiers % 22.86/3.78 Prover 11: Constructing countermodel ... % 29.18/4.62 Prover 10: Found proof (size 196) % 29.18/4.62 Prover 10: proved (1547ms) % 29.18/4.62 Prover 11: stopped % 29.18/4.62 Prover 7: stopped % 29.18/4.62 Prover 8: stopped % 29.18/4.62 Prover 4: stopped % 29.18/4.62 Prover 13: stopped % 29.18/4.63 Prover 1: stopped % 29.18/4.63 % 29.18/4.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.18/4.63 % 29.67/4.64 % SZS output start Proof for theBenchmark % 29.67/4.65 Assumptions after simplification: % 29.67/4.65 --------------------------------- % 29.67/4.65 % 29.67/4.65 (finite_domain_1) % 29.67/4.66 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, % 29.67/4.66 n1) | ~ leq(n0, v0)) % 29.67/4.66 % 29.67/4.66 (finite_domain_2) % 29.67/4.66 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 29.67/4.66 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0)) % 29.67/4.66 % 29.67/4.66 (gauss_init_0081) % 29.83/4.69 $i(pvar1402_init) & $i(pvar1401_init) & $i(pvar1400_init) & $i(loopcounter) & % 29.83/4.69 $i(s_center7_init) & $i(s_values7_init) & $i(init) & $i(simplex7_init) & % 29.83/4.69 $i(n3) & $i(n2) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 29.83/4.69 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 29.83/4.69 $i] : (minus(v0, n1) = v1 & plus(n1, n2) = v0 & $i(v7) & $i(v6) & $i(v4) & % 29.83/4.69 $i(v2) & $i(v1) & $i(v0) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : (v11 % 29.83/4.69 = init | ~ (a_select3(simplex7_init, v10, v9) = v11) | ~ $i(v10) | ~ % 29.83/4.69 $i(v9) | ~ leq(v10, n3) | ~ leq(v9, n2) | ~ leq(n0, v10) | ~ leq(n0, % 29.83/4.69 v9)) & ! [v9: $i] : ! [v10: $i] : (v10 = init | ~ % 29.83/4.69 (a_select2(s_center7_init, v9) = v10) | ~ $i(v9) | ~ leq(v9, v1) | ~ % 29.83/4.69 leq(n0, v9)) & ! [v9: $i] : ! [v10: $i] : (v10 = init | ~ % 29.83/4.69 (a_select2(s_values7_init, v9) = v10) | ~ $i(v9) | ~ leq(v9, n3) | ~ % 29.83/4.69 leq(n0, v9)) & ( ~ gt(loopcounter, n1) | (pvar1402_init = init & % 29.83/4.69 pvar1401_init = init & pvar1400_init = init)) & (( ~ (v8 = init) & % 29.83/4.69 a_select3(simplex7_init, v7, v6) = v8 & $i(v8) & leq(v7, n3) & leq(v6, % 29.83/4.69 n2) & leq(n0, v7) & leq(n0, v6)) | ( ~ (v5 = init) & % 29.83/4.69 a_select2(s_values7_init, v4) = v5 & $i(v5) & leq(v4, n3) & leq(n0, v4)) % 29.83/4.69 | ( ~ (v3 = init) & a_select2(s_center7_init, v2) = v3 & $i(v3) & leq(v2, % 29.83/4.69 n2) & leq(n0, v2)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) % 29.83/4.69 | ~ (pvar1401_init = init) | ~ (pvar1400_init = init))))) % 29.83/4.69 % 29.83/4.69 (leq_gt2) % 29.83/4.69 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 29.83/4.69 | gt(v1, v0)) % 29.83/4.69 % 29.83/4.69 (leq_gt_pred) % 29.83/4.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ % 29.83/4.69 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.83/4.69 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 29.83/4.69 v2)) % 29.83/4.69 % 29.83/4.69 (pred_minus_1) % 29.83/4.69 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 29.83/4.69 (pred(v0) = v1 & $i(v1))) % 29.83/4.69 % 29.83/4.69 (pred_succ) % 29.83/4.69 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 29.83/4.69 % 29.83/4.69 (succ_plus_1_l) % 29.83/4.69 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (plus(n1, v0) = v1) | ~ $i(v0) | % 29.83/4.69 (succ(v0) = v1 & $i(v1))) % 29.83/4.69 % 29.83/4.69 (successor_1) % 29.83/4.69 succ(n0) = n1 & $i(n1) & $i(n0) % 29.83/4.69 % 29.83/4.69 (successor_2) % 29.83/4.69 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 29.83/4.69 % 29.83/4.69 (successor_3) % 29.83/4.70 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 29.83/4.70 succ(n0) = v0 & $i(v1) & $i(v0)) % 29.83/4.70 % 29.83/4.70 (successor_4) % 29.83/4.70 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 29.83/4.70 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 29.83/4.70 % 29.83/4.70 (successor_5) % 29.83/4.70 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 29.83/4.70 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 29.83/4.70 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 29.83/4.70 % 29.83/4.70 (function-axioms) % 29.83/4.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 29.83/4.70 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 29.83/4.70 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 29.83/4.70 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 29.83/4.70 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 29.83/4.70 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 29.83/4.70 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 29.83/4.70 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 29.83/4.70 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 29.83/4.70 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 29.83/4.70 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 29.83/4.70 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 29.83/4.70 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 29.83/4.70 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 29.83/4.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 29.83/4.70 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 29.83/4.70 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 29.83/4.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 29.83/4.70 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 29.83/4.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 29.83/4.70 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 29.83/4.70 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 29.83/4.70 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 29.83/4.70 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 29.83/4.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 29.83/4.70 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 29.83/4.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ % 29.83/4.70 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 29.83/4.70 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 29.83/4.70 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : % 29.83/4.70 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = % 29.83/4.70 v0)) % 29.83/4.70 % 29.83/4.70 Further assumptions not needed in the proof: % 29.83/4.70 -------------------------------------------- % 29.83/4.70 const_array1_select, const_array2_select, defuse, finite_domain_0, % 29.83/4.70 finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0, % 29.83/4.70 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, % 29.83/4.70 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, % 29.83/4.70 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, % 29.83/4.70 leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 29.83/4.70 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 29.83/4.70 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 29.83/4.70 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 29.83/4.70 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_r, % 29.83/4.70 succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, % 29.83/4.70 succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, % 29.83/4.70 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 29.83/4.70 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 29.83/4.70 % 29.83/4.70 Those formulas are unsatisfiable: % 29.83/4.70 --------------------------------- % 29.83/4.70 % 29.83/4.70 Begin of proof % 29.83/4.71 | % 29.83/4.71 | ALPHA: (leq_gt_pred) implies: % 29.83/4.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 29.83/4.71 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (succ_plus_1_l) implies: % 29.83/4.71 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (plus(n1, v0) = v1) | ~ $i(v0) | % 29.83/4.71 | (succ(v0) = v1 & $i(v1))) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (pred_minus_1) implies: % 29.83/4.71 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 29.83/4.71 | (pred(v0) = v1 & $i(v1))) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (finite_domain_1) implies: % 29.83/4.71 | (4) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 29.83/4.71 | leq(n0, v0)) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (finite_domain_2) implies: % 29.83/4.71 | (5) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) % 29.83/4.71 | | ~ leq(n0, v0)) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (successor_4) implies: % 29.83/4.71 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 29.83/4.71 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (successor_5) implies: % 29.83/4.71 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 29.83/4.71 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 29.83/4.71 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (successor_1) implies: % 29.83/4.71 | (8) succ(n0) = n1 % 29.83/4.71 | % 29.83/4.71 | ALPHA: (successor_2) implies: % 29.83/4.71 | (9) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (successor_3) implies: % 29.83/4.71 | (10) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) % 29.83/4.71 | = v0 & $i(v1) & $i(v0)) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (gauss_init_0081) implies: % 29.83/4.71 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 29.83/4.71 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (minus(v0, n1) % 29.83/4.71 | = v1 & plus(n1, n2) = v0 & $i(v7) & $i(v6) & $i(v4) & $i(v2) & % 29.83/4.71 | $i(v1) & $i(v0) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : (v11 = % 29.83/4.71 | init | ~ (a_select3(simplex7_init, v10, v9) = v11) | ~ $i(v10) | % 29.83/4.71 | ~ $i(v9) | ~ leq(v10, n3) | ~ leq(v9, n2) | ~ leq(n0, v10) | % 29.83/4.71 | ~ leq(n0, v9)) & ! [v9: $i] : ! [v10: $i] : (v10 = init | ~ % 29.83/4.71 | (a_select2(s_center7_init, v9) = v10) | ~ $i(v9) | ~ leq(v9, v1) % 29.83/4.71 | | ~ leq(n0, v9)) & ! [v9: $i] : ! [v10: $i] : (v10 = init | ~ % 29.83/4.71 | (a_select2(s_values7_init, v9) = v10) | ~ $i(v9) | ~ leq(v9, n3) % 29.83/4.71 | | ~ leq(n0, v9)) & ( ~ gt(loopcounter, n1) | (pvar1402_init = % 29.83/4.71 | init & pvar1401_init = init & pvar1400_init = init)) & (( ~ (v8 % 29.83/4.71 | = init) & a_select3(simplex7_init, v7, v6) = v8 & $i(v8) & % 29.83/4.71 | leq(v7, n3) & leq(v6, n2) & leq(n0, v7) & leq(n0, v6)) | ( ~ (v5 % 29.83/4.71 | = init) & a_select2(s_values7_init, v4) = v5 & $i(v5) & % 29.83/4.71 | leq(v4, n3) & leq(n0, v4)) | ( ~ (v3 = init) & % 29.83/4.71 | a_select2(s_center7_init, v2) = v3 & $i(v3) & leq(v2, n2) & % 29.83/4.71 | leq(n0, v2)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) % 29.83/4.71 | | ~ (pvar1401_init = init) | ~ (pvar1400_init = init))))) % 29.83/4.71 | % 29.83/4.71 | ALPHA: (function-axioms) implies: % 29.83/4.72 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = % 29.83/4.72 | v1) | ~ (pred(v2) = v0)) % 29.83/4.72 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 29.83/4.72 | v1) | ~ (succ(v2) = v0)) % 29.83/4.72 | % 29.83/4.72 | DELTA: instantiating (9) with fresh symbol all_54_0 gives: % 29.83/4.72 | (14) succ(all_54_0) = n2 & succ(n0) = all_54_0 & $i(all_54_0) % 29.83/4.72 | % 29.83/4.72 | ALPHA: (14) implies: % 29.83/4.72 | (15) $i(all_54_0) % 29.83/4.72 | (16) succ(n0) = all_54_0 % 29.83/4.72 | (17) succ(all_54_0) = n2 % 29.83/4.72 | % 29.83/4.72 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1 gives: % 29.83/4.72 | (18) succ(all_56_0) = n3 & succ(all_56_1) = all_56_0 & succ(n0) = all_56_1 % 29.83/4.72 | & $i(all_56_0) & $i(all_56_1) % 29.83/4.72 | % 29.83/4.72 | ALPHA: (18) implies: % 29.83/4.72 | (19) $i(all_56_0) % 29.83/4.72 | (20) succ(n0) = all_56_1 % 29.83/4.72 | (21) succ(all_56_1) = all_56_0 % 29.83/4.72 | (22) succ(all_56_0) = n3 % 29.83/4.72 | % 29.83/4.72 | DELTA: instantiating (6) with fresh symbols all_59_0, all_59_1, all_59_2 % 29.83/4.72 | gives: % 29.83/4.72 | (23) succ(all_59_0) = n4 & succ(all_59_1) = all_59_0 & succ(all_59_2) = % 29.83/4.72 | all_59_1 & succ(n0) = all_59_2 & $i(all_59_0) & $i(all_59_1) & % 29.83/4.72 | $i(all_59_2) % 29.83/4.72 | % 29.83/4.72 | ALPHA: (23) implies: % 29.83/4.72 | (24) succ(n0) = all_59_2 % 29.83/4.72 | (25) succ(all_59_2) = all_59_1 % 29.83/4.72 | (26) succ(all_59_1) = all_59_0 % 29.83/4.72 | % 29.83/4.72 | DELTA: instantiating (7) with fresh symbols all_61_0, all_61_1, all_61_2, % 29.83/4.72 | all_61_3 gives: % 29.83/4.72 | (27) succ(all_61_0) = n5 & succ(all_61_1) = all_61_0 & succ(all_61_2) = % 29.83/4.72 | all_61_1 & succ(all_61_3) = all_61_2 & succ(n0) = all_61_3 & % 29.83/4.72 | $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3) % 29.83/4.72 | % 29.83/4.72 | ALPHA: (27) implies: % 29.83/4.72 | (28) succ(n0) = all_61_3 % 29.83/4.72 | (29) succ(all_61_3) = all_61_2 % 29.83/4.72 | (30) succ(all_61_2) = all_61_1 % 29.83/4.72 | % 29.83/4.72 | DELTA: instantiating (11) with fresh symbols all_69_0, all_69_1, all_69_2, % 29.83/4.72 | all_69_3, all_69_4, all_69_5, all_69_6, all_69_7, all_69_8 gives: % 29.83/4.72 | (31) minus(all_69_8, n1) = all_69_7 & plus(n1, n2) = all_69_8 & % 29.83/4.72 | $i(all_69_1) & $i(all_69_2) & $i(all_69_4) & $i(all_69_6) & % 29.83/4.72 | $i(all_69_7) & $i(all_69_8) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 29.83/4.72 | : (v2 = init | ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) % 29.83/4.72 | | ~ $i(v0) | ~ leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ % 29.83/4.72 | leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 29.83/4.72 | (a_select2(s_center7_init, v0) = v1) | ~ $i(v0) | ~ leq(v0, % 29.83/4.72 | all_69_7) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = % 29.83/4.72 | init | ~ (a_select2(s_values7_init, v0) = v1) | ~ $i(v0) | ~ % 29.83/4.72 | leq(v0, n3) | ~ leq(n0, v0)) & ( ~ gt(loopcounter, n1) | % 29.83/4.72 | (pvar1402_init = init & pvar1401_init = init & pvar1400_init = % 29.83/4.72 | init)) & (( ~ (all_69_0 = init) & a_select3(simplex7_init, % 29.83/4.72 | all_69_1, all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1, % 29.83/4.72 | n3) & leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2)) % 29.83/4.72 | | ( ~ (all_69_3 = init) & a_select2(s_values7_init, all_69_4) = % 29.83/4.72 | all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0, all_69_4)) | % 29.83/4.72 | ( ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) = % 29.83/4.72 | all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0, all_69_6)) | % 29.83/4.72 | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~ % 29.83/4.72 | (pvar1401_init = init) | ~ (pvar1400_init = init)))) % 29.83/4.72 | % 29.83/4.72 | ALPHA: (31) implies: % 29.83/4.72 | (32) $i(all_69_6) % 29.83/4.72 | (33) $i(all_69_4) % 29.83/4.72 | (34) $i(all_69_2) % 29.83/4.72 | (35) $i(all_69_1) % 29.83/4.72 | (36) plus(n1, n2) = all_69_8 % 29.83/4.72 | (37) minus(all_69_8, n1) = all_69_7 % 29.83/4.72 | (38) ( ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1, all_69_2) = % 29.83/4.72 | all_69_0 & $i(all_69_0) & leq(all_69_1, n3) & leq(all_69_2, n2) & % 29.83/4.72 | leq(n0, all_69_1) & leq(n0, all_69_2)) | ( ~ (all_69_3 = init) & % 29.83/4.72 | a_select2(s_values7_init, all_69_4) = all_69_3 & $i(all_69_3) & % 29.83/4.72 | leq(all_69_4, n3) & leq(n0, all_69_4)) | ( ~ (all_69_5 = init) & % 29.83/4.72 | a_select2(s_center7_init, all_69_6) = all_69_5 & $i(all_69_5) & % 29.83/4.72 | leq(all_69_6, n2) & leq(n0, all_69_6)) | (gt(loopcounter, n1) & ( ~ % 29.83/4.72 | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 29.83/4.72 | (pvar1400_init = init))) % 29.83/4.73 | (39) ~ gt(loopcounter, n1) | (pvar1402_init = init & pvar1401_init = init % 29.83/4.73 | & pvar1400_init = init) % 29.83/4.73 | (40) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 29.83/4.73 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0)) % 29.83/4.73 | (41) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 29.83/4.73 | v0) = v1) | ~ $i(v0) | ~ leq(v0, all_69_7) | ~ leq(n0, v0)) % 29.83/4.73 | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 29.83/4.73 | (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 29.83/4.73 | leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 29.83/4.73 | % 29.83/4.73 | GROUND_INST: instantiating (13) with all_56_1, all_59_2, n0, simplifying with % 29.83/4.73 | (20), (24) gives: % 29.83/4.73 | (43) all_59_2 = all_56_1 % 29.83/4.73 | % 29.83/4.73 | GROUND_INST: instantiating (13) with all_54_0, all_59_2, n0, simplifying with % 29.83/4.73 | (16), (24) gives: % 29.83/4.73 | (44) all_59_2 = all_54_0 % 29.83/4.73 | % 29.83/4.73 | GROUND_INST: instantiating (13) with all_59_2, all_61_3, n0, simplifying with % 29.83/4.73 | (24), (28) gives: % 29.83/4.73 | (45) all_61_3 = all_59_2 % 29.83/4.73 | % 29.83/4.73 | GROUND_INST: instantiating (13) with n1, all_61_3, n0, simplifying with (8), % 29.83/4.73 | (28) gives: % 29.83/4.73 | (46) all_61_3 = n1 % 29.83/4.73 | % 29.83/4.73 | COMBINE_EQS: (45), (46) imply: % 29.83/4.73 | (47) all_59_2 = n1 % 29.83/4.73 | % 29.83/4.73 | SIMP: (47) implies: % 29.83/4.73 | (48) all_59_2 = n1 % 29.83/4.73 | % 29.83/4.73 | COMBINE_EQS: (43), (48) imply: % 29.83/4.73 | (49) all_56_1 = n1 % 29.83/4.73 | % 29.83/4.73 | COMBINE_EQS: (43), (44) imply: % 29.83/4.73 | (50) all_56_1 = all_54_0 % 29.83/4.73 | % 29.83/4.73 | COMBINE_EQS: (49), (50) imply: % 29.83/4.73 | (51) all_54_0 = n1 % 29.83/4.73 | % 29.83/4.73 | REDUCE: (29), (46) imply: % 30.11/4.73 | (52) succ(n1) = all_61_2 % 30.11/4.73 | % 30.11/4.73 | REDUCE: (25), (48) imply: % 30.11/4.73 | (53) succ(n1) = all_59_1 % 30.11/4.73 | % 30.11/4.73 | REDUCE: (21), (49) imply: % 30.11/4.73 | (54) succ(n1) = all_56_0 % 30.11/4.73 | % 30.11/4.73 | REDUCE: (17), (51) imply: % 30.11/4.73 | (55) succ(n1) = n2 % 30.11/4.73 | % 30.11/4.73 | REDUCE: (15), (51) imply: % 30.11/4.73 | (56) $i(n1) % 30.11/4.73 | % 30.11/4.73 | GROUND_INST: instantiating (13) with all_56_0, all_59_1, n1, simplifying with % 30.11/4.73 | (53), (54) gives: % 30.11/4.73 | (57) all_59_1 = all_56_0 % 30.11/4.73 | % 30.11/4.73 | GROUND_INST: instantiating (13) with all_59_1, all_61_2, n1, simplifying with % 30.11/4.73 | (52), (53) gives: % 30.11/4.73 | (58) all_61_2 = all_59_1 % 30.11/4.73 | % 30.11/4.73 | GROUND_INST: instantiating (13) with n2, all_61_2, n1, simplifying with (52), % 30.11/4.73 | (55) gives: % 30.11/4.73 | (59) all_61_2 = n2 % 30.11/4.73 | % 30.11/4.73 | COMBINE_EQS: (58), (59) imply: % 30.11/4.73 | (60) all_59_1 = n2 % 30.11/4.73 | % 30.11/4.73 | SIMP: (60) implies: % 30.11/4.73 | (61) all_59_1 = n2 % 30.11/4.73 | % 30.11/4.73 | COMBINE_EQS: (57), (61) imply: % 30.11/4.73 | (62) all_56_0 = n2 % 30.11/4.73 | % 30.11/4.73 | REDUCE: (30), (59) imply: % 30.11/4.73 | (63) succ(n2) = all_61_1 % 30.11/4.73 | % 30.11/4.73 | REDUCE: (26), (61) imply: % 30.11/4.73 | (64) succ(n2) = all_59_0 % 30.11/4.73 | % 30.11/4.73 | REDUCE: (22), (62) imply: % 30.11/4.73 | (65) succ(n2) = n3 % 30.11/4.73 | % 30.11/4.73 | REDUCE: (19), (62) imply: % 30.11/4.73 | (66) $i(n2) % 30.11/4.73 | % 30.11/4.73 | GROUND_INST: instantiating (13) with all_59_0, all_61_1, n2, simplifying with % 30.11/4.73 | (63), (64) gives: % 30.11/4.73 | (67) all_61_1 = all_59_0 % 30.11/4.73 | % 30.11/4.73 | GROUND_INST: instantiating (13) with n3, all_61_1, n2, simplifying with (63), % 30.11/4.73 | (65) gives: % 30.11/4.73 | (68) all_61_1 = n3 % 30.11/4.73 | % 30.11/4.73 | COMBINE_EQS: (67), (68) imply: % 30.11/4.73 | (69) all_59_0 = n3 % 30.11/4.73 | % 30.11/4.73 | SIMP: (69) implies: % 30.11/4.73 | (70) all_59_0 = n3 % 30.11/4.73 | % 30.11/4.73 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (55), % 30.11/4.73 | (56) gives: % 30.11/4.73 | (71) pred(n2) = n1 % 30.11/4.73 | % 30.11/4.73 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (65), % 30.11/4.73 | (66) gives: % 30.11/4.74 | (72) pred(n3) = n2 % 30.11/4.74 | % 30.11/4.74 | GROUND_INST: instantiating (2) with n2, all_69_8, simplifying with (36), (66) % 30.11/4.74 | gives: % 30.11/4.74 | (73) succ(n2) = all_69_8 & $i(all_69_8) % 30.11/4.74 | % 30.11/4.74 | ALPHA: (73) implies: % 30.11/4.74 | (74) $i(all_69_8) % 30.11/4.74 | (75) succ(n2) = all_69_8 % 30.11/4.74 | % 30.11/4.74 | GROUND_INST: instantiating (3) with all_69_8, all_69_7, simplifying with (37), % 30.11/4.74 | (74) gives: % 30.11/4.74 | (76) pred(all_69_8) = all_69_7 & $i(all_69_7) % 30.11/4.74 | % 30.11/4.74 | ALPHA: (76) implies: % 30.11/4.74 | (77) $i(all_69_7) % 30.11/4.74 | (78) pred(all_69_8) = all_69_7 % 30.11/4.74 | % 30.11/4.74 | GROUND_INST: instantiating (13) with n3, all_69_8, n2, simplifying with (65), % 30.11/4.74 | (75) gives: % 30.11/4.74 | (79) all_69_8 = n3 % 30.11/4.74 | % 30.11/4.74 | REDUCE: (78), (79) imply: % 30.11/4.74 | (80) pred(n3) = all_69_7 % 30.11/4.74 | % 30.11/4.74 | GROUND_INST: instantiating (12) with n2, all_69_7, n3, simplifying with (72), % 30.11/4.74 | (80) gives: % 30.11/4.74 | (81) all_69_7 = n2 % 30.11/4.74 | % 30.11/4.74 | BETA: splitting (39) gives: % 30.11/4.74 | % 30.11/4.74 | Case 1: % 30.11/4.74 | | % 30.11/4.74 | | (82) ~ gt(loopcounter, n1) % 30.11/4.74 | | % 30.11/4.74 | | BETA: splitting (38) gives: % 30.11/4.74 | | % 30.11/4.74 | | Case 1: % 30.11/4.74 | | | % 30.11/4.74 | | | (83) ( ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1, % 30.11/4.74 | | | all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1, n3) & % 30.11/4.74 | | | leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2)) | ( ~ % 30.11/4.74 | | | (all_69_3 = init) & a_select2(s_values7_init, all_69_4) = % 30.11/4.74 | | | all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0, all_69_4)) % 30.11/4.74 | | | % 30.11/4.74 | | | BETA: splitting (83) gives: % 30.11/4.74 | | | % 30.11/4.74 | | | Case 1: % 30.11/4.74 | | | | % 30.11/4.74 | | | | (84) ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1, % 30.11/4.74 | | | | all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1, n3) & % 30.11/4.74 | | | | leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2) % 30.11/4.74 | | | | % 30.11/4.74 | | | | ALPHA: (84) implies: % 30.11/4.74 | | | | (85) ~ (all_69_0 = init) % 30.11/4.74 | | | | (86) leq(n0, all_69_2) % 30.11/4.74 | | | | (87) leq(n0, all_69_1) % 30.11/4.74 | | | | (88) leq(all_69_2, n2) % 30.11/4.74 | | | | (89) leq(all_69_1, n3) % 30.11/4.74 | | | | (90) a_select3(simplex7_init, all_69_1, all_69_2) = all_69_0 % 30.11/4.74 | | | | % 30.11/4.74 | | | | GROUND_INST: instantiating (42) with all_69_2, all_69_1, all_69_0, % 30.11/4.74 | | | | simplifying with (34), (35), (86), (87), (88), (89), (90) % 30.11/4.74 | | | | gives: % 30.11/4.74 | | | | (91) all_69_0 = init % 30.11/4.74 | | | | % 30.11/4.74 | | | | REDUCE: (85), (91) imply: % 30.11/4.74 | | | | (92) $false % 30.11/4.74 | | | | % 30.11/4.74 | | | | CLOSE: (92) is inconsistent. % 30.11/4.74 | | | | % 30.11/4.74 | | | Case 2: % 30.11/4.74 | | | | % 30.11/4.74 | | | | (93) ~ (all_69_3 = init) & a_select2(s_values7_init, all_69_4) = % 30.11/4.74 | | | | all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0, all_69_4) % 30.11/4.74 | | | | % 30.11/4.74 | | | | ALPHA: (93) implies: % 30.11/4.74 | | | | (94) ~ (all_69_3 = init) % 30.11/4.74 | | | | (95) leq(n0, all_69_4) % 30.11/4.74 | | | | (96) leq(all_69_4, n3) % 30.11/4.74 | | | | (97) a_select2(s_values7_init, all_69_4) = all_69_3 % 30.11/4.74 | | | | % 30.11/4.74 | | | | GROUND_INST: instantiating (40) with all_69_4, all_69_3, simplifying % 30.11/4.74 | | | | with (33), (95), (96), (97) gives: % 30.11/4.74 | | | | (98) all_69_3 = init % 30.11/4.74 | | | | % 30.11/4.74 | | | | REDUCE: (94), (98) imply: % 30.11/4.74 | | | | (99) $false % 30.11/4.74 | | | | % 30.11/4.74 | | | | CLOSE: (99) is inconsistent. % 30.11/4.74 | | | | % 30.11/4.74 | | | End of split % 30.11/4.74 | | | % 30.11/4.74 | | Case 2: % 30.11/4.74 | | | % 30.11/4.74 | | | (100) ( ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) = % 30.11/4.74 | | | all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0, % 30.11/4.74 | | | all_69_6)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = % 30.11/4.74 | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init = % 30.11/4.75 | | | init))) % 30.11/4.75 | | | % 30.11/4.75 | | | BETA: splitting (100) gives: % 30.11/4.75 | | | % 30.11/4.75 | | | Case 1: % 30.11/4.75 | | | | % 30.11/4.75 | | | | (101) ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) = % 30.11/4.75 | | | | all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0, all_69_6) % 30.11/4.75 | | | | % 30.11/4.75 | | | | REF_CLOSE: (1), (4), (5), (32), (41), (66), (71), (81), (101), (leq_gt2) % 30.11/4.75 | | | | are inconsistent by sub-proof #1. % 30.11/4.75 | | | | % 30.11/4.75 | | | Case 2: % 30.11/4.75 | | | | % 30.11/4.75 | | | | (102) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~ % 30.11/4.75 | | | | (pvar1401_init = init) | ~ (pvar1400_init = init)) % 30.11/4.75 | | | | % 30.11/4.75 | | | | ALPHA: (102) implies: % 30.11/4.75 | | | | (103) gt(loopcounter, n1) % 30.11/4.75 | | | | % 30.11/4.75 | | | | PRED_UNIFY: (82), (103) imply: % 30.11/4.75 | | | | (104) $false % 30.11/4.75 | | | | % 30.11/4.75 | | | | CLOSE: (104) is inconsistent. % 30.11/4.75 | | | | % 30.11/4.75 | | | End of split % 30.11/4.75 | | | % 30.11/4.75 | | End of split % 30.11/4.75 | | % 30.11/4.75 | Case 2: % 30.11/4.75 | | % 30.11/4.75 | | (105) pvar1402_init = init & pvar1401_init = init & pvar1400_init = init % 30.11/4.75 | | % 30.11/4.75 | | ALPHA: (105) implies: % 30.11/4.75 | | (106) pvar1400_init = init % 30.11/4.75 | | (107) pvar1401_init = init % 30.11/4.75 | | (108) pvar1402_init = init % 30.11/4.75 | | % 30.11/4.75 | | BETA: splitting (38) gives: % 30.11/4.75 | | % 30.11/4.75 | | Case 1: % 30.11/4.75 | | | % 30.11/4.75 | | | (109) ( ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1, % 30.11/4.75 | | | all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1, n3) & % 30.11/4.75 | | | leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2)) | ( % 30.11/4.75 | | | ~ (all_69_3 = init) & a_select2(s_values7_init, all_69_4) = % 30.11/4.75 | | | all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0, % 30.11/4.75 | | | all_69_4)) % 30.11/4.75 | | | % 30.11/4.75 | | | BETA: splitting (109) gives: % 30.11/4.75 | | | % 30.11/4.75 | | | Case 1: % 30.11/4.75 | | | | % 30.11/4.75 | | | | (110) ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1, % 30.11/4.75 | | | | all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1, n3) & % 30.11/4.75 | | | | leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2) % 30.11/4.75 | | | | % 30.11/4.75 | | | | ALPHA: (110) implies: % 30.11/4.75 | | | | (111) ~ (all_69_0 = init) % 30.11/4.75 | | | | (112) leq(n0, all_69_2) % 30.11/4.75 | | | | (113) leq(n0, all_69_1) % 30.11/4.75 | | | | (114) leq(all_69_2, n2) % 30.11/4.75 | | | | (115) leq(all_69_1, n3) % 30.11/4.75 | | | | (116) a_select3(simplex7_init, all_69_1, all_69_2) = all_69_0 % 30.11/4.75 | | | | % 30.11/4.75 | | | | GROUND_INST: instantiating (42) with all_69_2, all_69_1, all_69_0, % 30.11/4.75 | | | | simplifying with (34), (35), (112), (113), (114), (115), % 30.11/4.75 | | | | (116) gives: % 30.11/4.75 | | | | (117) all_69_0 = init % 30.11/4.75 | | | | % 30.11/4.75 | | | | REDUCE: (111), (117) imply: % 30.11/4.75 | | | | (118) $false % 30.11/4.75 | | | | % 30.11/4.75 | | | | CLOSE: (118) is inconsistent. % 30.11/4.75 | | | | % 30.11/4.75 | | | Case 2: % 30.11/4.75 | | | | % 30.11/4.75 | | | | (119) ~ (all_69_3 = init) & a_select2(s_values7_init, all_69_4) = % 30.11/4.75 | | | | all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0, all_69_4) % 30.11/4.75 | | | | % 30.11/4.75 | | | | ALPHA: (119) implies: % 30.11/4.75 | | | | (120) ~ (all_69_3 = init) % 30.11/4.75 | | | | (121) leq(n0, all_69_4) % 30.11/4.75 | | | | (122) leq(all_69_4, n3) % 30.11/4.75 | | | | (123) a_select2(s_values7_init, all_69_4) = all_69_3 % 30.11/4.75 | | | | % 30.11/4.75 | | | | GROUND_INST: instantiating (40) with all_69_4, all_69_3, simplifying % 30.11/4.75 | | | | with (33), (121), (122), (123) gives: % 30.11/4.75 | | | | (124) all_69_3 = init % 30.11/4.75 | | | | % 30.11/4.75 | | | | REDUCE: (120), (124) imply: % 30.11/4.75 | | | | (125) $false % 30.11/4.75 | | | | % 30.11/4.75 | | | | CLOSE: (125) is inconsistent. % 30.11/4.75 | | | | % 30.11/4.75 | | | End of split % 30.11/4.75 | | | % 30.11/4.75 | | Case 2: % 30.11/4.75 | | | % 30.11/4.75 | | | (126) ( ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) = % 30.11/4.75 | | | all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0, % 30.11/4.75 | | | all_69_6)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = % 30.11/4.75 | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init = % 30.11/4.75 | | | init))) % 30.11/4.75 | | | % 30.11/4.75 | | | BETA: splitting (126) gives: % 30.11/4.75 | | | % 30.11/4.75 | | | Case 1: % 30.11/4.75 | | | | % 30.11/4.75 | | | | (127) ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) = % 30.11/4.75 | | | | all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0, all_69_6) % 30.11/4.75 | | | | % 30.23/4.75 | | | | REF_CLOSE: (1), (4), (5), (32), (41), (66), (71), (81), (127), (leq_gt2) % 30.23/4.75 | | | | are inconsistent by sub-proof #1. % 30.23/4.75 | | | | % 30.23/4.75 | | | Case 2: % 30.23/4.75 | | | | % 30.23/4.75 | | | | (128) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~ % 30.23/4.75 | | | | (pvar1401_init = init) | ~ (pvar1400_init = init)) % 30.23/4.75 | | | | % 30.23/4.75 | | | | ALPHA: (128) implies: % 30.23/4.75 | | | | (129) ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 30.23/4.76 | | | | (pvar1400_init = init) % 30.23/4.76 | | | | % 30.23/4.76 | | | | BETA: splitting (129) gives: % 30.23/4.76 | | | | % 30.23/4.76 | | | | Case 1: % 30.23/4.76 | | | | | % 30.23/4.76 | | | | | (130) ~ (pvar1402_init = init) % 30.23/4.76 | | | | | % 30.23/4.76 | | | | | REDUCE: (108), (130) imply: % 30.23/4.76 | | | | | (131) $false % 30.23/4.76 | | | | | % 30.23/4.76 | | | | | CLOSE: (131) is inconsistent. % 30.23/4.76 | | | | | % 30.23/4.76 | | | | Case 2: % 30.23/4.76 | | | | | % 30.23/4.76 | | | | | (132) ~ (pvar1401_init = init) | ~ (pvar1400_init = init) % 30.23/4.76 | | | | | % 30.23/4.76 | | | | | BETA: splitting (132) gives: % 30.23/4.76 | | | | | % 30.23/4.76 | | | | | Case 1: % 30.23/4.76 | | | | | | % 30.23/4.76 | | | | | | (133) ~ (pvar1401_init = init) % 30.23/4.76 | | | | | | % 30.23/4.76 | | | | | | REDUCE: (107), (133) imply: % 30.23/4.76 | | | | | | (134) $false % 30.23/4.76 | | | | | | % 30.23/4.76 | | | | | | CLOSE: (134) is inconsistent. % 30.23/4.76 | | | | | | % 30.23/4.76 | | | | | Case 2: % 30.23/4.76 | | | | | | % 30.23/4.76 | | | | | | (135) ~ (pvar1400_init = init) % 30.23/4.76 | | | | | | % 30.23/4.76 | | | | | | REDUCE: (106), (135) imply: % 30.23/4.76 | | | | | | (136) $false % 30.23/4.76 | | | | | | % 30.23/4.76 | | | | | | CLOSE: (136) is inconsistent. % 30.23/4.76 | | | | | | % 30.23/4.76 | | | | | End of split % 30.23/4.76 | | | | | % 30.23/4.76 | | | | End of split % 30.23/4.76 | | | | % 30.23/4.76 | | | End of split % 30.23/4.76 | | | % 30.23/4.76 | | End of split % 30.23/4.76 | | % 30.23/4.76 | End of split % 30.23/4.76 | % 30.23/4.76 End of proof % 30.23/4.76 % 30.23/4.76 Sub-proof #1 shows that the following formulas are inconsistent: % 30.23/4.76 ---------------------------------------------------------------- % 30.23/4.76 (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 30.23/4.76 v1) | gt(v1, v0)) % 30.23/4.76 (2) all_69_7 = n2 % 30.23/4.76 (3) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) | % 30.23/4.76 ~ leq(n0, v0)) % 30.23/4.76 (4) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 30.23/4.76 v0) = v1) | ~ $i(v0) | ~ leq(v0, all_69_7) | ~ leq(n0, v0)) % 30.23/4.76 (5) pred(n2) = n1 % 30.23/4.76 (6) $i(all_69_6) % 30.23/4.76 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 30.23/4.76 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 30.23/4.76 (8) $i(n2) % 30.23/4.76 (9) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 30.23/4.76 leq(n0, v0)) % 30.23/4.76 (10) ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) = all_69_5 & % 30.23/4.76 $i(all_69_5) & leq(all_69_6, n2) & leq(n0, all_69_6) % 30.23/4.76 % 30.23/4.76 Begin of proof % 30.23/4.76 | % 30.23/4.76 | ALPHA: (10) implies: % 30.23/4.76 | (11) ~ (all_69_5 = init) % 30.23/4.76 | (12) leq(n0, all_69_6) % 30.23/4.76 | (13) leq(all_69_6, n2) % 30.23/4.76 | (14) a_select2(s_center7_init, all_69_6) = all_69_5 % 30.23/4.76 | % 30.23/4.76 | GROUND_INST: instantiating (3) with all_69_6, simplifying with (6), (12), (13) % 30.23/4.76 | gives: % 30.23/4.76 | (15) all_69_6 = n2 | all_69_6 = n1 | all_69_6 = n0 % 30.23/4.76 | % 30.23/4.76 | GROUND_INST: instantiating (1) with all_69_6, n2, simplifying with (6), (8), % 30.23/4.76 | (13) gives: % 30.23/4.76 | (16) all_69_6 = n2 | gt(n2, all_69_6) % 30.23/4.76 | % 30.23/4.76 | BETA: splitting (16) gives: % 30.23/4.76 | % 30.23/4.76 | Case 1: % 30.23/4.76 | | % 30.23/4.76 | | (17) gt(n2, all_69_6) % 30.23/4.76 | | % 30.23/4.76 | | GROUND_INST: instantiating (7) with all_69_6, n2, n1, simplifying with (5), % 30.23/4.76 | | (6), (8), (17) gives: % 30.23/4.76 | | (18) leq(all_69_6, n1) % 30.23/4.76 | | % 30.23/4.76 | | GROUND_INST: instantiating (9) with all_69_6, simplifying with (6), (12), % 30.23/4.76 | | (18) gives: % 30.23/4.76 | | (19) all_69_6 = n1 | all_69_6 = n0 % 30.23/4.76 | | % 30.23/4.76 | | BETA: splitting (15) gives: % 30.23/4.76 | | % 30.23/4.76 | | Case 1: % 30.23/4.76 | | | % 30.23/4.76 | | | (20) all_69_6 = n0 % 30.23/4.76 | | | % 30.23/4.76 | | | REDUCE: (14), (20) imply: % 30.23/4.76 | | | (21) a_select2(s_center7_init, n0) = all_69_5 % 30.23/4.76 | | | % 30.23/4.76 | | | REDUCE: (6), (20) imply: % 30.23/4.76 | | | (22) $i(n0) % 30.23/4.76 | | | % 30.23/4.76 | | | REDUCE: (13), (20) imply: % 30.23/4.76 | | | (23) leq(n0, n2) % 30.23/4.76 | | | % 30.23/4.76 | | | REDUCE: (12), (20) imply: % 30.23/4.76 | | | (24) leq(n0, n0) % 30.23/4.76 | | | % 30.23/4.76 | | | GROUND_INST: instantiating (4) with n0, all_69_5, simplifying with (21), % 30.23/4.76 | | | (22), (24) gives: % 30.23/4.76 | | | (25) all_69_5 = init | ~ leq(n0, all_69_7) % 30.23/4.76 | | | % 30.23/4.76 | | | BETA: splitting (25) gives: % 30.23/4.76 | | | % 30.23/4.76 | | | Case 1: % 30.23/4.76 | | | | % 30.23/4.76 | | | | (26) ~ leq(n0, all_69_7) % 30.23/4.76 | | | | % 30.23/4.76 | | | | REDUCE: (2), (26) imply: % 30.23/4.76 | | | | (27) ~ leq(n0, n2) % 30.23/4.76 | | | | % 30.23/4.76 | | | | PRED_UNIFY: (23), (27) imply: % 30.23/4.76 | | | | (28) $false % 30.23/4.76 | | | | % 30.23/4.76 | | | | CLOSE: (28) is inconsistent. % 30.23/4.76 | | | | % 30.23/4.76 | | | Case 2: % 30.23/4.76 | | | | % 30.23/4.76 | | | | (29) all_69_5 = init % 30.23/4.76 | | | | % 30.23/4.76 | | | | REDUCE: (11), (29) imply: % 30.23/4.76 | | | | (30) $false % 30.23/4.76 | | | | % 30.23/4.76 | | | | CLOSE: (30) is inconsistent. % 30.23/4.76 | | | | % 30.23/4.76 | | | End of split % 30.23/4.76 | | | % 30.23/4.76 | | Case 2: % 30.23/4.76 | | | % 30.23/4.76 | | | (31) ~ (all_69_6 = n0) % 30.23/4.76 | | | % 30.23/4.76 | | | BETA: splitting (19) gives: % 30.23/4.76 | | | % 30.23/4.76 | | | Case 1: % 30.23/4.76 | | | | % 30.23/4.76 | | | | (32) all_69_6 = n0 % 30.23/4.76 | | | | % 30.23/4.76 | | | | REDUCE: (31), (32) imply: % 30.23/4.76 | | | | (33) $false % 30.23/4.76 | | | | % 30.23/4.76 | | | | CLOSE: (33) is inconsistent. % 30.23/4.76 | | | | % 30.23/4.76 | | | Case 2: % 30.23/4.76 | | | | % 30.23/4.76 | | | | (34) all_69_6 = n1 % 30.23/4.76 | | | | % 30.23/4.76 | | | | REDUCE: (14), (34) imply: % 30.23/4.76 | | | | (35) a_select2(s_center7_init, n1) = all_69_5 % 30.23/4.76 | | | | % 30.23/4.76 | | | | REDUCE: (6), (34) imply: % 30.23/4.76 | | | | (36) $i(n1) % 30.23/4.76 | | | | % 30.23/4.76 | | | | REDUCE: (13), (34) imply: % 30.23/4.76 | | | | (37) leq(n1, n2) % 30.23/4.76 | | | | % 30.23/4.77 | | | | REDUCE: (12), (34) imply: % 30.23/4.77 | | | | (38) leq(n0, n1) % 30.23/4.77 | | | | % 30.23/4.77 | | | | GROUND_INST: instantiating (4) with n1, all_69_5, simplifying with (35), % 30.23/4.77 | | | | (36), (38) gives: % 30.23/4.77 | | | | (39) all_69_5 = init | ~ leq(n1, all_69_7) % 30.23/4.77 | | | | % 30.23/4.77 | | | | BETA: splitting (39) gives: % 30.23/4.77 | | | | % 30.23/4.77 | | | | Case 1: % 30.23/4.77 | | | | | % 30.23/4.77 | | | | | (40) ~ leq(n1, all_69_7) % 30.23/4.77 | | | | | % 30.23/4.77 | | | | | REDUCE: (2), (40) imply: % 30.23/4.77 | | | | | (41) ~ leq(n1, n2) % 30.23/4.77 | | | | | % 30.23/4.77 | | | | | PRED_UNIFY: (37), (41) imply: % 30.23/4.77 | | | | | (42) $false % 30.23/4.77 | | | | | % 30.23/4.77 | | | | | CLOSE: (42) is inconsistent. % 30.23/4.77 | | | | | % 30.23/4.77 | | | | Case 2: % 30.23/4.77 | | | | | % 30.23/4.77 | | | | | (43) all_69_5 = init % 30.23/4.77 | | | | | % 30.23/4.77 | | | | | REDUCE: (11), (43) imply: % 30.23/4.77 | | | | | (44) $false % 30.23/4.77 | | | | | % 30.23/4.77 | | | | | CLOSE: (44) is inconsistent. % 30.23/4.77 | | | | | % 30.23/4.77 | | | | End of split % 30.23/4.77 | | | | % 30.23/4.77 | | | End of split % 30.23/4.77 | | | % 30.23/4.77 | | End of split % 30.23/4.77 | | % 30.23/4.77 | Case 2: % 30.23/4.77 | | % 30.23/4.77 | | (45) all_69_6 = n2 % 30.23/4.77 | | % 30.23/4.77 | | REDUCE: (14), (45) imply: % 30.23/4.77 | | (46) a_select2(s_center7_init, n2) = all_69_5 % 30.23/4.77 | | % 30.23/4.77 | | REDUCE: (13), (45) imply: % 30.23/4.77 | | (47) leq(n2, n2) % 30.23/4.77 | | % 30.23/4.77 | | REDUCE: (12), (45) imply: % 30.23/4.77 | | (48) leq(n0, n2) % 30.23/4.77 | | % 30.23/4.77 | | GROUND_INST: instantiating (4) with n2, all_69_5, simplifying with (8), % 30.23/4.77 | | (46), (48) gives: % 30.23/4.77 | | (49) all_69_5 = init | ~ leq(n2, all_69_7) % 30.23/4.77 | | % 30.23/4.77 | | BETA: splitting (49) gives: % 30.23/4.77 | | % 30.23/4.77 | | Case 1: % 30.23/4.77 | | | % 30.23/4.77 | | | (50) ~ leq(n2, all_69_7) % 30.23/4.77 | | | % 30.23/4.77 | | | REDUCE: (2), (50) imply: % 30.23/4.77 | | | (51) ~ leq(n2, n2) % 30.23/4.77 | | | % 30.23/4.77 | | | PRED_UNIFY: (47), (51) imply: % 30.23/4.77 | | | (52) $false % 30.23/4.77 | | | % 30.23/4.77 | | | CLOSE: (52) is inconsistent. % 30.23/4.77 | | | % 30.23/4.77 | | Case 2: % 30.23/4.77 | | | % 30.23/4.77 | | | (53) all_69_5 = init % 30.23/4.77 | | | % 30.23/4.77 | | | REDUCE: (11), (53) imply: % 30.23/4.77 | | | (54) $false % 30.23/4.77 | | | % 30.23/4.77 | | | CLOSE: (54) is inconsistent. % 30.23/4.77 | | | % 30.23/4.77 | | End of split % 30.23/4.77 | | % 30.23/4.77 | End of split % 30.23/4.77 | % 30.23/4.77 End of proof % 30.23/4.77 % SZS output end Proof for theBenchmark % 30.23/4.77 % 30.23/4.77 4149ms %------------------------------------------------------------------------------