%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV036+1 : TPTP v8.1.2. Bugfixed v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 22:54:40 EDT 2023 % Result : Theorem 52.79s 7.72s % Output : Proof 53.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SWV036+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n014.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 07:53:15 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.67 ________ _____ % 0.20/0.67 ___ __ \_________(_)________________________________ % 0.20/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.67 % 0.20/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.67 (2023-06-19) % 0.20/0.67 % 0.20/0.67 (c) Philipp Rümmer, 2009-2023 % 0.20/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.67 Amanda Stjerna. % 0.20/0.67 Free software under BSD-3-Clause. % 0.20/0.67 % 0.20/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.67 % 0.20/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.68 Running up to 7 provers in parallel. % 0.20/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.43/1.53 Prover 1: Preprocessing ... % 5.43/1.57 Prover 4: Preprocessing ... % 5.43/1.57 Prover 2: Preprocessing ... % 5.43/1.57 Prover 6: Preprocessing ... % 5.43/1.57 Prover 5: Preprocessing ... % 5.43/1.57 Prover 0: Preprocessing ... % 5.43/1.57 Prover 3: Preprocessing ... % 11.72/2.38 Prover 1: Warning: ignoring some quantifiers % 12.02/2.43 Prover 3: Warning: ignoring some quantifiers % 12.24/2.46 Prover 3: Constructing countermodel ... % 12.24/2.47 Prover 1: Constructing countermodel ... % 12.24/2.47 Prover 4: Warning: ignoring some quantifiers % 12.24/2.51 Prover 6: Proving ... % 12.95/2.53 Prover 4: Constructing countermodel ... % 12.95/2.57 Prover 0: Proving ... % 13.42/2.62 Prover 2: Proving ... % 13.42/2.63 Prover 5: Proving ... % 52.09/7.71 Prover 1: Found proof (size 819) % 52.09/7.71 Prover 1: proved (7018ms) % 52.79/7.71 Prover 3: stopped % 52.79/7.71 Prover 5: stopped % 52.79/7.71 Prover 2: stopped % 52.79/7.71 Prover 0: stopped % 52.79/7.71 Prover 6: stopped % 52.79/7.71 Prover 4: stopped % 52.79/7.71 % 52.79/7.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 52.79/7.72 % 52.79/7.73 % SZS output start Proof for theBenchmark % 52.79/7.74 Assumptions after simplification: % 52.79/7.74 --------------------------------- % 52.79/7.74 % 52.79/7.74 (gauss_init_0057) % 52.79/7.78 $i(s_values7) & $i(pvar1402_init) & $i(pvar1401_init) & $i(pvar1400_init) & % 52.79/7.78 $i(loopcounter) & $i(s_center7_init) & $i(s_values7_init) & $i(simplex7_init) % 52.79/7.78 & $i(pv1388) & $i(s_worst7) & $i(s_sworst7) & $i(s_best7) & $i(s_worst7_init) % 52.79/7.78 & $i(s_sworst7_init) & $i(s_best7_init) & $i(init) & $i(n3) & $i(n2) & $i(n1) % 52.79/7.78 & $i(n0) & ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 52.79/7.78 $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] % 52.79/7.78 : ? [v10: $i] : ? [v11: any] : ? [v12: any] : (s_worst7_init = init & % 52.79/7.78 s_sworst7_init = init & s_best7_init = init & a_select2(s_values7, pv1388) = % 52.79/7.78 v3 & a_select2(s_values7, s_worst7) = v7 & a_select2(s_values7, s_sworst7) = % 52.79/7.78 v10 & a_select2(s_values7, s_best7) = v4 & a_select2(s_values7_init, pv1388) % 52.79/7.78 = v2 & a_select2(s_values7_init, s_worst7) = v6 & a_select2(s_values7_init, % 52.79/7.78 s_sworst7) = v9 & a_select2(s_values7_init, s_best7) = v1 & leq(v3, v10) = % 52.79/7.78 v11 & leq(v3, v7) = v8 & leq(pv1388, n3) = 0 & leq(s_worst7, n3) = 0 & % 52.79/7.78 leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = 0 & leq(n2, pv1388) = 0 & % 52.79/7.78 leq(n0, pv1388) = v12 & leq(n0, s_worst7) = 0 & leq(n0, s_sworst7) = 0 & % 52.79/7.78 leq(n0, s_best7) = 0 & gt(v3, v4) = v5 & gt(loopcounter, n1) = v0 & $i(v10) % 52.79/7.78 & $i(v9) & $i(v7) & $i(v6) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & ! [v13: % 52.79/7.78 $i] : ! [v14: $i] : (v14 = init | ~ (a_select2(s_center7_init, v13) = % 52.79/7.78 v14) | ~ $i(v13) | ? [v15: any] : ? [v16: any] : (leq(v13, n2) = v16 % 53.14/7.78 & leq(n0, v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v13: $i] : % 53.14/7.78 ! [v14: $i] : (v14 = init | ~ (a_select2(s_values7_init, v13) = v14) | ~ % 53.14/7.78 $i(v13) | ? [v15: any] : ? [v16: any] : (leq(v13, n3) = v16 & leq(n0, % 53.14/7.78 v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v13: $i] : ( ~ % 53.14/7.78 (leq(v13, n2) = 0) | ~ $i(v13) | ? [v14: int] : ( ~ (v14 = 0) & leq(n0, % 53.14/7.78 v13) = v14) | ! [v14: $i] : ! [v15: $i] : (v15 = init | ~ % 53.14/7.78 (a_select3(simplex7_init, v14, v13) = v15) | ~ $i(v14) | ? [v16: any] % 53.14/7.78 : ? [v17: any] : (leq(v14, n3) = v17 & leq(n0, v14) = v16 & ( ~ (v17 = % 53.14/7.78 0) | ~ (v16 = 0))))) & ( ~ (v2 = init) | ~ (v1 = init) | (v5 = 0 % 53.14/7.78 & ( ~ (v12 = 0) | ? [v13: $i] : ? [v14: $i] : ( ~ (v14 = init) & % 53.14/7.78 a_select2(s_center7_init, v13) = v14 & leq(v13, n2) = 0 & leq(n0, % 53.14/7.78 v13) = 0 & $i(v14) & $i(v13)) | ? [v13: $i] : ? [v14: $i] : ( ~ % 53.14/7.78 (v14 = init) & a_select2(s_values7_init, v13) = v14 & leq(v13, n3) = % 53.14/7.78 0 & leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? [v13: $i] : (leq(v13, % 53.14/7.78 n2) = 0 & leq(n0, v13) = 0 & $i(v13) & ? [v14: $i] : ? [v15: $i] % 53.14/7.79 : ( ~ (v15 = init) & a_select3(simplex7_init, v14, v13) = v15 & % 53.14/7.79 leq(v14, n3) = 0 & leq(n0, v14) = 0 & $i(v15) & $i(v14))) | (v0 = % 53.14/7.79 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 53.14/7.79 (pvar1400_init = init))))) | ( ~ (v5 = 0) & ( ~ (v6 = init) | (v8 % 53.14/7.79 = 0 & ( ~ (v12 = 0) | ? [v13: $i] : ? [v14: $i] : ( ~ (v14 = init) % 53.14/7.79 & a_select2(s_center7_init, v13) = v14 & leq(v13, n2) = 0 & % 53.14/7.79 leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? [v13: $i] : ? [v14: % 53.14/7.79 $i] : ( ~ (v14 = init) & a_select2(s_values7_init, v13) = v14 & % 53.14/7.79 leq(v13, n3) = 0 & leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? % 53.14/7.79 [v13: $i] : (leq(v13, n2) = 0 & leq(n0, v13) = 0 & $i(v13) & ? % 53.14/7.79 [v14: $i] : ? [v15: $i] : ( ~ (v15 = init) & % 53.14/7.79 a_select3(simplex7_init, v14, v13) = v15 & leq(v14, n3) = 0 & % 53.14/7.79 leq(n0, v14) = 0 & $i(v15) & $i(v14))) | (v0 = 0 & ( ~ % 53.14/7.79 (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 53.14/7.79 (pvar1400_init = init))))) | ( ~ (v8 = 0) & ( ~ (v9 = init) | % 53.14/7.79 (v11 = 0 & ( ~ (v12 = 0) | ? [v13: $i] : ? [v14: $i] : ( ~ (v14 % 53.14/7.79 = init) & a_select2(s_center7_init, v13) = v14 & leq(v13, % 53.14/7.79 n2) = 0 & leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? [v13: % 53.14/7.79 $i] : ? [v14: $i] : ( ~ (v14 = init) & % 53.14/7.79 a_select2(s_values7_init, v13) = v14 & leq(v13, n3) = 0 & % 53.14/7.79 leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? [v13: $i] : % 53.14/7.79 (leq(v13, n2) = 0 & leq(n0, v13) = 0 & $i(v13) & ? [v14: $i] % 53.14/7.79 : ? [v15: $i] : ( ~ (v15 = init) & a_select3(simplex7_init, % 53.14/7.79 v14, v13) = v15 & leq(v14, n3) = 0 & leq(n0, v14) = 0 & % 53.14/7.79 $i(v15) & $i(v14))) | (v0 = 0 & ( ~ (pvar1402_init = init) % 53.14/7.79 | ~ (pvar1401_init = init) | ~ (pvar1400_init = % 53.14/7.79 init))))) | ( ~ (v11 = 0) & ( ? [v13: $i] : ? [v14: $i] % 53.14/7.79 : ( ~ (v14 = init) & a_select2(s_center7_init, v13) = v14 & % 53.14/7.79 leq(v13, n2) = 0 & leq(n0, v13) = 0 & $i(v14) & $i(v13)) | % 53.14/7.79 ? [v13: $i] : ? [v14: $i] : ( ~ (v14 = init) & % 53.14/7.79 a_select2(s_values7_init, v13) = v14 & leq(v13, n3) = 0 & % 53.14/7.79 leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? [v13: $i] : % 53.14/7.79 (leq(v13, n2) = 0 & leq(n0, v13) = 0 & $i(v13) & ? [v14: $i] % 53.14/7.79 : ? [v15: $i] : ( ~ (v15 = init) & a_select3(simplex7_init, % 53.14/7.79 v14, v13) = v15 & leq(v14, n3) = 0 & leq(n0, v14) = 0 & % 53.14/7.79 $i(v15) & $i(v14))) | (v0 = 0 & ( ~ (pvar1402_init = init) % 53.14/7.79 | ~ (pvar1401_init = init) | ~ (pvar1400_init = % 53.14/7.79 init)))))))))) & ( ~ (v0 = 0) | (pvar1402_init = init & % 53.14/7.79 pvar1401_init = init & pvar1400_init = init))) % 53.14/7.79 % 53.14/7.79 (gt_2_0) % 53.14/7.79 gt(n2, n0) = 0 & $i(n2) & $i(n0) % 53.14/7.79 % 53.14/7.79 (leq_gt1) % 53.14/7.79 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 53.14/7.79 leq(v0, v1) = 0) % 53.14/7.79 % 53.14/7.79 (leq_succ_gt) % 53.14/7.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2, % 53.14/7.79 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 53.14/7.79 % 53.14/7.79 (leq_succ_gt_equiv) % 53.14/7.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 53.14/7.79 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 53.14/7.79 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 53.14/7.79 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 53.14/7.79 leq(v0, v1) = 0) % 53.14/7.79 % 53.14/7.79 (successor_1) % 53.14/7.79 succ(n0) = n1 & $i(n1) & $i(n0) % 53.14/7.79 % 53.14/7.79 (successor_2) % 53.14/7.79 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 53.14/7.79 % 53.14/7.79 (successor_3) % 53.14/7.79 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 53.14/7.79 succ(n0) = v0 & $i(v1) & $i(v0)) % 53.14/7.79 % 53.14/7.79 (successor_4) % 53.14/7.79 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 53.14/7.79 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 53.14/7.79 % 53.14/7.79 (successor_5) % 53.14/7.79 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 53.14/7.79 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 53.14/7.79 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 53.14/7.79 % 53.14/7.79 (transitivity_leq) % 53.14/7.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (leq(v0, % 53.14/7.79 v2) = v3) | ~ (leq(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 53.14/7.79 ? [v4: int] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) % 53.14/7.79 % 53.14/7.79 (function-axioms) % 53.14/7.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 53.14/7.80 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 53.14/7.80 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 53.14/7.80 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 53.14/7.80 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 53.14/7.80 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 53.14/7.80 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 53.14/7.80 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 53.14/7.80 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 53.14/7.80 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 53.14/7.80 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 53.14/7.80 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 53.14/7.80 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 53.14/7.80 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 53.14/7.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 53.14/7.80 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 53.14/7.80 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 53.14/7.80 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 53.14/7.80 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 53.14/7.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 53.14/7.80 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 53.14/7.80 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 53.14/7.80 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 53.14/7.80 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 53.14/7.80 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 53.14/7.80 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 53.14/7.80 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 53.14/7.80 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 53.14/7.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 53.14/7.80 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 53.14/7.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 53.14/7.80 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 53.14/7.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 53.14/7.80 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 53.14/7.80 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 53.14/7.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 53.14/7.80 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 53.14/7.80 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 53.14/7.80 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 53.14/7.80 % 53.14/7.80 Further assumptions not needed in the proof: % 53.14/7.80 -------------------------------------------- % 53.14/7.80 const_array1_select, const_array2_select, defuse, finite_domain_0, % 53.14/7.80 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 53.14/7.80 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_1, % 53.14/7.80 gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1, % 53.14/7.80 gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, % 53.14/7.80 gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt2, leq_gt_pred, % 53.14/7.80 leq_minus, leq_succ, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, % 53.14/7.80 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 53.14/7.80 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ, % 53.14/7.80 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 53.14/7.80 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 53.14/7.80 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 53.14/7.80 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, sum_plus_base, % 53.14/7.80 sum_plus_base_float, totality, transitivity_gt, ttrue, % 53.14/7.80 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 53.14/7.80 % 53.14/7.80 Those formulas are unsatisfiable: % 53.14/7.80 --------------------------------- % 53.14/7.80 % 53.14/7.80 Begin of proof % 53.14/7.80 | % 53.14/7.80 | ALPHA: (leq_succ_gt_equiv) implies: % 53.14/7.80 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 53.14/7.80 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0) % 53.14/7.80 | % 53.14/7.80 | ALPHA: (gt_2_0) implies: % 53.14/7.80 | (2) gt(n2, n0) = 0 % 53.14/7.80 | % 53.14/7.80 | ALPHA: (successor_4) implies: % 53.14/7.81 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 53.14/7.81 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 53.14/7.81 | % 53.14/7.81 | ALPHA: (successor_5) implies: % 53.14/7.81 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 53.14/7.81 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 53.14/7.81 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 53.14/7.81 | % 53.14/7.81 | ALPHA: (successor_1) implies: % 53.14/7.81 | (5) succ(n0) = n1 % 53.14/7.81 | % 53.14/7.81 | ALPHA: (successor_2) implies: % 53.14/7.81 | (6) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 53.14/7.81 | % 53.14/7.81 | ALPHA: (successor_3) implies: % 53.14/7.81 | (7) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) = % 53.14/7.81 | v0 & $i(v1) & $i(v0)) % 53.14/7.81 | % 53.14/7.81 | ALPHA: (gauss_init_0057) implies: % 53.14/7.81 | (8) $i(n0) % 53.14/7.81 | (9) $i(s_best7) % 53.14/7.81 | (10) $i(s_sworst7) % 53.14/7.81 | (11) $i(s_worst7) % 53.14/7.81 | (12) $i(pv1388) % 53.14/7.82 | (13) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 53.14/7.82 | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] % 53.14/7.82 | : ? [v10: $i] : ? [v11: any] : ? [v12: any] : (s_worst7_init = init % 53.14/7.82 | & s_sworst7_init = init & s_best7_init = init & a_select2(s_values7, % 53.14/7.82 | pv1388) = v3 & a_select2(s_values7, s_worst7) = v7 & % 53.14/7.82 | a_select2(s_values7, s_sworst7) = v10 & a_select2(s_values7, % 53.14/7.82 | s_best7) = v4 & a_select2(s_values7_init, pv1388) = v2 & % 53.14/7.82 | a_select2(s_values7_init, s_worst7) = v6 & a_select2(s_values7_init, % 53.14/7.82 | s_sworst7) = v9 & a_select2(s_values7_init, s_best7) = v1 & % 53.14/7.82 | leq(v3, v10) = v11 & leq(v3, v7) = v8 & leq(pv1388, n3) = 0 & % 53.14/7.82 | leq(s_worst7, n3) = 0 & leq(s_sworst7, n3) = 0 & leq(s_best7, n3) = % 53.14/7.82 | 0 & leq(n2, pv1388) = 0 & leq(n0, pv1388) = v12 & leq(n0, s_worst7) % 53.14/7.82 | = 0 & leq(n0, s_sworst7) = 0 & leq(n0, s_best7) = 0 & gt(v3, v4) = % 53.14/7.82 | v5 & gt(loopcounter, n1) = v0 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & % 53.14/7.82 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & ! [v13: $i] : ! [v14: $i] : % 53.14/7.82 | (v14 = init | ~ (a_select2(s_center7_init, v13) = v14) | ~ $i(v13) % 53.14/7.82 | | ? [v15: any] : ? [v16: any] : (leq(v13, n2) = v16 & leq(n0, % 53.14/7.82 | v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v13: $i] : % 53.14/7.82 | ! [v14: $i] : (v14 = init | ~ (a_select2(s_values7_init, v13) = % 53.14/7.82 | v14) | ~ $i(v13) | ? [v15: any] : ? [v16: any] : (leq(v13, % 53.14/7.82 | n3) = v16 & leq(n0, v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = % 53.14/7.82 | 0)))) & ! [v13: $i] : ( ~ (leq(v13, n2) = 0) | ~ $i(v13) | % 53.14/7.82 | ? [v14: int] : ( ~ (v14 = 0) & leq(n0, v13) = v14) | ! [v14: $i] % 53.14/7.82 | : ! [v15: $i] : (v15 = init | ~ (a_select3(simplex7_init, v14, % 53.14/7.82 | v13) = v15) | ~ $i(v14) | ? [v16: any] : ? [v17: any] : % 53.14/7.82 | (leq(v14, n3) = v17 & leq(n0, v14) = v16 & ( ~ (v17 = 0) | ~ % 53.14/7.82 | (v16 = 0))))) & ( ~ (v2 = init) | ~ (v1 = init) | (v5 = 0 & % 53.14/7.82 | ( ~ (v12 = 0) | ? [v13: $i] : ? [v14: $i] : ( ~ (v14 = init) & % 53.14/7.82 | a_select2(s_center7_init, v13) = v14 & leq(v13, n2) = 0 & % 53.14/7.82 | leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? [v13: $i] : ? % 53.14/7.82 | [v14: $i] : ( ~ (v14 = init) & a_select2(s_values7_init, v13) % 53.14/7.82 | = v14 & leq(v13, n3) = 0 & leq(n0, v13) = 0 & $i(v14) & % 53.14/7.82 | $i(v13)) | ? [v13: $i] : (leq(v13, n2) = 0 & leq(n0, v13) = % 53.14/7.82 | 0 & $i(v13) & ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = init) % 53.14/7.82 | & a_select3(simplex7_init, v14, v13) = v15 & leq(v14, n3) % 53.14/7.82 | = 0 & leq(n0, v14) = 0 & $i(v15) & $i(v14))) | (v0 = 0 & ( % 53.14/7.82 | ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 53.14/7.82 | (pvar1400_init = init))))) | ( ~ (v5 = 0) & ( ~ (v6 = % 53.14/7.82 | init) | (v8 = 0 & ( ~ (v12 = 0) | ? [v13: $i] : ? [v14: % 53.14/7.82 | $i] : ( ~ (v14 = init) & a_select2(s_center7_init, v13) % 53.14/7.82 | = v14 & leq(v13, n2) = 0 & leq(n0, v13) = 0 & $i(v14) & % 53.14/7.82 | $i(v13)) | ? [v13: $i] : ? [v14: $i] : ( ~ (v14 = % 53.14/7.82 | init) & a_select2(s_values7_init, v13) = v14 & % 53.14/7.82 | leq(v13, n3) = 0 & leq(n0, v13) = 0 & $i(v14) & $i(v13)) % 53.14/7.82 | | ? [v13: $i] : (leq(v13, n2) = 0 & leq(n0, v13) = 0 & % 53.14/7.82 | $i(v13) & ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = init) % 53.14/7.82 | & a_select3(simplex7_init, v14, v13) = v15 & leq(v14, % 53.14/7.82 | n3) = 0 & leq(n0, v14) = 0 & $i(v15) & $i(v14))) | % 53.14/7.82 | (v0 = 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = % 53.14/7.82 | init) | ~ (pvar1400_init = init))))) | ( ~ (v8 = 0) % 53.14/7.82 | & ( ~ (v9 = init) | (v11 = 0 & ( ~ (v12 = 0) | ? [v13: $i] % 53.14/7.82 | : ? [v14: $i] : ( ~ (v14 = init) & % 53.14/7.82 | a_select2(s_center7_init, v13) = v14 & leq(v13, n2) % 53.14/7.82 | = 0 & leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? % 53.14/7.82 | [v13: $i] : ? [v14: $i] : ( ~ (v14 = init) & % 53.14/7.82 | a_select2(s_values7_init, v13) = v14 & leq(v13, n3) % 53.14/7.82 | = 0 & leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? % 53.14/7.82 | [v13: $i] : (leq(v13, n2) = 0 & leq(n0, v13) = 0 & % 53.14/7.82 | $i(v13) & ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = % 53.14/7.82 | init) & a_select3(simplex7_init, v14, v13) = v15 % 53.14/7.82 | & leq(v14, n3) = 0 & leq(n0, v14) = 0 & $i(v15) & % 53.14/7.82 | $i(v14))) | (v0 = 0 & ( ~ (pvar1402_init = init) | % 53.14/7.82 | ~ (pvar1401_init = init) | ~ (pvar1400_init = % 53.14/7.82 | init))))) | ( ~ (v11 = 0) & ( ? [v13: $i] : ? % 53.14/7.82 | [v14: $i] : ( ~ (v14 = init) & % 53.14/7.82 | a_select2(s_center7_init, v13) = v14 & leq(v13, n2) % 53.14/7.82 | = 0 & leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? % 53.14/7.82 | [v13: $i] : ? [v14: $i] : ( ~ (v14 = init) & % 53.14/7.82 | a_select2(s_values7_init, v13) = v14 & leq(v13, n3) % 53.14/7.82 | = 0 & leq(n0, v13) = 0 & $i(v14) & $i(v13)) | ? % 53.14/7.82 | [v13: $i] : (leq(v13, n2) = 0 & leq(n0, v13) = 0 & % 53.14/7.82 | $i(v13) & ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = % 53.14/7.82 | init) & a_select3(simplex7_init, v14, v13) = v15 % 53.14/7.82 | & leq(v14, n3) = 0 & leq(n0, v14) = 0 & $i(v15) & % 53.14/7.82 | $i(v14))) | (v0 = 0 & ( ~ (pvar1402_init = init) | % 53.14/7.82 | ~ (pvar1401_init = init) | ~ (pvar1400_init = % 53.14/7.82 | init)))))))))) & ( ~ (v0 = 0) | (pvar1402_init = % 53.14/7.82 | init & pvar1401_init = init & pvar1400_init = init))) % 53.14/7.82 | % 53.14/7.82 | ALPHA: (function-axioms) implies: % 53.14/7.82 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 53.14/7.82 | v1) | ~ (succ(v2) = v0)) % 53.14/7.82 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 53.14/7.82 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 53.14/7.82 | v0)) % 53.14/7.82 | % 53.14/7.82 | DELTA: instantiating (6) with fresh symbol all_49_0 gives: % 53.14/7.82 | (16) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0) % 53.14/7.82 | % 53.14/7.82 | ALPHA: (16) implies: % 53.14/7.82 | (17) $i(all_49_0) % 53.14/7.82 | (18) succ(n0) = all_49_0 % 53.14/7.82 | (19) succ(all_49_0) = n2 % 53.14/7.82 | % 53.14/7.82 | DELTA: instantiating (7) with fresh symbols all_51_0, all_51_1 gives: % 53.14/7.82 | (20) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1 % 53.14/7.82 | & $i(all_51_0) & $i(all_51_1) % 53.14/7.82 | % 53.14/7.82 | ALPHA: (20) implies: % 53.14/7.82 | (21) succ(n0) = all_51_1 % 53.14/7.82 | (22) succ(all_51_1) = all_51_0 % 53.14/7.82 | % 53.14/7.82 | DELTA: instantiating (3) with fresh symbols all_53_0, all_53_1, all_53_2 % 53.14/7.82 | gives: % 53.14/7.83 | (23) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) = % 53.14/7.83 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) & % 53.14/7.83 | $i(all_53_2) % 53.14/7.83 | % 53.14/7.83 | ALPHA: (23) implies: % 53.14/7.83 | (24) succ(n0) = all_53_2 % 53.14/7.83 | (25) succ(all_53_2) = all_53_1 % 53.14/7.83 | % 53.14/7.83 | DELTA: instantiating (4) with fresh symbols all_55_0, all_55_1, all_55_2, % 53.14/7.83 | all_55_3 gives: % 53.14/7.83 | (26) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) = % 53.14/7.83 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 & % 53.14/7.83 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) % 53.14/7.83 | % 53.14/7.83 | ALPHA: (26) implies: % 53.14/7.83 | (27) succ(n0) = all_55_3 % 53.14/7.83 | (28) succ(all_55_3) = all_55_2 % 53.14/7.83 | % 53.14/7.83 | DELTA: instantiating (13) with fresh symbols all_76_0, all_76_1, all_76_2, % 53.14/7.83 | all_76_3, all_76_4, all_76_5, all_76_6, all_76_7, all_76_8, all_76_9, % 53.14/7.83 | all_76_10, all_76_11, all_76_12 gives: % 53.14/7.83 | (29) s_worst7_init = init & s_sworst7_init = init & s_best7_init = init & % 53.14/7.83 | a_select2(s_values7, pv1388) = all_76_9 & a_select2(s_values7, % 53.14/7.83 | s_worst7) = all_76_5 & a_select2(s_values7, s_sworst7) = all_76_2 & % 53.14/7.83 | a_select2(s_values7, s_best7) = all_76_8 & a_select2(s_values7_init, % 53.14/7.83 | pv1388) = all_76_10 & a_select2(s_values7_init, s_worst7) = all_76_6 % 53.14/7.83 | & a_select2(s_values7_init, s_sworst7) = all_76_3 & % 53.14/7.83 | a_select2(s_values7_init, s_best7) = all_76_11 & leq(all_76_9, % 53.14/7.83 | all_76_2) = all_76_1 & leq(all_76_9, all_76_5) = all_76_4 & % 53.14/7.83 | leq(pv1388, n3) = 0 & leq(s_worst7, n3) = 0 & leq(s_sworst7, n3) = 0 & % 53.14/7.83 | leq(s_best7, n3) = 0 & leq(n2, pv1388) = 0 & leq(n0, pv1388) = % 53.14/7.83 | all_76_0 & leq(n0, s_worst7) = 0 & leq(n0, s_sworst7) = 0 & leq(n0, % 53.14/7.83 | s_best7) = 0 & gt(all_76_9, all_76_8) = all_76_7 & gt(loopcounter, % 53.14/7.83 | n1) = all_76_12 & $i(all_76_2) & $i(all_76_3) & $i(all_76_5) & % 53.14/7.83 | $i(all_76_6) & $i(all_76_8) & $i(all_76_9) & $i(all_76_10) & % 53.14/7.83 | $i(all_76_11) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 53.14/7.83 | (a_select2(s_center7_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 53.14/7.83 | [v3: any] : (leq(v0, n2) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 53.14/7.83 | (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 53.14/7.83 | (a_select2(s_values7_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 53.14/7.83 | [v3: any] : (leq(v0, n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 53.14/7.83 | (v2 = 0)))) & ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | % 53.14/7.83 | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! % 53.14/7.83 | [v2: $i] : (v2 = init | ~ (a_select3(simplex7_init, v1, v0) = v2) | % 53.14/7.83 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n3) = v4 & % 53.14/7.83 | leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ( ~ % 53.14/7.83 | (all_76_10 = init) | ~ (all_76_11 = init) | (all_76_7 = 0 & ( ~ % 53.14/7.83 | (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.83 | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, % 53.14/7.83 | v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.14/7.83 | (v1 = init) & a_select2(s_values7_init, v0) = v1 & leq(v0, n3) % 53.14/7.83 | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : % 53.14/7.83 | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.14/7.83 | [v2: $i] : ( ~ (v2 = init) & a_select3(simplex7_init, v1, v0) % 53.14/7.83 | = v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 53.14/7.83 | | (all_76_12 = 0 & ( ~ (pvar1402_init = init) | ~ % 53.14/7.83 | (pvar1401_init = init) | ~ (pvar1400_init = init))))) | ( ~ % 53.14/7.83 | (all_76_7 = 0) & ( ~ (all_76_6 = init) | (all_76_4 = 0 & ( ~ % 53.14/7.83 | (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) % 53.14/7.83 | & a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & % 53.14/7.83 | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.14/7.83 | $i] : ( ~ (v1 = init) & a_select2(s_values7_init, v0) = v1 % 53.14/7.83 | & leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | % 53.14/7.83 | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & % 53.14/7.83 | ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.14/7.83 | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 % 53.14/7.83 | & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & % 53.14/7.83 | ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | % 53.14/7.83 | ~ (pvar1400_init = init))))) | ( ~ (all_76_4 = 0) & ( ~ % 53.14/7.83 | (all_76_3 = init) | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? % 53.14/7.83 | [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.83 | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & % 53.14/7.83 | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.14/7.83 | [v1: $i] : ( ~ (v1 = init) & a_select2(s_values7_init, % 53.14/7.83 | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.14/7.83 | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.14/7.83 | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : % 53.14/7.83 | ( ~ (v2 = init) & a_select3(simplex7_init, v1, v0) = % 53.14/7.83 | v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.14/7.83 | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.14/7.83 | init) | ~ (pvar1401_init = init) | ~ % 53.14/7.83 | (pvar1400_init = init))))) | ( ~ (all_76_1 = 0) & ( % 53.14/7.83 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.83 | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & % 53.14/7.84 | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.14/7.84 | [v1: $i] : ( ~ (v1 = init) & a_select2(s_values7_init, % 53.14/7.84 | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.14/7.84 | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.14/7.84 | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : % 53.14/7.84 | ( ~ (v2 = init) & a_select3(simplex7_init, v1, v0) = % 53.14/7.84 | v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.14/7.84 | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.14/7.84 | init) | ~ (pvar1401_init = init) | ~ % 53.14/7.84 | (pvar1400_init = init)))))))))) & ( ~ (all_76_12 = % 53.14/7.84 | 0) | (pvar1402_init = init & pvar1401_init = init & pvar1400_init % 53.14/7.84 | = init)) % 53.14/7.84 | % 53.14/7.84 | ALPHA: (29) implies: % 53.14/7.84 | (30) leq(n0, s_best7) = 0 % 53.14/7.84 | (31) leq(n0, s_sworst7) = 0 % 53.14/7.84 | (32) leq(n0, s_worst7) = 0 % 53.14/7.84 | (33) leq(n0, pv1388) = all_76_0 % 53.14/7.84 | (34) leq(n2, pv1388) = 0 % 53.14/7.84 | (35) leq(s_best7, n3) = 0 % 53.14/7.84 | (36) leq(s_sworst7, n3) = 0 % 53.14/7.84 | (37) leq(s_worst7, n3) = 0 % 53.14/7.84 | (38) leq(pv1388, n3) = 0 % 53.14/7.84 | (39) a_select2(s_values7_init, s_best7) = all_76_11 % 53.14/7.84 | (40) a_select2(s_values7_init, s_sworst7) = all_76_3 % 53.14/7.84 | (41) a_select2(s_values7_init, s_worst7) = all_76_6 % 53.14/7.84 | (42) a_select2(s_values7_init, pv1388) = all_76_10 % 53.14/7.84 | (43) ~ (all_76_12 = 0) | (pvar1402_init = init & pvar1401_init = init & % 53.14/7.84 | pvar1400_init = init) % 53.14/7.84 | (44) ~ (all_76_10 = init) | ~ (all_76_11 = init) | (all_76_7 = 0 & ( ~ % 53.14/7.84 | (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.84 | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, % 53.14/7.84 | v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.14/7.84 | (v1 = init) & a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = % 53.14/7.84 | 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.14/7.84 | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] % 53.14/7.84 | : ( ~ (v2 = init) & a_select3(simplex7_init, v1, v0) = v2 & % 53.14/7.84 | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | % 53.14/7.84 | (all_76_12 = 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = % 53.14/7.84 | init) | ~ (pvar1400_init = init))))) | ( ~ (all_76_7 = 0) & % 53.14/7.84 | ( ~ (all_76_6 = init) | (all_76_4 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.14/7.84 | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.84 | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & % 53.14/7.84 | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.14/7.84 | $i] : ( ~ (v1 = init) & a_select2(s_values7_init, v0) = v1 & % 53.14/7.84 | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.14/7.84 | [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.14/7.84 | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.14/7.84 | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & % 53.14/7.84 | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.14/7.84 | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 53.14/7.84 | (pvar1400_init = init))))) | ( ~ (all_76_4 = 0) & ( ~ % 53.14/7.84 | (all_76_3 = init) | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? % 53.14/7.84 | [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.84 | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & % 53.14/7.84 | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.14/7.84 | [v1: $i] : ( ~ (v1 = init) & a_select2(s_values7_init, v0) % 53.14/7.84 | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.14/7.84 | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = % 53.14/7.84 | 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 53.14/7.84 | & a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) % 53.14/7.84 | = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_12 % 53.14/7.84 | = 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = % 53.14/7.84 | init) | ~ (pvar1400_init = init))))) | ( ~ % 53.14/7.84 | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 53.14/7.84 | init) & a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.14/7.84 | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: % 53.14/7.84 | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.84 | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & % 53.14/7.84 | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : % 53.14/7.84 | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] % 53.14/7.84 | : ? [v2: $i] : ( ~ (v2 = init) & % 53.14/7.84 | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = % 53.14/7.84 | 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_12 = % 53.14/7.84 | 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = % 53.14/7.84 | init) | ~ (pvar1400_init = init))))))))) % 53.14/7.84 | (45) ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 53.14/7.84 | (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = % 53.14/7.84 | init | ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ? % 53.14/7.84 | [v3: any] : ? [v4: any] : (leq(v1, n3) = v4 & leq(n0, v1) = v3 & % 53.14/7.84 | ( ~ (v4 = 0) | ~ (v3 = 0))))) % 53.14/7.84 | (46) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 53.14/7.84 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, % 53.14/7.84 | n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.14/7.84 | (47) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 53.14/7.84 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, % 53.14/7.84 | n2) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.14/7.84 | % 53.14/7.85 | GROUND_INST: instantiating (14) with all_51_1, all_53_2, n0, simplifying with % 53.14/7.85 | (21), (24) gives: % 53.14/7.85 | (48) all_53_2 = all_51_1 % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (14) with all_49_0, all_53_2, n0, simplifying with % 53.14/7.85 | (18), (24) gives: % 53.14/7.85 | (49) all_53_2 = all_49_0 % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (14) with all_53_2, all_55_3, n0, simplifying with % 53.14/7.85 | (24), (27) gives: % 53.14/7.85 | (50) all_55_3 = all_53_2 % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (14) with n1, all_55_3, n0, simplifying with (5), % 53.14/7.85 | (27) gives: % 53.14/7.85 | (51) all_55_3 = n1 % 53.14/7.85 | % 53.14/7.85 | COMBINE_EQS: (50), (51) imply: % 53.14/7.85 | (52) all_53_2 = n1 % 53.14/7.85 | % 53.14/7.85 | SIMP: (52) implies: % 53.14/7.85 | (53) all_53_2 = n1 % 53.14/7.85 | % 53.14/7.85 | COMBINE_EQS: (48), (49) imply: % 53.14/7.85 | (54) all_51_1 = all_49_0 % 53.14/7.85 | % 53.14/7.85 | COMBINE_EQS: (48), (53) imply: % 53.14/7.85 | (55) all_51_1 = n1 % 53.14/7.85 | % 53.14/7.85 | COMBINE_EQS: (54), (55) imply: % 53.14/7.85 | (56) all_49_0 = n1 % 53.14/7.85 | % 53.14/7.85 | SIMP: (56) implies: % 53.14/7.85 | (57) all_49_0 = n1 % 53.14/7.85 | % 53.14/7.85 | REDUCE: (28), (51) imply: % 53.14/7.85 | (58) succ(n1) = all_55_2 % 53.14/7.85 | % 53.14/7.85 | REDUCE: (25), (53) imply: % 53.14/7.85 | (59) succ(n1) = all_53_1 % 53.14/7.85 | % 53.14/7.85 | REDUCE: (22), (55) imply: % 53.14/7.85 | (60) succ(n1) = all_51_0 % 53.14/7.85 | % 53.14/7.85 | REDUCE: (19), (57) imply: % 53.14/7.85 | (61) succ(n1) = n2 % 53.14/7.85 | % 53.14/7.85 | REDUCE: (17), (57) imply: % 53.14/7.85 | (62) $i(n1) % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (14) with all_51_0, all_53_1, n1, simplifying with % 53.14/7.85 | (59), (60) gives: % 53.14/7.85 | (63) all_53_1 = all_51_0 % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (14) with all_53_1, all_55_2, n1, simplifying with % 53.14/7.85 | (58), (59) gives: % 53.14/7.85 | (64) all_55_2 = all_53_1 % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (14) with n2, all_55_2, n1, simplifying with (58), % 53.14/7.85 | (61) gives: % 53.14/7.85 | (65) all_55_2 = n2 % 53.14/7.85 | % 53.14/7.85 | COMBINE_EQS: (64), (65) imply: % 53.14/7.85 | (66) all_53_1 = n2 % 53.14/7.85 | % 53.14/7.85 | SIMP: (66) implies: % 53.14/7.85 | (67) all_53_1 = n2 % 53.14/7.85 | % 53.14/7.85 | COMBINE_EQS: (63), (67) imply: % 53.14/7.85 | (68) all_51_0 = n2 % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (leq_succ_gt) with n1, pv1388, n2, simplifying with % 53.14/7.85 | (12), (34), (61), (62) gives: % 53.14/7.85 | (69) gt(pv1388, n1) = 0 % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (1) with n0, n1, n2, simplifying with (2), (8), % 53.14/7.85 | (61), (62) gives: % 53.14/7.85 | (70) leq(n0, n1) = 0 % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (46) with s_best7, all_76_11, simplifying with (9), % 53.14/7.85 | (39) gives: % 53.14/7.85 | (71) all_76_11 = init | ? [v0: any] : ? [v1: any] : (leq(s_best7, n3) = % 53.14/7.85 | v1 & leq(n0, s_best7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (46) with s_sworst7, all_76_3, simplifying with % 53.14/7.85 | (10), (40) gives: % 53.14/7.85 | (72) all_76_3 = init | ? [v0: any] : ? [v1: any] : (leq(s_sworst7, n3) = % 53.14/7.85 | v1 & leq(n0, s_sworst7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (46) with s_worst7, all_76_6, simplifying with % 53.14/7.85 | (11), (41) gives: % 53.14/7.85 | (73) all_76_6 = init | ? [v0: any] : ? [v1: any] : (leq(s_worst7, n3) = % 53.14/7.85 | v1 & leq(n0, s_worst7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.14/7.85 | % 53.14/7.85 | GROUND_INST: instantiating (46) with pv1388, all_76_10, simplifying with (12), % 53.14/7.85 | (42) gives: % 53.14/7.85 | (74) all_76_10 = init | ? [v0: any] : ? [v1: any] : (leq(pv1388, n3) = v1 % 53.14/7.85 | & leq(n0, pv1388) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.14/7.85 | % 53.14/7.85 | BETA: splitting (73) gives: % 53.14/7.85 | % 53.14/7.85 | Case 1: % 53.14/7.85 | | % 53.14/7.85 | | (75) all_76_6 = init % 53.14/7.85 | | % 53.14/7.85 | | BETA: splitting (72) gives: % 53.14/7.85 | | % 53.14/7.85 | | Case 1: % 53.14/7.85 | | | % 53.14/7.85 | | | (76) all_76_3 = init % 53.14/7.85 | | | % 53.14/7.85 | | | BETA: splitting (71) gives: % 53.14/7.85 | | | % 53.14/7.85 | | | Case 1: % 53.14/7.85 | | | | % 53.14/7.85 | | | | (77) all_76_11 = init % 53.14/7.85 | | | | % 53.14/7.85 | | | | GROUND_INST: instantiating (leq_gt1) with n1, pv1388, simplifying with % 53.14/7.85 | | | | (12), (62), (69) gives: % 53.14/7.85 | | | | (78) leq(n1, pv1388) = 0 % 53.14/7.85 | | | | % 53.14/7.85 | | | | GROUND_INST: instantiating (transitivity_leq) with n0, n1, pv1388, % 53.14/7.85 | | | | all_76_0, simplifying with (8), (12), (33), (62), (70) % 53.14/7.85 | | | | gives: % 53.14/7.85 | | | | (79) all_76_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & leq(n1, pv1388) = % 53.14/7.85 | | | | v0) % 53.14/7.85 | | | | % 53.14/7.85 | | | | BETA: splitting (79) gives: % 53.14/7.85 | | | | % 53.14/7.85 | | | | Case 1: % 53.14/7.85 | | | | | % 53.14/7.85 | | | | | (80) all_76_0 = 0 % 53.14/7.85 | | | | | % 53.14/7.85 | | | | | REDUCE: (33), (80) imply: % 53.14/7.85 | | | | | (81) leq(n0, pv1388) = 0 % 53.14/7.85 | | | | | % 53.14/7.85 | | | | | BETA: splitting (74) gives: % 53.14/7.85 | | | | | % 53.14/7.85 | | | | | Case 1: % 53.14/7.85 | | | | | | % 53.14/7.85 | | | | | | (82) all_76_10 = init % 53.14/7.85 | | | | | | % 53.14/7.85 | | | | | | BETA: splitting (43) gives: % 53.14/7.85 | | | | | | % 53.14/7.85 | | | | | | Case 1: % 53.14/7.85 | | | | | | | % 53.14/7.85 | | | | | | | (83) ~ (all_76_12 = 0) % 53.14/7.85 | | | | | | | % 53.14/7.85 | | | | | | | BETA: splitting (44) gives: % 53.14/7.85 | | | | | | | % 53.14/7.85 | | | | | | | Case 1: % 53.14/7.85 | | | | | | | | % 53.14/7.85 | | | | | | | | (84) ~ (all_76_10 = init) % 53.14/7.85 | | | | | | | | % 53.14/7.85 | | | | | | | | REDUCE: (82), (84) imply: % 53.14/7.85 | | | | | | | | (85) $false % 53.14/7.86 | | | | | | | | % 53.14/7.86 | | | | | | | | CLOSE: (85) is inconsistent. % 53.14/7.86 | | | | | | | | % 53.14/7.86 | | | | | | | Case 2: % 53.14/7.86 | | | | | | | | % 53.14/7.86 | | | | | | | | (86) ~ (all_76_11 = init) | (all_76_7 = 0 & ( ~ (all_76_0 = % 53.14/7.86 | | | | | | | | 0) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = % 53.14/7.86 | | | | | | | | 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: % 53.14/7.86 | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = % 53.14/7.86 | | | | | | | | 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: % 53.14/7.86 | | | | | | | | $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) % 53.14/7.86 | | | | | | | | & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.14/7.86 | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, % 53.14/7.86 | | | | | | | | n3) = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 53.14/7.86 | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = init) | ~ % 53.14/7.86 | | | | | | | | (pvar1401_init = init) | ~ (pvar1400_init = % 53.14/7.86 | | | | | | | | init))))) | ( ~ (all_76_7 = 0) & ( ~ (all_76_6 % 53.14/7.86 | | | | | | | | = init) | (all_76_4 = 0 & ( ~ (all_76_0 = 0) | ? % 53.14/7.86 | | | | | | | | [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.14/7.86 | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.14/7.86 | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.14/7.86 | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.14/7.86 | | | | | | | | | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = % 53.14/7.86 | | | | | | | | 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.14/7.86 | | | | | | | | (v2 = init) & a_select3(simplex7_init, v1, % 53.14/7.86 | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = % 53.14/7.86 | | | | | | | | 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.14/7.86 | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.14/7.86 | | | | | | | | init) | ~ (pvar1400_init = init))))) | ( % 53.14/7.86 | | | | | | | | ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.14/7.86 | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] % 53.14/7.86 | | | | | | | | : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.14/7.86 | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.14/7.86 | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( % 53.14/7.86 | | | | | | | | ~ (v1 = init) & a_select2(s_values7_init, % 53.14/7.86 | | | | | | | | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) % 53.14/7.86 | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : % 53.14/7.86 | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) % 53.14/7.86 | | | | | | | | & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.14/7.86 | | | | | | | | init) & a_select3(simplex7_init, v1, % 53.14/7.86 | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, % 53.14/7.86 | | | | | | | | v1) = 0 & $i(v2) & $i(v1))) | % 53.14/7.86 | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = init) % 53.14/7.86 | | | | | | | | | ~ (pvar1401_init = init) | ~ % 53.14/7.86 | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.14/7.86 | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : % 53.14/7.86 | | | | | | | | ( ~ (v1 = init) & a_select2(s_center7_init, % 53.14/7.86 | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) % 53.14/7.86 | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.14/7.86 | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.14/7.86 | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.14/7.86 | | | | | | | | & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 % 53.14/7.86 | | | | | | | | & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : % 53.14/7.86 | | | | | | | | ? [v2: $i] : ( ~ (v2 = init) & % 53.14/7.86 | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.14/7.86 | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.14/7.86 | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.14/7.86 | | | | | | | | (pvar1402_init = init) | ~ % 53.14/7.86 | | | | | | | | (pvar1401_init = init) | ~ % 53.14/7.86 | | | | | | | | (pvar1400_init = init))))))))) % 53.14/7.86 | | | | | | | | % 53.14/7.86 | | | | | | | | BETA: splitting (86) gives: % 53.14/7.86 | | | | | | | | % 53.14/7.86 | | | | | | | | Case 1: % 53.14/7.86 | | | | | | | | | % 53.14/7.86 | | | | | | | | | (87) ~ (all_76_11 = init) % 53.14/7.86 | | | | | | | | | % 53.14/7.86 | | | | | | | | | REDUCE: (77), (87) imply: % 53.14/7.86 | | | | | | | | | (88) $false % 53.14/7.86 | | | | | | | | | % 53.14/7.86 | | | | | | | | | CLOSE: (88) is inconsistent. % 53.14/7.86 | | | | | | | | | % 53.14/7.86 | | | | | | | | Case 2: % 53.14/7.86 | | | | | | | | | % 53.14/7.86 | | | | | | | | | (89) (all_76_7 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : ? % 53.14/7.86 | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) % 53.14/7.86 | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.14/7.86 | | | | | | | | | [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) % 53.14/7.86 | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.14/7.86 | | | | | | | | | [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.14/7.86 | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.14/7.86 | | | | | | | | | init) & a_select3(simplex7_init, v1, v0) = % 53.14/7.86 | | | | | | | | | v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.14/7.86 | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.14/7.86 | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.14/7.86 | | | | | | | | | init) | ~ (pvar1400_init = init))))) | ( ~ % 53.14/7.86 | | | | | | | | | (all_76_7 = 0) & ( ~ (all_76_6 = init) | (all_76_4 = % 53.14/7.86 | | | | | | | | | 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : ? [v1: % 53.14/7.86 | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.14/7.86 | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.14/7.86 | | | | | | | | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.14/7.86 | | | | | | | | | (v1 = init) & a_select2(s_values7_init, v0) % 53.14/7.86 | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.14/7.86 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.14/7.86 | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.14/7.86 | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.14/7.86 | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.14/7.86 | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.14/7.86 | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.14/7.86 | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.14/7.86 | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.14/7.86 | | | | | | | | | | ( ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.14/7.86 | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.14/7.86 | | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.14/7.86 | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.14/7.86 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.14/7.86 | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.14/7.86 | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.14/7.86 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.14/7.86 | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.14/7.86 | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.14/7.86 | | | | | | | | | (v2 = init) & a_select3(simplex7_init, % 53.14/7.86 | | | | | | | | | v1, v0) = v2 & leq(v1, n3) = 0 & % 53.14/7.86 | | | | | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | % 53.14/7.86 | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.14/7.86 | | | | | | | | | init) | ~ (pvar1401_init = init) | % 53.14/7.86 | | | | | | | | | ~ (pvar1400_init = init))))) | ( ~ % 53.14/7.86 | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.14/7.86 | | | | | | | | | : ( ~ (v1 = init) & % 53.14/7.86 | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.14/7.86 | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.14/7.87 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.14/7.87 | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.14/7.87 | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.14/7.87 | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.14/7.87 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.14/7.87 | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.14/7.87 | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.14/7.87 | | | | | | | | | (v2 = init) & a_select3(simplex7_init, % 53.14/7.87 | | | | | | | | | v1, v0) = v2 & leq(v1, n3) = 0 & % 53.14/7.87 | | | | | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | % 53.14/7.87 | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.14/7.87 | | | | | | | | | init) | ~ (pvar1401_init = init) | % 53.14/7.87 | | | | | | | | | ~ (pvar1400_init = init))))))))) % 53.14/7.87 | | | | | | | | | % 53.14/7.87 | | | | | | | | | BETA: splitting (89) gives: % 53.14/7.87 | | | | | | | | | % 53.14/7.87 | | | | | | | | | Case 1: % 53.14/7.87 | | | | | | | | | | % 53.14/7.87 | | | | | | | | | | (90) all_76_7 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : ? % 53.14/7.87 | | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.14/7.87 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) % 53.14/7.87 | | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.14/7.87 | | | | | | | | | | [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.14/7.87 | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) % 53.14/7.87 | | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.14/7.87 | | | | | | | | | | [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.14/7.87 | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.14/7.87 | | | | | | | | | | init) & a_select3(simplex7_init, v1, v0) = % 53.14/7.87 | | | | | | | | | | v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.14/7.87 | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.14/7.87 | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.14/7.87 | | | | | | | | | | init) | ~ (pvar1400_init = init)))) % 53.14/7.87 | | | | | | | | | | % 53.14/7.87 | | | | | | | | | | ALPHA: (90) implies: % 53.14/7.87 | | | | | | | | | | (91) all_76_7 = 0 % 53.14/7.87 | | | | | | | | | | % 53.14/7.87 | | | | | | | | | | BETA: splitting (89) gives: % 53.14/7.87 | | | | | | | | | | % 53.14/7.87 | | | | | | | | | | Case 1: % 53.14/7.87 | | | | | | | | | | | % 53.14/7.87 | | | | | | | | | | | % 53.14/7.87 | | | | | | | | | | | ALPHA: (90) implies: % 53.14/7.87 | | | | | | | | | | | (92) ~ (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( % 53.14/7.87 | | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, v0) = % 53.14/7.87 | | | | | | | | | | | v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.14/7.87 | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 % 53.14/7.87 | | | | | | | | | | | = init) & a_select2(s_values7_init, v0) = v1 & % 53.14/7.87 | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.14/7.87 | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.14/7.87 | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 53.14/7.87 | | | | | | | | | | | $i] : ( ~ (v2 = init) & % 53.14/7.87 | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.14/7.87 | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.14/7.87 | | | | | | | | | | | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init % 53.14/7.87 | | | | | | | | | | | = init) | ~ (pvar1401_init = init) | ~ % 53.14/7.87 | | | | | | | | | | | (pvar1400_init = init))) % 53.14/7.87 | | | | | | | | | | | % 53.14/7.87 | | | | | | | | | | | REF_CLOSE: (15), (45), (46), (47), (80), (83), (92) are % 53.14/7.87 | | | | | | | | | | | inconsistent by sub-proof #3. % 53.14/7.87 | | | | | | | | | | | % 53.14/7.87 | | | | | | | | | | Case 2: % 53.14/7.87 | | | | | | | | | | | % 53.55/7.87 | | | | | | | | | | | (93) ~ (all_76_7 = 0) & ( ~ (all_76_6 = init) | % 53.55/7.87 | | | | | | | | | | | (all_76_4 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] % 53.55/7.87 | | | | | | | | | | | : ? [v1: $i] : ( ~ (v1 = init) & % 53.55/7.87 | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.55/7.87 | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.55/7.87 | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( % 53.55/7.87 | | | | | | | | | | | ~ (v1 = init) & a_select2(s_values7_init, % 53.55/7.87 | | | | | | | | | | | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) % 53.55/7.87 | | | | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : % 53.55/7.87 | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) % 53.55/7.87 | | | | | | | | | | | & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.55/7.87 | | | | | | | | | | | init) & a_select3(simplex7_init, v1, % 53.55/7.87 | | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, % 53.55/7.87 | | | | | | | | | | | v1) = 0 & $i(v2) & $i(v1))) | % 53.55/7.87 | | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = init) % 53.55/7.87 | | | | | | | | | | | | ~ (pvar1401_init = init) | ~ % 53.55/7.87 | | | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.55/7.87 | | | | | | | | | | | (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.55/7.87 | | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.55/7.87 | | | | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.55/7.87 | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.55/7.87 | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.55/7.87 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.55/7.87 | | | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.55/7.87 | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.55/7.87 | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.55/7.87 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.55/7.87 | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.55/7.87 | | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( % 53.55/7.87 | | | | | | | | | | | ~ (v2 = init) & % 53.55/7.87 | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = % 53.55/7.87 | | | | | | | | | | | v2 & leq(v1, n3) = 0 & leq(n0, v1) = % 53.55/7.87 | | | | | | | | | | | 0 & $i(v2) & $i(v1))) | (all_76_12 = % 53.55/7.87 | | | | | | | | | | | 0 & ( ~ (pvar1402_init = init) | ~ % 53.55/7.87 | | | | | | | | | | | (pvar1401_init = init) | ~ % 53.55/7.87 | | | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.55/7.87 | | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: % 53.55/7.87 | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.55/7.87 | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.55/7.87 | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.55/7.87 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.55/7.87 | | | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.55/7.87 | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.55/7.87 | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.55/7.87 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.55/7.87 | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.55/7.87 | | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( % 53.55/7.87 | | | | | | | | | | | ~ (v2 = init) & % 53.55/7.87 | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = % 53.55/7.87 | | | | | | | | | | | v2 & leq(v1, n3) = 0 & leq(n0, v1) = % 53.55/7.87 | | | | | | | | | | | 0 & $i(v2) & $i(v1))) | (all_76_12 = % 53.55/7.87 | | | | | | | | | | | 0 & ( ~ (pvar1402_init = init) | ~ % 53.55/7.87 | | | | | | | | | | | (pvar1401_init = init) | ~ % 53.55/7.87 | | | | | | | | | | | (pvar1400_init = init)))))))) % 53.55/7.87 | | | | | | | | | | | % 53.55/7.87 | | | | | | | | | | | ALPHA: (93) implies: % 53.55/7.87 | | | | | | | | | | | (94) ~ (all_76_7 = 0) % 53.55/7.87 | | | | | | | | | | | % 53.55/7.87 | | | | | | | | | | | REDUCE: (91), (94) imply: % 53.55/7.87 | | | | | | | | | | | (95) $false % 53.55/7.87 | | | | | | | | | | | % 53.55/7.87 | | | | | | | | | | | CLOSE: (95) is inconsistent. % 53.55/7.87 | | | | | | | | | | | % 53.55/7.87 | | | | | | | | | | End of split % 53.55/7.87 | | | | | | | | | | % 53.55/7.87 | | | | | | | | | Case 2: % 53.55/7.87 | | | | | | | | | | % 53.55/7.88 | | | | | | | | | | (96) ~ (all_76_7 = 0) & ( ~ (all_76_6 = init) | % 53.55/7.88 | | | | | | | | | | (all_76_4 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.55/7.88 | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.55/7.88 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.55/7.88 | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.55/7.88 | | | | | | | | | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.55/7.88 | | | | | | | | | | (v1 = init) & a_select2(s_values7_init, v0) % 53.55/7.88 | | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.55/7.88 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.55/7.88 | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.55/7.88 | | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.55/7.88 | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.55/7.88 | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.55/7.88 | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.55/7.88 | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.55/7.88 | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.55/7.88 | | | | | | | | | | | ( ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.55/7.88 | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.55/7.88 | | | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.55/7.88 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.55/7.88 | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.55/7.88 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.55/7.88 | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.55/7.88 | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.55/7.88 | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.55/7.88 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.55/7.88 | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.55/7.88 | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.55/7.88 | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, % 53.55/7.88 | | | | | | | | | | v1, v0) = v2 & leq(v1, n3) = 0 & % 53.55/7.88 | | | | | | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | % 53.55/7.88 | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.55/7.88 | | | | | | | | | | init) | ~ (pvar1401_init = init) | % 53.55/7.88 | | | | | | | | | | ~ (pvar1400_init = init))))) | ( ~ % 53.55/7.88 | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.55/7.88 | | | | | | | | | | : ( ~ (v1 = init) & % 53.55/7.88 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.55/7.88 | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.55/7.88 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.55/7.88 | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.55/7.88 | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.55/7.88 | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.55/7.88 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.55/7.88 | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.55/7.88 | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.55/7.88 | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, % 53.55/7.88 | | | | | | | | | | v1, v0) = v2 & leq(v1, n3) = 0 & % 53.55/7.88 | | | | | | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | % 53.55/7.88 | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.55/7.88 | | | | | | | | | | init) | ~ (pvar1401_init = init) | % 53.55/7.88 | | | | | | | | | | ~ (pvar1400_init = init)))))))) % 53.55/7.88 | | | | | | | | | | % 53.55/7.88 | | | | | | | | | | ALPHA: (96) implies: % 53.55/7.88 | | | | | | | | | | (97) ~ (all_76_6 = init) | (all_76_4 = 0 & ( ~ (all_76_0 % 53.55/7.88 | | | | | | | | | | = 0) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 53.55/7.88 | | | | | | | | | | init) & a_select2(s_center7_init, v0) = v1 & % 53.55/7.88 | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.55/7.88 | | | | | | | | | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 % 53.55/7.88 | | | | | | | | | | = init) & a_select2(s_values7_init, v0) = v1 % 53.55/7.88 | | | | | | | | | | & leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.55/7.88 | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.55/7.88 | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.55/7.88 | | | | | | | | | | [v2: $i] : ( ~ (v2 = init) & % 53.55/7.88 | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.55/7.88 | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.55/7.88 | | | | | | | | | | $i(v1))) | (all_76_12 = 0 & ( ~ % 53.55/7.88 | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.55/7.88 | | | | | | | | | | init) | ~ (pvar1400_init = init))))) | ( % 53.55/7.88 | | | | | | | | | | ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.55/7.88 | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] % 53.55/7.88 | | | | | | | | | | : ? [v1: $i] : ( ~ (v1 = init) & % 53.55/7.88 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.55/7.88 | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.55/7.88 | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( % 53.55/7.88 | | | | | | | | | | ~ (v1 = init) & a_select2(s_values7_init, % 53.55/7.88 | | | | | | | | | | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) % 53.55/7.88 | | | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : % 53.55/7.88 | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) % 53.55/7.88 | | | | | | | | | | & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.55/7.88 | | | | | | | | | | init) & a_select3(simplex7_init, v1, % 53.55/7.88 | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, % 53.55/7.88 | | | | | | | | | | v1) = 0 & $i(v2) & $i(v1))) | % 53.55/7.88 | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = init) % 53.55/7.88 | | | | | | | | | | | ~ (pvar1401_init = init) | ~ % 53.55/7.88 | | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.55/7.88 | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : % 53.55/7.88 | | | | | | | | | | ( ~ (v1 = init) & a_select2(s_center7_init, % 53.55/7.88 | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) % 53.55/7.88 | | | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.55/7.88 | | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.55/7.88 | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.55/7.88 | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.55/7.88 | | | | | | | | | | & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 % 53.55/7.88 | | | | | | | | | | & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : % 53.55/7.88 | | | | | | | | | | ? [v2: $i] : ( ~ (v2 = init) & % 53.55/7.88 | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.55/7.88 | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.55/7.88 | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.55/7.88 | | | | | | | | | | (pvar1402_init = init) | ~ % 53.55/7.88 | | | | | | | | | | (pvar1401_init = init) | ~ % 53.55/7.88 | | | | | | | | | | (pvar1400_init = init))))))) % 53.55/7.88 | | | | | | | | | | % 53.55/7.88 | | | | | | | | | | BETA: splitting (97) gives: % 53.55/7.88 | | | | | | | | | | % 53.55/7.88 | | | | | | | | | | Case 1: % 53.55/7.88 | | | | | | | | | | | % 53.55/7.88 | | | | | | | | | | | (98) ~ (all_76_6 = init) % 53.55/7.88 | | | | | | | | | | | % 53.55/7.88 | | | | | | | | | | | REDUCE: (75), (98) imply: % 53.55/7.88 | | | | | | | | | | | (99) $false % 53.55/7.88 | | | | | | | | | | | % 53.55/7.88 | | | | | | | | | | | CLOSE: (99) is inconsistent. % 53.55/7.88 | | | | | | | | | | | % 53.55/7.88 | | | | | | | | | | Case 2: % 53.55/7.88 | | | | | | | | | | | % 53.60/7.88 | | | | | | | | | | | (100) (all_76_4 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.60/7.88 | | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.88 | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.88 | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.88 | | | | | | | | | | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.60/7.88 | | | | | | | | | | | (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.88 | | | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.88 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.88 | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.88 | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.88 | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.88 | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.88 | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.88 | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.88 | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.88 | | | | | | | | | | | | ( ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.60/7.88 | | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.60/7.88 | | | | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.88 | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.88 | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.88 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.88 | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.88 | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.88 | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.88 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.88 | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.88 | | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.88 | | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, % 53.60/7.88 | | | | | | | | | | | v1, v0) = v2 & leq(v1, n3) = 0 & % 53.60/7.88 | | | | | | | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | % 53.60/7.88 | | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.60/7.88 | | | | | | | | | | | init) | ~ (pvar1401_init = init) | % 53.60/7.88 | | | | | | | | | | | ~ (pvar1400_init = init))))) | ( ~ % 53.60/7.88 | | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.60/7.88 | | | | | | | | | | | : ( ~ (v1 = init) & % 53.60/7.88 | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.88 | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.88 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.88 | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.88 | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.88 | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.88 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.88 | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.88 | | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.88 | | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, % 53.60/7.88 | | | | | | | | | | | v1, v0) = v2 & leq(v1, n3) = 0 & % 53.60/7.88 | | | | | | | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | % 53.60/7.88 | | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.60/7.88 | | | | | | | | | | | init) | ~ (pvar1401_init = init) | % 53.60/7.88 | | | | | | | | | | | ~ (pvar1400_init = init))))))) % 53.60/7.88 | | | | | | | | | | | % 53.60/7.88 | | | | | | | | | | | BETA: splitting (100) gives: % 53.60/7.88 | | | | | | | | | | | % 53.60/7.88 | | | | | | | | | | | Case 1: % 53.60/7.88 | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | (101) all_76_4 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.60/7.89 | | | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.89 | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.89 | | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.89 | | | | | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.89 | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.89 | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.89 | | | | | | | | | | | | | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.89 | | | | | | | | | | | | 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.89 | | | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, v1, % 53.60/7.89 | | | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = % 53.60/7.89 | | | | | | | | | | | | 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.89 | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.89 | | | | | | | | | | | | init) | ~ (pvar1400_init = init)))) % 53.60/7.89 | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | ALPHA: (101) implies: % 53.60/7.89 | | | | | | | | | | | | (102) all_76_4 = 0 % 53.60/7.89 | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | BETA: splitting (100) gives: % 53.60/7.89 | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | Case 1: % 53.60/7.89 | | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | | ALPHA: (101) implies: % 53.60/7.89 | | | | | | | | | | | | | (103) ~ (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.89 | | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, v0) = % 53.60/7.89 | | | | | | | | | | | | | v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.89 | | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 % 53.60/7.89 | | | | | | | | | | | | | = init) & a_select2(s_values7_init, v0) = v1 & % 53.60/7.89 | | | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.89 | | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.89 | | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 53.60/7.89 | | | | | | | | | | | | | $i] : ( ~ (v2 = init) & % 53.60/7.89 | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.89 | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.60/7.89 | | | | | | | | | | | | | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init % 53.60/7.89 | | | | | | | | | | | | | = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.89 | | | | | | | | | | | | | (pvar1400_init = init))) % 53.60/7.89 | | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | | REF_CLOSE: (15), (45), (46), (47), (80), (83), (103) are % 53.60/7.89 | | | | | | | | | | | | | inconsistent by sub-proof #3. % 53.60/7.89 | | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | Case 2: % 53.60/7.89 | | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | | (104) ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.60/7.89 | | | | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] % 53.60/7.89 | | | | | | | | | | | | | : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.89 | | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.89 | | | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.89 | | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.89 | | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_values7_init, % 53.60/7.89 | | | | | | | | | | | | | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) % 53.60/7.89 | | | | | | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.89 | | | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) % 53.60/7.89 | | | | | | | | | | | | | & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.60/7.89 | | | | | | | | | | | | | init) & a_select3(simplex7_init, v1, % 53.60/7.89 | | | | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, % 53.60/7.89 | | | | | | | | | | | | | v1) = 0 & $i(v2) & $i(v1))) | % 53.60/7.89 | | | | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = init) % 53.60/7.89 | | | | | | | | | | | | | | ~ (pvar1401_init = init) | ~ % 53.60/7.89 | | | | | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.60/7.89 | | | | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : % 53.60/7.89 | | | | | | | | | | | | | ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.89 | | | | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) % 53.60/7.89 | | | | | | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.60/7.89 | | | | | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.60/7.89 | | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.89 | | | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.89 | | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 % 53.60/7.89 | | | | | | | | | | | | | & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : % 53.60/7.89 | | | | | | | | | | | | | ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.89 | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.89 | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.89 | | | | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.89 | | | | | | | | | | | | | (pvar1402_init = init) | ~ % 53.60/7.89 | | | | | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.89 | | | | | | | | | | | | | (pvar1400_init = init)))))) % 53.60/7.89 | | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | | ALPHA: (104) implies: % 53.60/7.89 | | | | | | | | | | | | | (105) ~ (all_76_4 = 0) % 53.60/7.89 | | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | | REDUCE: (102), (105) imply: % 53.60/7.89 | | | | | | | | | | | | | (106) $false % 53.60/7.89 | | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | | CLOSE: (106) is inconsistent. % 53.60/7.89 | | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | End of split % 53.60/7.89 | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | Case 2: % 53.60/7.89 | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | (107) ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.60/7.89 | | | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] % 53.60/7.89 | | | | | | | | | | | | : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.89 | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.89 | | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.89 | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.89 | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_values7_init, % 53.60/7.89 | | | | | | | | | | | | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) % 53.60/7.89 | | | | | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.89 | | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) % 53.60/7.89 | | | | | | | | | | | | & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.60/7.89 | | | | | | | | | | | | init) & a_select3(simplex7_init, v1, % 53.60/7.89 | | | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, % 53.60/7.89 | | | | | | | | | | | | v1) = 0 & $i(v2) & $i(v1))) | % 53.60/7.89 | | | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = init) % 53.60/7.89 | | | | | | | | | | | | | ~ (pvar1401_init = init) | ~ % 53.60/7.89 | | | | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.60/7.89 | | | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : % 53.60/7.89 | | | | | | | | | | | | ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.89 | | | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) % 53.60/7.89 | | | | | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.60/7.89 | | | | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.60/7.89 | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.89 | | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.89 | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 % 53.60/7.89 | | | | | | | | | | | | & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : % 53.60/7.89 | | | | | | | | | | | | ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.89 | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.89 | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.89 | | | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.89 | | | | | | | | | | | | (pvar1402_init = init) | ~ % 53.60/7.89 | | | | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.89 | | | | | | | | | | | | (pvar1400_init = init)))))) % 53.60/7.89 | | | | | | | | | | | | % 53.60/7.89 | | | | | | | | | | | | ALPHA: (107) implies: % 53.60/7.89 | | | | | | | | | | | | (108) ~ (all_76_3 = init) | (all_76_1 = 0 & ( ~ % 53.60/7.89 | | | | | | | | | | | | (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.89 | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.89 | | | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.89 | | | | | | | | | | | | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.89 | | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.89 | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.89 | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.89 | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.89 | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.60/7.89 | | | | | | | | | | | | [v2: $i] : ( ~ (v2 = init) & % 53.60/7.89 | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.89 | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.89 | | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.89 | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.89 | | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.89 | | | | | | | | | | | | | ( ~ (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.60/7.89 | | | | | | | | | | | | : ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.89 | | | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.89 | | | | | | | | | | | | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.89 | | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.90 | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.90 | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.90 | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.90 | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.60/7.90 | | | | | | | | | | | | [v2: $i] : ( ~ (v2 = init) & % 53.60/7.90 | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.90 | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.90 | | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.90 | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.90 | | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.90 | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | BETA: splitting (108) gives: % 53.60/7.90 | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | Case 1: % 53.60/7.90 | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | (109) ~ (all_76_3 = init) % 53.60/7.90 | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | REDUCE: (76), (109) imply: % 53.60/7.90 | | | | | | | | | | | | | (110) $false % 53.60/7.90 | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | CLOSE: (110) is inconsistent. % 53.60/7.90 | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | Case 2: % 53.60/7.90 | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | (111) (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.60/7.90 | | | | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.90 | | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.90 | | | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.90 | | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.60/7.90 | | | | | | | | | | | | | (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.90 | | | | | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.90 | | | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.90 | | | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.90 | | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.90 | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.90 | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.90 | | | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.90 | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.90 | | | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.90 | | | | | | | | | | | | | | ( ~ (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.60/7.90 | | | | | | | | | | | | | : ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.90 | | | | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.90 | | | | | | | | | | | | | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.90 | | | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.90 | | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.90 | | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.90 | | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.90 | | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.60/7.90 | | | | | | | | | | | | | [v2: $i] : ( ~ (v2 = init) & % 53.60/7.90 | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.90 | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.90 | | | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.90 | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.90 | | | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.90 | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | BETA: splitting (111) gives: % 53.60/7.90 | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | Case 1: % 53.60/7.90 | | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | | (112) all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.60/7.90 | | | | | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.90 | | | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.90 | | | | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.90 | | | | | | | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.90 | | | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.90 | | | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.90 | | | | | | | | | | | | | | | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.90 | | | | | | | | | | | | | | 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.90 | | | | | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, v1, % 53.60/7.90 | | | | | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = % 53.60/7.90 | | | | | | | | | | | | | | 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.90 | | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.90 | | | | | | | | | | | | | | init) | ~ (pvar1400_init = init)))) % 53.60/7.90 | | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | | ALPHA: (112) implies: % 53.60/7.90 | | | | | | | | | | | | | | (113) ~ (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.90 | | | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, v0) = % 53.60/7.90 | | | | | | | | | | | | | | v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.90 | | | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 % 53.60/7.90 | | | | | | | | | | | | | | = init) & a_select2(s_values7_init, v0) = v1 & % 53.60/7.90 | | | | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.90 | | | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.90 | | | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 53.60/7.90 | | | | | | | | | | | | | | $i] : ( ~ (v2 = init) & % 53.60/7.90 | | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.90 | | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.60/7.90 | | | | | | | | | | | | | | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init % 53.60/7.90 | | | | | | | | | | | | | | = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.90 | | | | | | | | | | | | | | (pvar1400_init = init))) % 53.60/7.90 | | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | | REF_CLOSE: (15), (45), (46), (47), (80), (83), (113) are % 53.60/7.90 | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 53.60/7.90 | | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | Case 2: % 53.60/7.90 | | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | | (114) ~ (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.90 | | | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, v0) % 53.60/7.90 | | | | | | | | | | | | | | = v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.90 | | | | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 53.60/7.90 | | | | | | | | | | | | | | ( ~ (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.90 | | | | | | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.90 | | | | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) % 53.60/7.90 | | | | | | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : % 53.60/7.90 | | | | | | | | | | | | | | ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.90 | | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.90 | | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.60/7.90 | | | | | | | | | | | | | | $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.90 | | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.90 | | | | | | | | | | | | | | init) | ~ (pvar1400_init = init)))) % 53.60/7.90 | | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | | ALPHA: (114) implies: % 53.60/7.90 | | | | | | | | | | | | | | (115) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.90 | | | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) % 53.60/7.90 | | | | | | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.60/7.90 | | | | | | | | | | | | | | [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.90 | | | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) % 53.60/7.90 | | | | | | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.60/7.90 | | | | | | | | | | | | | | [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.90 | | | | | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.60/7.90 | | | | | | | | | | | | | | init) & a_select3(simplex7_init, v1, v0) = % 53.60/7.90 | | | | | | | | | | | | | | v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.90 | | | | | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.90 | | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.90 | | | | | | | | | | | | | | init) | ~ (pvar1400_init = init))) % 53.60/7.90 | | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | | REF_CLOSE: (15), (45), (46), (47), (83), (115) are % 53.60/7.90 | | | | | | | | | | | | | | inconsistent by sub-proof #4. % 53.60/7.90 | | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | | End of split % 53.60/7.90 | | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | | End of split % 53.60/7.90 | | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | | End of split % 53.60/7.90 | | | | | | | | | | | % 53.60/7.90 | | | | | | | | | | End of split % 53.60/7.90 | | | | | | | | | | % 53.60/7.90 | | | | | | | | | End of split % 53.60/7.90 | | | | | | | | | % 53.60/7.90 | | | | | | | | End of split % 53.60/7.90 | | | | | | | | % 53.60/7.90 | | | | | | | End of split % 53.60/7.90 | | | | | | | % 53.60/7.90 | | | | | | Case 2: % 53.60/7.90 | | | | | | | % 53.60/7.90 | | | | | | | (116) pvar1402_init = init & pvar1401_init = init & % 53.60/7.90 | | | | | | | pvar1400_init = init % 53.60/7.90 | | | | | | | % 53.60/7.90 | | | | | | | ALPHA: (116) implies: % 53.60/7.90 | | | | | | | (117) pvar1400_init = init % 53.60/7.90 | | | | | | | (118) pvar1401_init = init % 53.60/7.90 | | | | | | | (119) pvar1402_init = init % 53.60/7.90 | | | | | | | % 53.60/7.90 | | | | | | | BETA: splitting (44) gives: % 53.60/7.90 | | | | | | | % 53.60/7.90 | | | | | | | Case 1: % 53.60/7.90 | | | | | | | | % 53.60/7.90 | | | | | | | | (120) ~ (all_76_10 = init) % 53.60/7.90 | | | | | | | | % 53.60/7.90 | | | | | | | | REDUCE: (82), (120) imply: % 53.60/7.90 | | | | | | | | (121) $false % 53.60/7.90 | | | | | | | | % 53.60/7.90 | | | | | | | | CLOSE: (121) is inconsistent. % 53.60/7.90 | | | | | | | | % 53.60/7.90 | | | | | | | Case 2: % 53.60/7.90 | | | | | | | | % 53.60/7.91 | | | | | | | | (122) ~ (all_76_11 = init) | (all_76_7 = 0 & ( ~ (all_76_0 = % 53.60/7.91 | | | | | | | | 0) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) % 53.60/7.91 | | | | | | | | & a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.91 | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | % 53.60/7.91 | | | | | | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) % 53.60/7.91 | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.60/7.91 | | | | | | | | [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.60/7.91 | | | | | | | | init) & a_select3(simplex7_init, v1, v0) = v2 % 53.60/7.91 | | | | | | | | & leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.60/7.91 | | | | | | | | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init % 53.60/7.91 | | | | | | | | = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.91 | | | | | | | | (pvar1400_init = init))))) | ( ~ (all_76_7 = 0) % 53.60/7.91 | | | | | | | | & ( ~ (all_76_6 = init) | (all_76_4 = 0 & ( ~ % 53.60/7.91 | | | | | | | | (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.91 | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, v0) % 53.60/7.91 | | | | | | | | = v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] % 53.60/7.91 | | | | | | | | : ( ~ (v1 = init) & a_select2(s_values7_init, % 53.60/7.91 | | | | | | | | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = % 53.60/7.91 | | | | | | | | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.91 | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.91 | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.91 | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.91 | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.91 | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.91 | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.91 | | | | | | | | = init) | ~ (pvar1400_init = init))))) | % 53.60/7.91 | | | | | | | | ( ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.60/7.91 | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.60/7.91 | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.91 | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.91 | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.91 | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.91 | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.91 | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 53.60/7.91 | | | | | | | | & a_select3(simplex7_init, v1, v0) = v2 % 53.60/7.91 | | | | | | | | & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.91 | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( % 53.60/7.91 | | | | | | | | ~ (pvar1402_init = init) | ~ % 53.60/7.91 | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.91 | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.60/7.91 | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : % 53.60/7.91 | | | | | | | | ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.91 | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, % 53.60/7.91 | | | | | | | | v0) = 0 & $i(v1) & $i(v0)) | ? [v0: % 53.60/7.91 | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.91 | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.91 | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.91 | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 53.60/7.91 | | | | | | | | & a_select3(simplex7_init, v1, v0) = v2 % 53.60/7.91 | | | | | | | | & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.91 | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( % 53.60/7.91 | | | | | | | | ~ (pvar1402_init = init) | ~ % 53.60/7.91 | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.91 | | | | | | | | (pvar1400_init = init))))))))) % 53.60/7.91 | | | | | | | | % 53.60/7.91 | | | | | | | | BETA: splitting (122) gives: % 53.60/7.91 | | | | | | | | % 53.60/7.91 | | | | | | | | Case 1: % 53.60/7.91 | | | | | | | | | % 53.60/7.91 | | | | | | | | | (123) ~ (all_76_11 = init) % 53.60/7.91 | | | | | | | | | % 53.60/7.91 | | | | | | | | | REDUCE: (77), (123) imply: % 53.60/7.91 | | | | | | | | | (124) $false % 53.60/7.91 | | | | | | | | | % 53.60/7.91 | | | | | | | | | CLOSE: (124) is inconsistent. % 53.60/7.91 | | | | | | | | | % 53.60/7.91 | | | | | | | | Case 2: % 53.60/7.91 | | | | | | | | | % 53.60/7.91 | | | | | | | | | (125) (all_76_7 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : ? % 53.60/7.91 | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.91 | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.91 | | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.91 | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.91 | | | | | | | | | | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.91 | | | | | | | | | 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.91 | | | | | | | | | (v2 = init) & a_select3(simplex7_init, v1, % 53.60/7.91 | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = % 53.60/7.91 | | | | | | | | | 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.91 | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.91 | | | | | | | | | init) | ~ (pvar1400_init = init))))) | ( ~ % 53.60/7.91 | | | | | | | | | (all_76_7 = 0) & ( ~ (all_76_6 = init) | (all_76_4 % 53.60/7.91 | | | | | | | | | = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : ? % 53.60/7.91 | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.91 | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.91 | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.60/7.91 | | | | | | | | | (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.91 | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.91 | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.91 | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.91 | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.91 | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.91 | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.91 | | | | | | | | | (pvar1402_init = init) | ~ % 53.60/7.91 | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.91 | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.60/7.91 | | | | | | | | | (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.60/7.91 | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.60/7.91 | | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.91 | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.60/7.91 | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.91 | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.91 | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( % 53.60/7.91 | | | | | | | | | ~ (v2 = init) & % 53.60/7.91 | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 % 53.60/7.91 | | | | | | | | | & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.91 | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & % 53.60/7.91 | | | | | | | | | ( ~ (pvar1402_init = init) | ~ % 53.60/7.91 | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.91 | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.60/7.91 | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.60/7.91 | | | | | | | | | : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.91 | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.60/7.91 | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.60/7.91 | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.91 | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.91 | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.91 | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( % 53.60/7.91 | | | | | | | | | ~ (v2 = init) & % 53.60/7.91 | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 % 53.60/7.91 | | | | | | | | | & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.91 | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & % 53.60/7.91 | | | | | | | | | ( ~ (pvar1402_init = init) | ~ % 53.60/7.91 | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.91 | | | | | | | | | (pvar1400_init = init))))))))) % 53.60/7.91 | | | | | | | | | % 53.60/7.91 | | | | | | | | | BETA: splitting (125) gives: % 53.60/7.91 | | | | | | | | | % 53.60/7.91 | | | | | | | | | Case 1: % 53.60/7.91 | | | | | | | | | | % 53.60/7.92 | | | | | | | | | | (126) all_76_7 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.60/7.92 | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.92 | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.92 | | | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.92 | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.92 | | | | | | | | | | | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.92 | | | | | | | | | | 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.92 | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, v1, % 53.60/7.92 | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = % 53.60/7.92 | | | | | | | | | | 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.92 | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.92 | | | | | | | | | | init) | ~ (pvar1400_init = init)))) % 53.60/7.92 | | | | | | | | | | % 53.60/7.92 | | | | | | | | | | ALPHA: (126) implies: % 53.60/7.92 | | | | | | | | | | (127) ~ (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.60/7.92 | | | | | | | | | | (v1 = init) & a_select2(s_center7_init, v0) = v1 % 53.60/7.92 | | | | | | | | | | & leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.92 | | | | | | | | | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 53.60/7.92 | | | | | | | | | | init) & a_select2(s_values7_init, v0) = v1 & % 53.60/7.92 | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.92 | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.92 | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 53.60/7.92 | | | | | | | | | | $i] : ( ~ (v2 = init) & % 53.60/7.92 | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, % 53.60/7.92 | | | | | | | | | | n3) = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 53.60/7.92 | | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1401_init = init) | ~ (pvar1400_init = % 53.60/7.92 | | | | | | | | | | init))) % 53.60/7.92 | | | | | | | | | | % 53.60/7.92 | | | | | | | | | | REF_CLOSE: (15), (45), (46), (47), (80), (117), (118), (119), % 53.60/7.92 | | | | | | | | | | (127) are inconsistent by sub-proof #1. % 53.60/7.92 | | | | | | | | | | % 53.60/7.92 | | | | | | | | | Case 2: % 53.60/7.92 | | | | | | | | | | % 53.60/7.92 | | | | | | | | | | (128) ~ (all_76_7 = 0) & ( ~ (all_76_6 = init) | % 53.60/7.92 | | | | | | | | | | (all_76_4 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] % 53.60/7.92 | | | | | | | | | | : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.92 | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.92 | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.60/7.92 | | | | | | | | | | (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.92 | | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.92 | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.92 | | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.92 | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.92 | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.92 | | | | | | | | | | (pvar1402_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.60/7.92 | | | | | | | | | | (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.60/7.92 | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.60/7.92 | | | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.92 | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.60/7.92 | | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.92 | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.92 | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( % 53.60/7.92 | | | | | | | | | | ~ (v2 = init) & % 53.60/7.92 | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 % 53.60/7.92 | | | | | | | | | | & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & % 53.60/7.92 | | | | | | | | | | ( ~ (pvar1402_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.60/7.92 | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.60/7.92 | | | | | | | | | | : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.92 | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.60/7.92 | | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.92 | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.92 | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( % 53.60/7.92 | | | | | | | | | | ~ (v2 = init) & % 53.60/7.92 | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 % 53.60/7.92 | | | | | | | | | | & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & % 53.60/7.92 | | | | | | | | | | ( ~ (pvar1402_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1400_init = init)))))))) % 53.60/7.92 | | | | | | | | | | % 53.60/7.92 | | | | | | | | | | ALPHA: (128) implies: % 53.60/7.92 | | | | | | | | | | (129) ~ (all_76_6 = init) | (all_76_4 = 0 & ( ~ % 53.60/7.92 | | | | | | | | | | (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.92 | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, v0) % 53.60/7.92 | | | | | | | | | | = v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] % 53.60/7.92 | | | | | | | | | | : ( ~ (v1 = init) & a_select2(s_values7_init, % 53.60/7.92 | | | | | | | | | | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = % 53.60/7.92 | | | | | | | | | | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.92 | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.92 | | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.92 | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.92 | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.92 | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.92 | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.92 | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) | % 53.60/7.92 | | | | | | | | | | ( ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.60/7.92 | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.60/7.92 | | | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.92 | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.92 | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.92 | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.92 | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.92 | | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 53.60/7.92 | | | | | | | | | | & a_select3(simplex7_init, v1, v0) = v2 % 53.60/7.92 | | | | | | | | | | & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( % 53.60/7.92 | | | | | | | | | | ~ (pvar1402_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.60/7.92 | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : % 53.60/7.92 | | | | | | | | | | ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.92 | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, % 53.60/7.92 | | | | | | | | | | v0) = 0 & $i(v1) & $i(v0)) | ? [v0: % 53.60/7.92 | | | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.92 | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.92 | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.92 | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.92 | | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 53.60/7.92 | | | | | | | | | | & a_select3(simplex7_init, v1, v0) = v2 % 53.60/7.92 | | | | | | | | | | & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.92 | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( % 53.60/7.92 | | | | | | | | | | ~ (pvar1402_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.92 | | | | | | | | | | (pvar1400_init = init))))))) % 53.60/7.92 | | | | | | | | | | % 53.60/7.92 | | | | | | | | | | BETA: splitting (129) gives: % 53.60/7.92 | | | | | | | | | | % 53.60/7.92 | | | | | | | | | | Case 1: % 53.60/7.92 | | | | | | | | | | | % 53.60/7.92 | | | | | | | | | | | (130) ~ (all_76_6 = init) % 53.60/7.92 | | | | | | | | | | | % 53.60/7.92 | | | | | | | | | | | REDUCE: (75), (130) imply: % 53.60/7.93 | | | | | | | | | | | (131) $false % 53.60/7.93 | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | | CLOSE: (131) is inconsistent. % 53.60/7.93 | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | Case 2: % 53.60/7.93 | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | | (132) (all_76_4 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.60/7.93 | | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.93 | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.93 | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.93 | | | | | | | | | | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.60/7.93 | | | | | | | | | | | (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.93 | | | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.93 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.93 | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.93 | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.93 | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.93 | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.93 | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.93 | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.93 | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.93 | | | | | | | | | | | | ( ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.60/7.93 | | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: % 53.60/7.93 | | | | | | | | | | | $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.93 | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.93 | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.93 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.93 | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.93 | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.93 | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.93 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.93 | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.93 | | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.93 | | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, % 53.60/7.93 | | | | | | | | | | | v1, v0) = v2 & leq(v1, n3) = 0 & % 53.60/7.93 | | | | | | | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | % 53.60/7.93 | | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.60/7.93 | | | | | | | | | | | init) | ~ (pvar1401_init = init) | % 53.60/7.93 | | | | | | | | | | | ~ (pvar1400_init = init))))) | ( ~ % 53.60/7.93 | | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.60/7.93 | | | | | | | | | | | : ( ~ (v1 = init) & % 53.60/7.93 | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.93 | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.93 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.93 | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.93 | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.93 | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.93 | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.93 | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.93 | | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.93 | | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, % 53.60/7.93 | | | | | | | | | | | v1, v0) = v2 & leq(v1, n3) = 0 & % 53.60/7.93 | | | | | | | | | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) | % 53.60/7.93 | | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = % 53.60/7.93 | | | | | | | | | | | init) | ~ (pvar1401_init = init) | % 53.60/7.93 | | | | | | | | | | | ~ (pvar1400_init = init))))))) % 53.60/7.93 | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | | BETA: splitting (132) gives: % 53.60/7.93 | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | | Case 1: % 53.60/7.93 | | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | | | (133) all_76_4 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.60/7.93 | | | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.93 | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.93 | | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.93 | | | | | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.93 | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.93 | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.93 | | | | | | | | | | | | | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.93 | | | | | | | | | | | | 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.93 | | | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, v1, % 53.60/7.93 | | | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = % 53.60/7.93 | | | | | | | | | | | | 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.93 | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.93 | | | | | | | | | | | | init) | ~ (pvar1400_init = init)))) % 53.60/7.93 | | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | | | ALPHA: (133) implies: % 53.60/7.93 | | | | | | | | | | | | (134) ~ (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.93 | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, v0) = % 53.60/7.93 | | | | | | | | | | | | v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.93 | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 % 53.60/7.93 | | | | | | | | | | | | = init) & a_select2(s_values7_init, v0) = v1 & % 53.60/7.93 | | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.93 | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.93 | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 53.60/7.93 | | | | | | | | | | | | $i] : ( ~ (v2 = init) & % 53.60/7.93 | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.93 | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.60/7.93 | | | | | | | | | | | | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init % 53.60/7.93 | | | | | | | | | | | | = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.93 | | | | | | | | | | | | (pvar1400_init = init))) % 53.60/7.93 | | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | | | REF_CLOSE: (15), (45), (46), (47), (80), (117), (118), (119), % 53.60/7.93 | | | | | | | | | | | | (134) are inconsistent by sub-proof #1. % 53.60/7.93 | | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | | Case 2: % 53.60/7.93 | | | | | | | | | | | | % 53.60/7.93 | | | | | | | | | | | | (135) ~ (all_76_4 = 0) & ( ~ (all_76_3 = init) | % 53.60/7.93 | | | | | | | | | | | | (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] % 53.60/7.93 | | | | | | | | | | | | : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.93 | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & % 53.60/7.93 | | | | | | | | | | | | leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.93 | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.93 | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_values7_init, % 53.60/7.93 | | | | | | | | | | | | v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) % 53.60/7.93 | | | | | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : % 53.60/7.93 | | | | | | | | | | | | (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) % 53.60/7.93 | | | | | | | | | | | | & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.60/7.93 | | | | | | | | | | | | init) & a_select3(simplex7_init, v1, % 53.60/7.93 | | | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, % 53.60/7.93 | | | | | | | | | | | | v1) = 0 & $i(v2) & $i(v1))) | % 53.60/7.93 | | | | | | | | | | | | (all_76_12 = 0 & ( ~ (pvar1402_init = init) % 53.60/7.93 | | | | | | | | | | | | | ~ (pvar1401_init = init) | ~ % 53.60/7.93 | | | | | | | | | | | | (pvar1400_init = init))))) | ( ~ % 53.60/7.93 | | | | | | | | | | | | (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : % 53.60/7.93 | | | | | | | | | | | | ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.93 | | | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) % 53.60/7.93 | | | | | | | | | | | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? % 53.60/7.93 | | | | | | | | | | | | [v1: $i] : ( ~ (v1 = init) & % 53.60/7.93 | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & % 53.60/7.93 | | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.93 | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 % 53.60/7.93 | | | | | | | | | | | | & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : % 53.60/7.93 | | | | | | | | | | | | ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.93 | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.93 | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.94 | | | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.94 | | | | | | | | | | | | (pvar1402_init = init) | ~ % 53.60/7.94 | | | | | | | | | | | | (pvar1401_init = init) | ~ % 53.60/7.94 | | | | | | | | | | | | (pvar1400_init = init)))))) % 53.60/7.94 | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | ALPHA: (135) implies: % 53.60/7.94 | | | | | | | | | | | | (136) ~ (all_76_3 = init) | (all_76_1 = 0 & ( ~ % 53.60/7.94 | | | | | | | | | | | | (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.94 | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.94 | | | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.94 | | | | | | | | | | | | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.94 | | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.94 | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.94 | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.94 | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.94 | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.60/7.94 | | | | | | | | | | | | [v2: $i] : ( ~ (v2 = init) & % 53.60/7.94 | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.94 | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.94 | | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.94 | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.94 | | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.94 | | | | | | | | | | | | | ( ~ (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.60/7.94 | | | | | | | | | | | | : ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.94 | | | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.94 | | | | | | | | | | | | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.94 | | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.94 | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.94 | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.94 | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.94 | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.60/7.94 | | | | | | | | | | | | [v2: $i] : ( ~ (v2 = init) & % 53.60/7.94 | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.94 | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.94 | | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.94 | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.94 | | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.94 | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | BETA: splitting (136) gives: % 53.60/7.94 | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | Case 1: % 53.60/7.94 | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | (137) ~ (all_76_3 = init) % 53.60/7.94 | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | REDUCE: (76), (137) imply: % 53.60/7.94 | | | | | | | | | | | | | (138) $false % 53.60/7.94 | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 53.60/7.94 | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | Case 2: % 53.60/7.94 | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | (139) (all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.60/7.94 | | | | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.94 | | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.94 | | | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.94 | | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ % 53.60/7.94 | | | | | | | | | | | | | (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.94 | | | | | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.94 | | | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, % 53.60/7.94 | | | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.94 | | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.94 | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.94 | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.94 | | | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.94 | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.94 | | | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.94 | | | | | | | | | | | | | | ( ~ (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] % 53.60/7.94 | | | | | | | | | | | | | : ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.94 | | | | | | | | | | | | | v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.94 | | | | | | | | | | | | | 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: % 53.60/7.94 | | | | | | | | | | | | | $i] : ( ~ (v1 = init) & % 53.60/7.94 | | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.94 | | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.94 | | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.94 | | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.60/7.94 | | | | | | | | | | | | | [v2: $i] : ( ~ (v2 = init) & % 53.60/7.94 | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.94 | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) % 53.60/7.94 | | | | | | | | | | | | | & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.94 | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init % 53.60/7.94 | | | | | | | | | | | | | = init) | ~ (pvar1400_init = init))))) % 53.60/7.94 | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | BETA: splitting (139) gives: % 53.60/7.94 | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | Case 1: % 53.60/7.94 | | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | | (140) all_76_1 = 0 & ( ~ (all_76_0 = 0) | ? [v0: $i] : % 53.60/7.94 | | | | | | | | | | | | | | ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.94 | | | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, % 53.60/7.94 | | | | | | | | | | | | | | n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.94 | | | | | | | | | | | | | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.94 | | | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, % 53.60/7.94 | | | | | | | | | | | | | | n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.94 | | | | | | | | | | | | | | | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = % 53.60/7.94 | | | | | | | | | | | | | | 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ % 53.60/7.94 | | | | | | | | | | | | | | (v2 = init) & a_select3(simplex7_init, v1, % 53.60/7.94 | | | | | | | | | | | | | | v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = % 53.60/7.94 | | | | | | | | | | | | | | 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.94 | | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.94 | | | | | | | | | | | | | | init) | ~ (pvar1400_init = init)))) % 53.60/7.94 | | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | | ALPHA: (140) implies: % 53.60/7.94 | | | | | | | | | | | | | | (141) ~ (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.94 | | | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, v0) = % 53.60/7.94 | | | | | | | | | | | | | | v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) % 53.60/7.94 | | | | | | | | | | | | | | & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 % 53.60/7.94 | | | | | | | | | | | | | | = init) & a_select2(s_values7_init, v0) = v1 & % 53.60/7.94 | | | | | | | | | | | | | | leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & % 53.60/7.94 | | | | | | | | | | | | | | $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & % 53.60/7.94 | | | | | | | | | | | | | | leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: % 53.60/7.94 | | | | | | | | | | | | | | $i] : ( ~ (v2 = init) & % 53.60/7.94 | | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.94 | | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.60/7.94 | | | | | | | | | | | | | | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init % 53.60/7.94 | | | | | | | | | | | | | | = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.94 | | | | | | | | | | | | | | (pvar1400_init = init))) % 53.60/7.94 | | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | | REF_CLOSE: (15), (45), (46), (47), (80), (117), (118), (119), % 53.60/7.94 | | | | | | | | | | | | | | (141) are inconsistent by sub-proof #1. % 53.60/7.94 | | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | Case 2: % 53.60/7.94 | | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | | (142) ~ (all_76_1 = 0) & ( ? [v0: $i] : ? [v1: $i] : ( % 53.60/7.94 | | | | | | | | | | | | | | ~ (v1 = init) & a_select2(s_center7_init, v0) % 53.60/7.94 | | | | | | | | | | | | | | = v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.94 | | | | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : % 53.60/7.94 | | | | | | | | | | | | | | ( ~ (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.94 | | | | | | | | | | | | | | = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & % 53.60/7.94 | | | | | | | | | | | | | | $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) % 53.60/7.94 | | | | | | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : % 53.60/7.94 | | | | | | | | | | | | | | ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.94 | | | | | | | | | | | | | | a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.94 | | | | | | | | | | | | | | leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.60/7.94 | | | | | | | | | | | | | | $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.94 | | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.94 | | | | | | | | | | | | | | init) | ~ (pvar1400_init = init)))) % 53.60/7.94 | | | | | | | | | | | | | | % 53.60/7.94 | | | | | | | | | | | | | | ALPHA: (142) implies: % 53.60/7.95 | | | | | | | | | | | | | | (143) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.95 | | | | | | | | | | | | | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) % 53.60/7.95 | | | | | | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.60/7.95 | | | | | | | | | | | | | | [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.95 | | | | | | | | | | | | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) % 53.60/7.95 | | | | | | | | | | | | | | = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.60/7.95 | | | | | | | | | | | | | | [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.95 | | | | | | | | | | | | | | $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 53.60/7.95 | | | | | | | | | | | | | | init) & a_select3(simplex7_init, v1, v0) = % 53.60/7.95 | | | | | | | | | | | | | | v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & % 53.60/7.95 | | | | | | | | | | | | | | $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.95 | | | | | | | | | | | | | | (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.95 | | | | | | | | | | | | | | init) | ~ (pvar1400_init = init))) % 53.60/7.95 | | | | | | | | | | | | | | % 53.60/7.95 | | | | | | | | | | | | | | REF_CLOSE: (15), (45), (46), (47), (117), (118), (119), (143) % 53.60/7.95 | | | | | | | | | | | | | | are inconsistent by sub-proof #2. % 53.60/7.95 | | | | | | | | | | | | | | % 53.60/7.95 | | | | | | | | | | | | | End of split % 53.60/7.95 | | | | | | | | | | | | | % 53.60/7.95 | | | | | | | | | | | | End of split % 53.60/7.95 | | | | | | | | | | | | % 53.60/7.95 | | | | | | | | | | | End of split % 53.60/7.95 | | | | | | | | | | | % 53.60/7.95 | | | | | | | | | | End of split % 53.60/7.95 | | | | | | | | | | % 53.60/7.95 | | | | | | | | | End of split % 53.60/7.95 | | | | | | | | | % 53.60/7.95 | | | | | | | | End of split % 53.60/7.95 | | | | | | | | % 53.60/7.95 | | | | | | | End of split % 53.60/7.95 | | | | | | | % 53.60/7.95 | | | | | | End of split % 53.60/7.95 | | | | | | % 53.60/7.95 | | | | | Case 2: % 53.60/7.95 | | | | | | % 53.60/7.95 | | | | | | (144) ? [v0: any] : ? [v1: any] : (leq(pv1388, n3) = v1 & % 53.60/7.95 | | | | | | leq(n0, pv1388) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/7.95 | | | | | | % 53.60/7.95 | | | | | | DELTA: instantiating (144) with fresh symbols all_134_0, all_134_1 % 53.60/7.95 | | | | | | gives: % 53.60/7.95 | | | | | | (145) leq(pv1388, n3) = all_134_0 & leq(n0, pv1388) = all_134_1 & % 53.60/7.95 | | | | | | ( ~ (all_134_0 = 0) | ~ (all_134_1 = 0)) % 53.60/7.95 | | | | | | % 53.60/7.95 | | | | | | ALPHA: (145) implies: % 53.60/7.95 | | | | | | (146) leq(n0, pv1388) = all_134_1 % 53.60/7.95 | | | | | | (147) leq(pv1388, n3) = all_134_0 % 53.60/7.95 | | | | | | (148) ~ (all_134_0 = 0) | ~ (all_134_1 = 0) % 53.60/7.95 | | | | | | % 53.60/7.95 | | | | | | GROUND_INST: instantiating (15) with 0, all_134_1, pv1388, n0, % 53.60/7.95 | | | | | | simplifying with (81), (146) gives: % 53.60/7.95 | | | | | | (149) all_134_1 = 0 % 53.60/7.95 | | | | | | % 53.60/7.95 | | | | | | GROUND_INST: instantiating (15) with 0, all_134_0, n3, pv1388, % 53.60/7.95 | | | | | | simplifying with (38), (147) gives: % 53.60/7.95 | | | | | | (150) all_134_0 = 0 % 53.60/7.95 | | | | | | % 53.60/7.95 | | | | | | BETA: splitting (148) gives: % 53.60/7.95 | | | | | | % 53.60/7.95 | | | | | | Case 1: % 53.60/7.95 | | | | | | | % 53.60/7.95 | | | | | | | (151) ~ (all_134_0 = 0) % 53.60/7.95 | | | | | | | % 53.60/7.95 | | | | | | | REDUCE: (150), (151) imply: % 53.60/7.95 | | | | | | | (152) $false % 53.60/7.95 | | | | | | | % 53.60/7.95 | | | | | | | CLOSE: (152) is inconsistent. % 53.60/7.95 | | | | | | | % 53.60/7.95 | | | | | | Case 2: % 53.60/7.95 | | | | | | | % 53.60/7.95 | | | | | | | (153) ~ (all_134_1 = 0) % 53.60/7.95 | | | | | | | % 53.60/7.95 | | | | | | | REDUCE: (149), (153) imply: % 53.60/7.95 | | | | | | | (154) $false % 53.60/7.95 | | | | | | | % 53.60/7.95 | | | | | | | CLOSE: (154) is inconsistent. % 53.60/7.95 | | | | | | | % 53.60/7.95 | | | | | | End of split % 53.60/7.95 | | | | | | % 53.60/7.95 | | | | | End of split % 53.60/7.95 | | | | | % 53.60/7.95 | | | | Case 2: % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | (155) ? [v0: int] : ( ~ (v0 = 0) & leq(n1, pv1388) = v0) % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | DELTA: instantiating (155) with fresh symbol all_127_0 gives: % 53.60/7.95 | | | | | (156) ~ (all_127_0 = 0) & leq(n1, pv1388) = all_127_0 % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | ALPHA: (156) implies: % 53.60/7.95 | | | | | (157) ~ (all_127_0 = 0) % 53.60/7.95 | | | | | (158) leq(n1, pv1388) = all_127_0 % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | GROUND_INST: instantiating (15) with 0, all_127_0, pv1388, n1, % 53.60/7.95 | | | | | simplifying with (78), (158) gives: % 53.60/7.95 | | | | | (159) all_127_0 = 0 % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | REDUCE: (157), (159) imply: % 53.60/7.95 | | | | | (160) $false % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | CLOSE: (160) is inconsistent. % 53.60/7.95 | | | | | % 53.60/7.95 | | | | End of split % 53.60/7.95 | | | | % 53.60/7.95 | | | Case 2: % 53.60/7.95 | | | | % 53.60/7.95 | | | | (161) ? [v0: any] : ? [v1: any] : (leq(s_best7, n3) = v1 & leq(n0, % 53.60/7.95 | | | | s_best7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/7.95 | | | | % 53.60/7.95 | | | | DELTA: instantiating (161) with fresh symbols all_113_0, all_113_1 % 53.60/7.95 | | | | gives: % 53.60/7.95 | | | | (162) leq(s_best7, n3) = all_113_0 & leq(n0, s_best7) = all_113_1 & ( % 53.60/7.95 | | | | ~ (all_113_0 = 0) | ~ (all_113_1 = 0)) % 53.60/7.95 | | | | % 53.60/7.95 | | | | ALPHA: (162) implies: % 53.60/7.95 | | | | (163) leq(n0, s_best7) = all_113_1 % 53.60/7.95 | | | | (164) leq(s_best7, n3) = all_113_0 % 53.60/7.95 | | | | (165) ~ (all_113_0 = 0) | ~ (all_113_1 = 0) % 53.60/7.95 | | | | % 53.60/7.95 | | | | GROUND_INST: instantiating (15) with 0, all_113_1, s_best7, n0, % 53.60/7.95 | | | | simplifying with (30), (163) gives: % 53.60/7.95 | | | | (166) all_113_1 = 0 % 53.60/7.95 | | | | % 53.60/7.95 | | | | GROUND_INST: instantiating (15) with 0, all_113_0, n3, s_best7, % 53.60/7.95 | | | | simplifying with (35), (164) gives: % 53.60/7.95 | | | | (167) all_113_0 = 0 % 53.60/7.95 | | | | % 53.60/7.95 | | | | BETA: splitting (165) gives: % 53.60/7.95 | | | | % 53.60/7.95 | | | | Case 1: % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | (168) ~ (all_113_0 = 0) % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | REDUCE: (167), (168) imply: % 53.60/7.95 | | | | | (169) $false % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | CLOSE: (169) is inconsistent. % 53.60/7.95 | | | | | % 53.60/7.95 | | | | Case 2: % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | (170) ~ (all_113_1 = 0) % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | REDUCE: (166), (170) imply: % 53.60/7.95 | | | | | (171) $false % 53.60/7.95 | | | | | % 53.60/7.95 | | | | | CLOSE: (171) is inconsistent. % 53.60/7.95 | | | | | % 53.60/7.95 | | | | End of split % 53.60/7.95 | | | | % 53.60/7.95 | | | End of split % 53.60/7.95 | | | % 53.60/7.95 | | Case 2: % 53.60/7.95 | | | % 53.60/7.95 | | | (172) ? [v0: any] : ? [v1: any] : (leq(s_sworst7, n3) = v1 & leq(n0, % 53.60/7.95 | | | s_sworst7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/7.95 | | | % 53.60/7.95 | | | DELTA: instantiating (172) with fresh symbols all_109_0, all_109_1 gives: % 53.60/7.95 | | | (173) leq(s_sworst7, n3) = all_109_0 & leq(n0, s_sworst7) = all_109_1 & % 53.60/7.95 | | | ( ~ (all_109_0 = 0) | ~ (all_109_1 = 0)) % 53.60/7.95 | | | % 53.60/7.95 | | | ALPHA: (173) implies: % 53.60/7.95 | | | (174) leq(n0, s_sworst7) = all_109_1 % 53.60/7.95 | | | (175) leq(s_sworst7, n3) = all_109_0 % 53.60/7.95 | | | (176) ~ (all_109_0 = 0) | ~ (all_109_1 = 0) % 53.60/7.95 | | | % 53.60/7.95 | | | GROUND_INST: instantiating (15) with 0, all_109_1, s_sworst7, n0, % 53.60/7.95 | | | simplifying with (31), (174) gives: % 53.60/7.95 | | | (177) all_109_1 = 0 % 53.60/7.95 | | | % 53.60/7.95 | | | GROUND_INST: instantiating (15) with 0, all_109_0, n3, s_sworst7, % 53.60/7.95 | | | simplifying with (36), (175) gives: % 53.60/7.95 | | | (178) all_109_0 = 0 % 53.60/7.95 | | | % 53.60/7.95 | | | BETA: splitting (176) gives: % 53.60/7.95 | | | % 53.60/7.95 | | | Case 1: % 53.60/7.95 | | | | % 53.60/7.95 | | | | (179) ~ (all_109_0 = 0) % 53.60/7.95 | | | | % 53.60/7.95 | | | | REDUCE: (178), (179) imply: % 53.60/7.95 | | | | (180) $false % 53.60/7.95 | | | | % 53.60/7.95 | | | | CLOSE: (180) is inconsistent. % 53.60/7.95 | | | | % 53.60/7.95 | | | Case 2: % 53.60/7.95 | | | | % 53.60/7.95 | | | | (181) ~ (all_109_1 = 0) % 53.60/7.95 | | | | % 53.60/7.95 | | | | REDUCE: (177), (181) imply: % 53.60/7.95 | | | | (182) $false % 53.60/7.95 | | | | % 53.60/7.95 | | | | CLOSE: (182) is inconsistent. % 53.60/7.95 | | | | % 53.60/7.95 | | | End of split % 53.60/7.95 | | | % 53.60/7.96 | | End of split % 53.60/7.96 | | % 53.60/7.96 | Case 2: % 53.60/7.96 | | % 53.60/7.96 | | (183) ? [v0: any] : ? [v1: any] : (leq(s_worst7, n3) = v1 & leq(n0, % 53.60/7.96 | | s_worst7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/7.96 | | % 53.60/7.96 | | DELTA: instantiating (183) with fresh symbols all_105_0, all_105_1 gives: % 53.60/7.96 | | (184) leq(s_worst7, n3) = all_105_0 & leq(n0, s_worst7) = all_105_1 & ( ~ % 53.60/7.96 | | (all_105_0 = 0) | ~ (all_105_1 = 0)) % 53.60/7.96 | | % 53.60/7.96 | | ALPHA: (184) implies: % 53.60/7.96 | | (185) leq(n0, s_worst7) = all_105_1 % 53.60/7.96 | | (186) leq(s_worst7, n3) = all_105_0 % 53.60/7.96 | | (187) ~ (all_105_0 = 0) | ~ (all_105_1 = 0) % 53.60/7.96 | | % 53.60/7.96 | | GROUND_INST: instantiating (15) with 0, all_105_1, s_worst7, n0, simplifying % 53.60/7.96 | | with (32), (185) gives: % 53.60/7.96 | | (188) all_105_1 = 0 % 53.60/7.96 | | % 53.60/7.96 | | GROUND_INST: instantiating (15) with 0, all_105_0, n3, s_worst7, simplifying % 53.60/7.96 | | with (37), (186) gives: % 53.60/7.96 | | (189) all_105_0 = 0 % 53.60/7.96 | | % 53.60/7.96 | | BETA: splitting (187) gives: % 53.60/7.96 | | % 53.60/7.96 | | Case 1: % 53.60/7.96 | | | % 53.60/7.96 | | | (190) ~ (all_105_0 = 0) % 53.60/7.96 | | | % 53.60/7.96 | | | REDUCE: (189), (190) imply: % 53.60/7.96 | | | (191) $false % 53.60/7.96 | | | % 53.60/7.96 | | | CLOSE: (191) is inconsistent. % 53.60/7.96 | | | % 53.60/7.96 | | Case 2: % 53.60/7.96 | | | % 53.60/7.96 | | | (192) ~ (all_105_1 = 0) % 53.60/7.96 | | | % 53.60/7.96 | | | REDUCE: (188), (192) imply: % 53.60/7.96 | | | (193) $false % 53.60/7.96 | | | % 53.60/7.96 | | | CLOSE: (193) is inconsistent. % 53.60/7.96 | | | % 53.60/7.96 | | End of split % 53.60/7.96 | | % 53.60/7.96 | End of split % 53.60/7.96 | % 53.60/7.96 End of proof % 53.60/7.96 % 53.60/7.96 Sub-proof #1 shows that the following formulas are inconsistent: % 53.60/7.96 ---------------------------------------------------------------- % 53.60/7.96 (1) ~ (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.96 a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 % 53.60/7.96 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.96 a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 % 53.60/7.96 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.96 $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.96 a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) % 53.60/7.96 = 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init = init) % 53.60/7.96 | ~ (pvar1401_init = init) | ~ (pvar1400_init = init))) % 53.60/7.96 (2) ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 53.60/7.96 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 53.60/7.96 ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ? [v3: any] % 53.60/7.96 : ? [v4: any] : (leq(v1, n3) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) % 53.60/7.96 | ~ (v3 = 0))))) % 53.60/7.96 (3) all_76_0 = 0 % 53.60/7.96 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 53.60/7.96 ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 53.60/7.96 (5) pvar1400_init = init % 53.60/7.96 (6) pvar1401_init = init % 53.60/7.96 (7) pvar1402_init = init % 53.60/7.96 (8) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 53.60/7.96 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n2) % 53.60/7.96 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/7.96 (9) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 53.60/7.96 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n3) % 53.60/7.96 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/7.96 % 53.60/7.96 Begin of proof % 53.60/7.96 | % 53.60/7.96 | BETA: splitting (1) gives: % 53.60/7.96 | % 53.60/7.96 | Case 1: % 53.60/7.96 | | % 53.60/7.96 | | (10) ~ (all_76_0 = 0) % 53.60/7.96 | | % 53.60/7.96 | | REDUCE: (3), (10) imply: % 53.60/7.96 | | (11) $false % 53.60/7.96 | | % 53.60/7.96 | | CLOSE: (11) is inconsistent. % 53.60/7.96 | | % 53.60/7.96 | Case 2: % 53.60/7.96 | | % 53.60/7.96 | | (12) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.96 | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) % 53.60/7.96 | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 53.60/7.96 | | init) & a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & % 53.60/7.96 | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = % 53.60/7.96 | | 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 % 53.60/7.96 | | = init) & a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) % 53.60/7.96 | | = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.96 | | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.96 | | (pvar1400_init = init))) % 53.60/7.96 | | % 53.60/7.96 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (12) are inconsistent by % 53.60/7.96 | | sub-proof #2. % 53.60/7.96 | | % 53.60/7.96 | End of split % 53.60/7.96 | % 53.60/7.96 End of proof % 53.60/7.96 % 53.60/7.96 Sub-proof #2 shows that the following formulas are inconsistent: % 53.60/7.96 ---------------------------------------------------------------- % 53.60/7.96 (1) ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 53.60/7.96 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 53.60/7.96 ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ? [v3: any] % 53.60/7.96 : ? [v4: any] : (leq(v1, n3) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) % 53.60/7.96 | ~ (v3 = 0))))) % 53.60/7.96 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 53.60/7.96 ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 53.60/7.97 (3) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.97 v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.60/7.97 [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.97 = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: % 53.60/7.97 $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.60/7.97 [v2: $i] : ( ~ (v2 = init) & a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.97 leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_12 = % 53.60/7.97 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.97 (pvar1400_init = init))) % 53.60/7.97 (4) pvar1400_init = init % 53.60/7.97 (5) pvar1401_init = init % 53.60/7.97 (6) pvar1402_init = init % 53.60/7.97 (7) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 53.60/7.97 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n2) % 53.60/7.97 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/7.97 (8) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 53.60/7.97 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n3) % 53.60/7.97 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/7.97 % 53.60/7.97 Begin of proof % 53.60/7.97 | % 53.60/7.97 | BETA: splitting (3) gives: % 53.60/7.97 | % 53.60/7.97 | Case 1: % 53.60/7.97 | | % 53.60/7.97 | | (9) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.97 | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) % 53.60/7.97 | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 53.60/7.97 | | init) & a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & % 53.60/7.97 | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.97 | | % 53.60/7.97 | | BETA: splitting (9) gives: % 53.60/7.97 | | % 53.60/7.97 | | Case 1: % 53.60/7.97 | | | % 53.60/7.97 | | | (10) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.97 | | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, % 53.60/7.97 | | | v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.97 | | | % 53.60/7.97 | | | DELTA: instantiating (10) with fresh symbols all_1146_0, all_1146_1 gives: % 53.60/7.97 | | | (11) ~ (all_1146_0 = init) & a_select2(s_center7_init, all_1146_1) = % 53.60/7.97 | | | all_1146_0 & leq(all_1146_1, n2) = 0 & leq(n0, all_1146_1) = 0 & % 53.60/7.97 | | | $i(all_1146_0) & $i(all_1146_1) % 53.60/7.97 | | | % 53.60/7.97 | | | ALPHA: (11) implies: % 53.60/7.97 | | | (12) ~ (all_1146_0 = init) % 53.60/7.97 | | | (13) $i(all_1146_1) % 53.60/7.97 | | | (14) leq(n0, all_1146_1) = 0 % 53.60/7.97 | | | (15) leq(all_1146_1, n2) = 0 % 53.60/7.97 | | | (16) a_select2(s_center7_init, all_1146_1) = all_1146_0 % 53.60/7.97 | | | % 53.60/7.97 | | | GROUND_INST: instantiating (7) with all_1146_1, all_1146_0, simplifying % 53.60/7.97 | | | with (13), (16) gives: % 53.60/7.97 | | | (17) all_1146_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_1146_1, % 53.60/7.97 | | | n2) = v1 & leq(n0, all_1146_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 53.60/7.97 | | | 0))) % 53.60/7.97 | | | % 53.60/7.97 | | | BETA: splitting (17) gives: % 53.60/7.97 | | | % 53.60/7.97 | | | Case 1: % 53.60/7.97 | | | | % 53.60/7.97 | | | | (18) all_1146_0 = init % 53.60/7.97 | | | | % 53.60/7.97 | | | | REDUCE: (12), (18) imply: % 53.60/7.97 | | | | (19) $false % 53.60/7.97 | | | | % 53.60/7.97 | | | | CLOSE: (19) is inconsistent. % 53.60/7.97 | | | | % 53.60/7.97 | | | Case 2: % 53.60/7.97 | | | | % 53.60/7.97 | | | | (20) ? [v0: any] : ? [v1: any] : (leq(all_1146_1, n2) = v1 & % 53.60/7.97 | | | | leq(n0, all_1146_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/7.97 | | | | % 53.60/7.97 | | | | DELTA: instantiating (20) with fresh symbols all_1164_0, all_1164_1 % 53.60/7.97 | | | | gives: % 53.60/7.97 | | | | (21) leq(all_1146_1, n2) = all_1164_0 & leq(n0, all_1146_1) = % 53.60/7.97 | | | | all_1164_1 & ( ~ (all_1164_0 = 0) | ~ (all_1164_1 = 0)) % 53.60/7.97 | | | | % 53.60/7.97 | | | | ALPHA: (21) implies: % 53.60/7.97 | | | | (22) leq(n0, all_1146_1) = all_1164_1 % 53.60/7.97 | | | | (23) leq(all_1146_1, n2) = all_1164_0 % 53.60/7.97 | | | | (24) ~ (all_1164_0 = 0) | ~ (all_1164_1 = 0) % 53.60/7.97 | | | | % 53.60/7.97 | | | | GROUND_INST: instantiating (2) with 0, all_1164_1, all_1146_1, n0, % 53.60/7.97 | | | | simplifying with (14), (22) gives: % 53.60/7.97 | | | | (25) all_1164_1 = 0 % 53.60/7.97 | | | | % 53.60/7.97 | | | | GROUND_INST: instantiating (2) with 0, all_1164_0, n2, all_1146_1, % 53.60/7.97 | | | | simplifying with (15), (23) gives: % 53.60/7.97 | | | | (26) all_1164_0 = 0 % 53.60/7.97 | | | | % 53.60/7.97 | | | | BETA: splitting (24) gives: % 53.60/7.97 | | | | % 53.60/7.97 | | | | Case 1: % 53.60/7.97 | | | | | % 53.60/7.97 | | | | | (27) ~ (all_1164_0 = 0) % 53.60/7.97 | | | | | % 53.60/7.97 | | | | | REDUCE: (26), (27) imply: % 53.60/7.97 | | | | | (28) $false % 53.60/7.97 | | | | | % 53.60/7.97 | | | | | CLOSE: (28) is inconsistent. % 53.60/7.97 | | | | | % 53.60/7.97 | | | | Case 2: % 53.60/7.97 | | | | | % 53.60/7.97 | | | | | (29) ~ (all_1164_1 = 0) % 53.60/7.97 | | | | | % 53.60/7.97 | | | | | REDUCE: (25), (29) imply: % 53.60/7.97 | | | | | (30) $false % 53.60/7.97 | | | | | % 53.60/7.97 | | | | | CLOSE: (30) is inconsistent. % 53.60/7.97 | | | | | % 53.60/7.97 | | | | End of split % 53.60/7.97 | | | | % 53.60/7.97 | | | End of split % 53.60/7.97 | | | % 53.60/7.97 | | Case 2: % 53.60/7.97 | | | % 53.60/7.97 | | | (31) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.97 | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, % 53.60/7.97 | | | v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.97 | | | % 53.60/7.97 | | | DELTA: instantiating (31) with fresh symbols all_1146_0, all_1146_1 gives: % 53.60/7.97 | | | (32) ~ (all_1146_0 = init) & a_select2(s_values7_init, all_1146_1) = % 53.60/7.97 | | | all_1146_0 & leq(all_1146_1, n3) = 0 & leq(n0, all_1146_1) = 0 & % 53.60/7.97 | | | $i(all_1146_0) & $i(all_1146_1) % 53.60/7.97 | | | % 53.60/7.97 | | | ALPHA: (32) implies: % 53.60/7.97 | | | (33) ~ (all_1146_0 = init) % 53.60/7.97 | | | (34) $i(all_1146_1) % 53.60/7.97 | | | (35) leq(n0, all_1146_1) = 0 % 53.60/7.97 | | | (36) leq(all_1146_1, n3) = 0 % 53.60/7.97 | | | (37) a_select2(s_values7_init, all_1146_1) = all_1146_0 % 53.60/7.97 | | | % 53.60/7.97 | | | GROUND_INST: instantiating (8) with all_1146_1, all_1146_0, simplifying % 53.60/7.97 | | | with (34), (37) gives: % 53.60/7.97 | | | (38) all_1146_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_1146_1, % 53.60/7.97 | | | n3) = v1 & leq(n0, all_1146_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 53.60/7.97 | | | 0))) % 53.60/7.97 | | | % 53.60/7.97 | | | BETA: splitting (38) gives: % 53.60/7.97 | | | % 53.60/7.97 | | | Case 1: % 53.60/7.97 | | | | % 53.60/7.97 | | | | (39) all_1146_0 = init % 53.60/7.97 | | | | % 53.60/7.97 | | | | REDUCE: (33), (39) imply: % 53.60/7.97 | | | | (40) $false % 53.60/7.97 | | | | % 53.60/7.97 | | | | CLOSE: (40) is inconsistent. % 53.60/7.97 | | | | % 53.60/7.97 | | | Case 2: % 53.60/7.97 | | | | % 53.60/7.97 | | | | (41) ? [v0: any] : ? [v1: any] : (leq(all_1146_1, n3) = v1 & % 53.60/7.97 | | | | leq(n0, all_1146_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/7.97 | | | | % 53.60/7.98 | | | | DELTA: instantiating (41) with fresh symbols all_1164_0, all_1164_1 % 53.60/7.98 | | | | gives: % 53.60/7.98 | | | | (42) leq(all_1146_1, n3) = all_1164_0 & leq(n0, all_1146_1) = % 53.60/7.98 | | | | all_1164_1 & ( ~ (all_1164_0 = 0) | ~ (all_1164_1 = 0)) % 53.60/7.98 | | | | % 53.60/7.98 | | | | ALPHA: (42) implies: % 53.60/7.98 | | | | (43) leq(n0, all_1146_1) = all_1164_1 % 53.60/7.98 | | | | (44) leq(all_1146_1, n3) = all_1164_0 % 53.60/7.98 | | | | (45) ~ (all_1164_0 = 0) | ~ (all_1164_1 = 0) % 53.60/7.98 | | | | % 53.60/7.98 | | | | GROUND_INST: instantiating (2) with 0, all_1164_1, all_1146_1, n0, % 53.60/7.98 | | | | simplifying with (35), (43) gives: % 53.60/7.98 | | | | (46) all_1164_1 = 0 % 53.60/7.98 | | | | % 53.60/7.98 | | | | GROUND_INST: instantiating (2) with 0, all_1164_0, n3, all_1146_1, % 53.60/7.98 | | | | simplifying with (36), (44) gives: % 53.60/7.98 | | | | (47) all_1164_0 = 0 % 53.60/7.98 | | | | % 53.60/7.98 | | | | BETA: splitting (45) gives: % 53.60/7.98 | | | | % 53.60/7.98 | | | | Case 1: % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | (48) ~ (all_1164_0 = 0) % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | REDUCE: (47), (48) imply: % 53.60/7.98 | | | | | (49) $false % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | CLOSE: (49) is inconsistent. % 53.60/7.98 | | | | | % 53.60/7.98 | | | | Case 2: % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | (50) ~ (all_1164_1 = 0) % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | REDUCE: (46), (50) imply: % 53.60/7.98 | | | | | (51) $false % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | CLOSE: (51) is inconsistent. % 53.60/7.98 | | | | | % 53.60/7.98 | | | | End of split % 53.60/7.98 | | | | % 53.60/7.98 | | | End of split % 53.60/7.98 | | | % 53.60/7.98 | | End of split % 53.60/7.98 | | % 53.60/7.98 | Case 2: % 53.60/7.98 | | % 53.60/7.98 | | (52) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: % 53.60/7.98 | | $i] : ? [v2: $i] : ( ~ (v2 = init) & a_select3(simplex7_init, % 53.60/7.98 | | v1, v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.60/7.98 | | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init = init) | ~ % 53.60/7.98 | | (pvar1401_init = init) | ~ (pvar1400_init = init))) % 53.60/7.98 | | % 53.60/7.98 | | BETA: splitting (52) gives: % 53.60/7.98 | | % 53.60/7.98 | | Case 1: % 53.60/7.98 | | | % 53.60/7.98 | | | (53) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/7.98 | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.98 | | | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & % 53.60/7.98 | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 53.60/7.98 | | | % 53.60/7.98 | | | DELTA: instantiating (53) with fresh symbol all_1146_0 gives: % 53.60/7.98 | | | (54) leq(all_1146_0, n2) = 0 & leq(n0, all_1146_0) = 0 & $i(all_1146_0) % 53.60/7.98 | | | & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.98 | | | a_select3(simplex7_init, v0, all_1146_0) = v1 & leq(v0, n3) = 0 % 53.60/7.98 | | | & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.98 | | | % 53.60/7.98 | | | ALPHA: (54) implies: % 53.60/7.98 | | | (55) $i(all_1146_0) % 53.60/7.98 | | | (56) leq(n0, all_1146_0) = 0 % 53.60/7.98 | | | (57) leq(all_1146_0, n2) = 0 % 53.60/7.98 | | | (58) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.98 | | | a_select3(simplex7_init, v0, all_1146_0) = v1 & leq(v0, n3) = 0 % 53.60/7.98 | | | & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/7.98 | | | % 53.60/7.98 | | | DELTA: instantiating (58) with fresh symbols all_1148_0, all_1148_1 gives: % 53.60/7.98 | | | (59) ~ (all_1148_0 = init) & a_select3(simplex7_init, all_1148_1, % 53.60/7.98 | | | all_1146_0) = all_1148_0 & leq(all_1148_1, n3) = 0 & leq(n0, % 53.60/7.98 | | | all_1148_1) = 0 & $i(all_1148_0) & $i(all_1148_1) % 53.60/7.98 | | | % 53.60/7.98 | | | ALPHA: (59) implies: % 53.60/7.98 | | | (60) ~ (all_1148_0 = init) % 53.60/7.98 | | | (61) $i(all_1148_1) % 53.60/7.98 | | | (62) leq(n0, all_1148_1) = 0 % 53.60/7.98 | | | (63) leq(all_1148_1, n3) = 0 % 53.60/7.98 | | | (64) a_select3(simplex7_init, all_1148_1, all_1146_0) = all_1148_0 % 53.60/7.98 | | | % 53.60/7.98 | | | GROUND_INST: instantiating (1) with all_1146_0, simplifying with (55), % 53.60/7.98 | | | (57) gives: % 53.60/7.98 | | | (65) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_1146_0) = v0) | ! [v0: % 53.60/7.98 | | | $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(simplex7_init, % 53.60/7.98 | | | v0, all_1146_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 53.60/7.98 | | | any] : (leq(v0, n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | % 53.60/7.98 | | | ~ (v2 = 0)))) % 53.60/7.98 | | | % 53.60/7.98 | | | BETA: splitting (65) gives: % 53.60/7.98 | | | % 53.60/7.98 | | | Case 1: % 53.60/7.98 | | | | % 53.60/7.98 | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_1146_0) = v0) % 53.60/7.98 | | | | % 53.60/7.98 | | | | DELTA: instantiating (66) with fresh symbol all_1165_0 gives: % 53.60/7.98 | | | | (67) ~ (all_1165_0 = 0) & leq(n0, all_1146_0) = all_1165_0 % 53.60/7.98 | | | | % 53.60/7.98 | | | | ALPHA: (67) implies: % 53.60/7.98 | | | | (68) ~ (all_1165_0 = 0) % 53.60/7.98 | | | | (69) leq(n0, all_1146_0) = all_1165_0 % 53.60/7.98 | | | | % 53.60/7.98 | | | | GROUND_INST: instantiating (2) with 0, all_1165_0, all_1146_0, n0, % 53.60/7.98 | | | | simplifying with (56), (69) gives: % 53.60/7.98 | | | | (70) all_1165_0 = 0 % 53.60/7.98 | | | | % 53.60/7.98 | | | | REDUCE: (68), (70) imply: % 53.60/7.98 | | | | (71) $false % 53.60/7.98 | | | | % 53.60/7.98 | | | | CLOSE: (71) is inconsistent. % 53.60/7.98 | | | | % 53.60/7.98 | | | Case 2: % 53.60/7.98 | | | | % 53.60/7.98 | | | | (72) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 53.60/7.98 | | | | (a_select3(simplex7_init, v0, all_1146_0) = v1) | ~ $i(v0) | % 53.60/7.98 | | | | ? [v2: any] : ? [v3: any] : (leq(v0, n3) = v3 & leq(n0, v0) = % 53.60/7.98 | | | | v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/7.98 | | | | % 53.60/7.98 | | | | GROUND_INST: instantiating (72) with all_1148_1, all_1148_0, simplifying % 53.60/7.98 | | | | with (61), (64) gives: % 53.60/7.98 | | | | (73) all_1148_0 = init | ? [v0: any] : ? [v1: any] : % 53.60/7.98 | | | | (leq(all_1148_1, n3) = v1 & leq(n0, all_1148_1) = v0 & ( ~ (v1 = % 53.60/7.98 | | | | 0) | ~ (v0 = 0))) % 53.60/7.98 | | | | % 53.60/7.98 | | | | BETA: splitting (73) gives: % 53.60/7.98 | | | | % 53.60/7.98 | | | | Case 1: % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | (74) all_1148_0 = init % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | REDUCE: (60), (74) imply: % 53.60/7.98 | | | | | (75) $false % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | CLOSE: (75) is inconsistent. % 53.60/7.98 | | | | | % 53.60/7.98 | | | | Case 2: % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | (76) ? [v0: any] : ? [v1: any] : (leq(all_1148_1, n3) = v1 & % 53.60/7.98 | | | | | leq(n0, all_1148_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | DELTA: instantiating (76) with fresh symbols all_1179_0, all_1179_1 % 53.60/7.98 | | | | | gives: % 53.60/7.98 | | | | | (77) leq(all_1148_1, n3) = all_1179_0 & leq(n0, all_1148_1) = % 53.60/7.98 | | | | | all_1179_1 & ( ~ (all_1179_0 = 0) | ~ (all_1179_1 = 0)) % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | ALPHA: (77) implies: % 53.60/7.98 | | | | | (78) leq(n0, all_1148_1) = all_1179_1 % 53.60/7.98 | | | | | (79) leq(all_1148_1, n3) = all_1179_0 % 53.60/7.98 | | | | | (80) ~ (all_1179_0 = 0) | ~ (all_1179_1 = 0) % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | GROUND_INST: instantiating (2) with 0, all_1179_1, all_1148_1, n0, % 53.60/7.98 | | | | | simplifying with (62), (78) gives: % 53.60/7.98 | | | | | (81) all_1179_1 = 0 % 53.60/7.98 | | | | | % 53.60/7.98 | | | | | GROUND_INST: instantiating (2) with 0, all_1179_0, n3, all_1148_1, % 53.60/7.99 | | | | | simplifying with (63), (79) gives: % 53.60/7.99 | | | | | (82) all_1179_0 = 0 % 53.60/7.99 | | | | | % 53.60/7.99 | | | | | BETA: splitting (80) gives: % 53.60/7.99 | | | | | % 53.60/7.99 | | | | | Case 1: % 53.60/7.99 | | | | | | % 53.60/7.99 | | | | | | (83) ~ (all_1179_0 = 0) % 53.60/7.99 | | | | | | % 53.60/7.99 | | | | | | REDUCE: (82), (83) imply: % 53.60/7.99 | | | | | | (84) $false % 53.60/7.99 | | | | | | % 53.60/7.99 | | | | | | CLOSE: (84) is inconsistent. % 53.60/7.99 | | | | | | % 53.60/7.99 | | | | | Case 2: % 53.60/7.99 | | | | | | % 53.60/7.99 | | | | | | (85) ~ (all_1179_1 = 0) % 53.60/7.99 | | | | | | % 53.60/7.99 | | | | | | REDUCE: (81), (85) imply: % 53.60/7.99 | | | | | | (86) $false % 53.60/7.99 | | | | | | % 53.60/7.99 | | | | | | CLOSE: (86) is inconsistent. % 53.60/7.99 | | | | | | % 53.60/7.99 | | | | | End of split % 53.60/7.99 | | | | | % 53.60/7.99 | | | | End of split % 53.60/7.99 | | | | % 53.60/7.99 | | | End of split % 53.60/7.99 | | | % 53.60/7.99 | | Case 2: % 53.60/7.99 | | | % 53.60/7.99 | | | (87) all_76_12 = 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/7.99 | | | init) | ~ (pvar1400_init = init)) % 53.60/7.99 | | | % 53.60/7.99 | | | ALPHA: (87) implies: % 53.60/7.99 | | | (88) ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.99 | | | (pvar1400_init = init) % 53.60/7.99 | | | % 53.60/7.99 | | | BETA: splitting (88) gives: % 53.60/7.99 | | | % 53.60/7.99 | | | Case 1: % 53.60/7.99 | | | | % 53.60/7.99 | | | | (89) ~ (pvar1402_init = init) % 53.60/7.99 | | | | % 53.60/7.99 | | | | REDUCE: (6), (89) imply: % 53.60/7.99 | | | | (90) $false % 53.60/7.99 | | | | % 53.60/7.99 | | | | CLOSE: (90) is inconsistent. % 53.60/7.99 | | | | % 53.60/7.99 | | | Case 2: % 53.60/7.99 | | | | % 53.60/7.99 | | | | (91) ~ (pvar1401_init = init) | ~ (pvar1400_init = init) % 53.60/7.99 | | | | % 53.60/7.99 | | | | BETA: splitting (91) gives: % 53.60/7.99 | | | | % 53.60/7.99 | | | | Case 1: % 53.60/7.99 | | | | | % 53.60/7.99 | | | | | (92) ~ (pvar1401_init = init) % 53.60/7.99 | | | | | % 53.60/7.99 | | | | | REDUCE: (5), (92) imply: % 53.60/7.99 | | | | | (93) $false % 53.60/7.99 | | | | | % 53.60/7.99 | | | | | CLOSE: (93) is inconsistent. % 53.60/7.99 | | | | | % 53.60/7.99 | | | | Case 2: % 53.60/7.99 | | | | | % 53.60/7.99 | | | | | (94) ~ (pvar1400_init = init) % 53.60/7.99 | | | | | % 53.60/7.99 | | | | | REDUCE: (4), (94) imply: % 53.60/7.99 | | | | | (95) $false % 53.60/7.99 | | | | | % 53.60/7.99 | | | | | CLOSE: (95) is inconsistent. % 53.60/7.99 | | | | | % 53.60/7.99 | | | | End of split % 53.60/7.99 | | | | % 53.60/7.99 | | | End of split % 53.60/7.99 | | | % 53.60/7.99 | | End of split % 53.60/7.99 | | % 53.60/7.99 | End of split % 53.60/7.99 | % 53.60/7.99 End of proof % 53.60/7.99 % 53.60/7.99 Sub-proof #3 shows that the following formulas are inconsistent: % 53.60/7.99 ---------------------------------------------------------------- % 53.60/7.99 (1) ~ (all_76_0 = 0) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.99 a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 % 53.60/7.99 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.99 a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 % 53.60/7.99 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & % 53.60/7.99 $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/7.99 a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) % 53.60/7.99 = 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init = init) % 53.60/7.99 | ~ (pvar1401_init = init) | ~ (pvar1400_init = init))) % 53.60/7.99 (2) ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 53.60/7.99 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 53.60/7.99 ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ? [v3: any] % 53.60/7.99 : ? [v4: any] : (leq(v1, n3) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) % 53.60/7.99 | ~ (v3 = 0))))) % 53.60/7.99 (3) all_76_0 = 0 % 53.60/7.99 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 53.60/7.99 ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 53.60/7.99 (5) ~ (all_76_12 = 0) % 53.60/7.99 (6) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 53.60/7.99 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n2) % 53.60/7.99 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/7.99 (7) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 53.60/7.99 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n3) % 53.60/7.99 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/7.99 % 53.60/7.99 Begin of proof % 53.60/7.99 | % 53.60/7.99 | BETA: splitting (1) gives: % 53.60/7.99 | % 53.60/7.99 | Case 1: % 53.60/7.99 | | % 53.60/7.99 | | (8) ~ (all_76_0 = 0) % 53.60/7.99 | | % 53.60/7.99 | | REDUCE: (3), (8) imply: % 53.60/7.99 | | (9) $false % 53.60/7.99 | | % 53.60/7.99 | | CLOSE: (9) is inconsistent. % 53.60/7.99 | | % 53.60/7.99 | Case 2: % 53.60/7.99 | | % 53.60/7.99 | | (10) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/7.99 | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) % 53.60/7.99 | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 53.60/7.99 | | init) & a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & % 53.60/7.99 | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : (leq(v0, n2) = % 53.60/7.99 | | 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 % 53.60/7.99 | | = init) & a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) % 53.60/7.99 | | = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_12 = 0 & ( ~ % 53.60/7.99 | | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.99 | | (pvar1400_init = init))) % 53.60/7.99 | | % 53.60/7.99 | | REF_CLOSE: (2), (4), (5), (6), (7), (10) are inconsistent by sub-proof #4. % 53.60/7.99 | | % 53.60/7.99 | End of split % 53.60/7.99 | % 53.60/7.99 End of proof % 53.60/7.99 % 53.60/7.99 Sub-proof #4 shows that the following formulas are inconsistent: % 53.60/7.99 ---------------------------------------------------------------- % 53.60/7.99 (1) ! [v0: $i] : ( ~ (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 53.60/7.99 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 53.60/7.99 ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ? [v3: any] % 53.60/7.99 : ? [v4: any] : (leq(v1, n3) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) % 53.60/7.99 | ~ (v3 = 0))))) % 53.60/7.99 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 53.60/7.99 ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 53.60/7.99 (3) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(s_center7_init, % 53.60/7.99 v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? % 53.60/7.99 [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(s_values7_init, v0) % 53.60/7.99 = v1 & leq(v0, n3) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) | ? [v0: % 53.60/7.99 $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: $i] : ? % 53.60/7.99 [v2: $i] : ( ~ (v2 = init) & a_select3(simplex7_init, v1, v0) = v2 & % 53.60/7.99 leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & $i(v1))) | (all_76_12 = % 53.60/7.99 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 53.60/7.99 (pvar1400_init = init))) % 53.60/7.99 (4) ~ (all_76_12 = 0) % 53.60/8.00 (5) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 53.60/8.00 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n2) % 53.60/8.00 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/8.00 (6) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 53.60/8.00 v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n3) % 53.60/8.00 = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/8.00 % 53.60/8.00 Begin of proof % 53.60/8.00 | % 53.60/8.00 | BETA: splitting (3) gives: % 53.60/8.00 | % 53.60/8.00 | Case 1: % 53.60/8.00 | | % 53.60/8.00 | | (7) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/8.00 | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, v0) % 53.60/8.00 | | = 0 & $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 53.60/8.00 | | init) & a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & % 53.60/8.00 | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/8.00 | | % 53.60/8.00 | | BETA: splitting (7) gives: % 53.60/8.00 | | % 53.60/8.00 | | Case 1: % 53.60/8.00 | | | % 53.60/8.00 | | | (8) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/8.00 | | | a_select2(s_center7_init, v0) = v1 & leq(v0, n2) = 0 & leq(n0, % 53.60/8.00 | | | v0) = 0 & $i(v1) & $i(v0)) % 53.60/8.00 | | | % 53.60/8.00 | | | DELTA: instantiating (8) with fresh symbols all_992_0, all_992_1 gives: % 53.60/8.00 | | | (9) ~ (all_992_0 = init) & a_select2(s_center7_init, all_992_1) = % 53.60/8.00 | | | all_992_0 & leq(all_992_1, n2) = 0 & leq(n0, all_992_1) = 0 & % 53.60/8.00 | | | $i(all_992_0) & $i(all_992_1) % 53.60/8.00 | | | % 53.60/8.00 | | | ALPHA: (9) implies: % 53.60/8.00 | | | (10) ~ (all_992_0 = init) % 53.60/8.00 | | | (11) $i(all_992_1) % 53.60/8.00 | | | (12) leq(n0, all_992_1) = 0 % 53.60/8.00 | | | (13) leq(all_992_1, n2) = 0 % 53.60/8.00 | | | (14) a_select2(s_center7_init, all_992_1) = all_992_0 % 53.60/8.00 | | | % 53.60/8.00 | | | GROUND_INST: instantiating (1) with all_992_1, simplifying with (11), (13) % 53.60/8.00 | | | gives: % 53.60/8.00 | | | (15) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_992_1) = v0) | ! [v0: % 53.60/8.00 | | | $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(simplex7_init, % 53.60/8.00 | | | v0, all_992_1) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 53.60/8.00 | | | any] : (leq(v0, n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | % 53.60/8.00 | | | ~ (v2 = 0)))) % 53.60/8.00 | | | % 53.60/8.00 | | | GROUND_INST: instantiating (5) with all_992_1, all_992_0, simplifying with % 53.60/8.00 | | | (11), (14) gives: % 53.60/8.00 | | | (16) all_992_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_992_1, % 53.60/8.00 | | | n2) = v1 & leq(n0, all_992_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 53.60/8.00 | | | 0))) % 53.60/8.00 | | | % 53.60/8.00 | | | BETA: splitting (16) gives: % 53.60/8.00 | | | % 53.60/8.00 | | | Case 1: % 53.60/8.00 | | | | % 53.60/8.00 | | | | (17) all_992_0 = init % 53.60/8.00 | | | | % 53.60/8.00 | | | | REDUCE: (10), (17) imply: % 53.60/8.00 | | | | (18) $false % 53.60/8.00 | | | | % 53.60/8.00 | | | | CLOSE: (18) is inconsistent. % 53.60/8.00 | | | | % 53.60/8.00 | | | Case 2: % 53.60/8.00 | | | | % 53.60/8.00 | | | | (19) ? [v0: any] : ? [v1: any] : (leq(all_992_1, n2) = v1 & leq(n0, % 53.60/8.00 | | | | all_992_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/8.00 | | | | % 53.60/8.00 | | | | BETA: splitting (15) gives: % 53.60/8.00 | | | | % 53.60/8.00 | | | | Case 1: % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | (20) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_992_1) = v0) % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | DELTA: instantiating (19) with fresh symbols all_1022_0, all_1022_1 % 53.60/8.00 | | | | | gives: % 53.60/8.00 | | | | | (21) leq(all_992_1, n2) = all_1022_0 & leq(n0, all_992_1) = % 53.60/8.00 | | | | | all_1022_1 & ( ~ (all_1022_0 = 0) | ~ (all_1022_1 = 0)) % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | ALPHA: (21) implies: % 53.60/8.00 | | | | | (22) leq(n0, all_992_1) = all_1022_1 % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | DELTA: instantiating (20) with fresh symbol all_1024_0 gives: % 53.60/8.00 | | | | | (23) ~ (all_1024_0 = 0) & leq(n0, all_992_1) = all_1024_0 % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | ALPHA: (23) implies: % 53.60/8.00 | | | | | (24) ~ (all_1024_0 = 0) % 53.60/8.00 | | | | | (25) leq(n0, all_992_1) = all_1024_0 % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | GROUND_INST: instantiating (2) with 0, all_1024_0, all_992_1, n0, % 53.60/8.00 | | | | | simplifying with (12), (25) gives: % 53.60/8.00 | | | | | (26) all_1024_0 = 0 % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | GROUND_INST: instantiating (2) with all_1022_1, all_1024_0, all_992_1, % 53.60/8.00 | | | | | n0, simplifying with (22), (25) gives: % 53.60/8.00 | | | | | (27) all_1024_0 = all_1022_1 % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | COMBINE_EQS: (26), (27) imply: % 53.60/8.00 | | | | | (28) all_1022_1 = 0 % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | REDUCE: (24), (26) imply: % 53.60/8.00 | | | | | (29) $false % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | CLOSE: (29) is inconsistent. % 53.60/8.00 | | | | | % 53.60/8.00 | | | | Case 2: % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | DELTA: instantiating (19) with fresh symbols all_1023_0, all_1023_1 % 53.60/8.00 | | | | | gives: % 53.60/8.00 | | | | | (30) leq(all_992_1, n2) = all_1023_0 & leq(n0, all_992_1) = % 53.60/8.00 | | | | | all_1023_1 & ( ~ (all_1023_0 = 0) | ~ (all_1023_1 = 0)) % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | ALPHA: (30) implies: % 53.60/8.00 | | | | | (31) leq(n0, all_992_1) = all_1023_1 % 53.60/8.00 | | | | | (32) leq(all_992_1, n2) = all_1023_0 % 53.60/8.00 | | | | | (33) ~ (all_1023_0 = 0) | ~ (all_1023_1 = 0) % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | GROUND_INST: instantiating (2) with 0, all_1023_1, all_992_1, n0, % 53.60/8.00 | | | | | simplifying with (12), (31) gives: % 53.60/8.00 | | | | | (34) all_1023_1 = 0 % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | GROUND_INST: instantiating (2) with 0, all_1023_0, n2, all_992_1, % 53.60/8.00 | | | | | simplifying with (13), (32) gives: % 53.60/8.00 | | | | | (35) all_1023_0 = 0 % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | BETA: splitting (33) gives: % 53.60/8.00 | | | | | % 53.60/8.00 | | | | | Case 1: % 53.60/8.00 | | | | | | % 53.60/8.00 | | | | | | (36) ~ (all_1023_0 = 0) % 53.60/8.00 | | | | | | % 53.60/8.00 | | | | | | REDUCE: (35), (36) imply: % 53.60/8.00 | | | | | | (37) $false % 53.60/8.00 | | | | | | % 53.60/8.00 | | | | | | CLOSE: (37) is inconsistent. % 53.60/8.00 | | | | | | % 53.60/8.00 | | | | | Case 2: % 53.60/8.00 | | | | | | % 53.60/8.00 | | | | | | (38) ~ (all_1023_1 = 0) % 53.60/8.00 | | | | | | % 53.60/8.00 | | | | | | REDUCE: (34), (38) imply: % 53.60/8.00 | | | | | | (39) $false % 53.60/8.00 | | | | | | % 53.60/8.00 | | | | | | CLOSE: (39) is inconsistent. % 53.60/8.00 | | | | | | % 53.60/8.00 | | | | | End of split % 53.60/8.00 | | | | | % 53.60/8.00 | | | | End of split % 53.60/8.00 | | | | % 53.60/8.00 | | | End of split % 53.60/8.00 | | | % 53.60/8.00 | | Case 2: % 53.60/8.00 | | | % 53.60/8.00 | | | (40) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/8.00 | | | a_select2(s_values7_init, v0) = v1 & leq(v0, n3) = 0 & leq(n0, % 53.60/8.00 | | | v0) = 0 & $i(v1) & $i(v0)) % 53.60/8.00 | | | % 53.60/8.00 | | | DELTA: instantiating (40) with fresh symbols all_992_0, all_992_1 gives: % 53.60/8.00 | | | (41) ~ (all_992_0 = init) & a_select2(s_values7_init, all_992_1) = % 53.60/8.00 | | | all_992_0 & leq(all_992_1, n3) = 0 & leq(n0, all_992_1) = 0 & % 53.60/8.00 | | | $i(all_992_0) & $i(all_992_1) % 53.60/8.00 | | | % 53.60/8.00 | | | ALPHA: (41) implies: % 53.60/8.00 | | | (42) ~ (all_992_0 = init) % 53.60/8.00 | | | (43) $i(all_992_1) % 53.60/8.00 | | | (44) leq(n0, all_992_1) = 0 % 53.60/8.00 | | | (45) leq(all_992_1, n3) = 0 % 53.60/8.00 | | | (46) a_select2(s_values7_init, all_992_1) = all_992_0 % 53.60/8.00 | | | % 53.60/8.01 | | | GROUND_INST: instantiating (6) with all_992_1, all_992_0, simplifying with % 53.60/8.01 | | | (43), (46) gives: % 53.60/8.01 | | | (47) all_992_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_992_1, % 53.60/8.01 | | | n3) = v1 & leq(n0, all_992_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 53.60/8.01 | | | 0))) % 53.60/8.01 | | | % 53.60/8.01 | | | BETA: splitting (47) gives: % 53.60/8.01 | | | % 53.60/8.01 | | | Case 1: % 53.60/8.01 | | | | % 53.60/8.01 | | | | (48) all_992_0 = init % 53.60/8.01 | | | | % 53.60/8.01 | | | | REDUCE: (42), (48) imply: % 53.60/8.01 | | | | (49) $false % 53.60/8.01 | | | | % 53.60/8.01 | | | | CLOSE: (49) is inconsistent. % 53.60/8.01 | | | | % 53.60/8.01 | | | Case 2: % 53.60/8.01 | | | | % 53.60/8.01 | | | | (50) ? [v0: any] : ? [v1: any] : (leq(all_992_1, n3) = v1 & leq(n0, % 53.60/8.01 | | | | all_992_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/8.01 | | | | % 53.60/8.01 | | | | DELTA: instantiating (50) with fresh symbols all_1020_0, all_1020_1 % 53.60/8.01 | | | | gives: % 53.60/8.01 | | | | (51) leq(all_992_1, n3) = all_1020_0 & leq(n0, all_992_1) = % 53.60/8.01 | | | | all_1020_1 & ( ~ (all_1020_0 = 0) | ~ (all_1020_1 = 0)) % 53.60/8.01 | | | | % 53.60/8.01 | | | | ALPHA: (51) implies: % 53.60/8.01 | | | | (52) leq(n0, all_992_1) = all_1020_1 % 53.60/8.01 | | | | (53) leq(all_992_1, n3) = all_1020_0 % 53.60/8.01 | | | | (54) ~ (all_1020_0 = 0) | ~ (all_1020_1 = 0) % 53.60/8.01 | | | | % 53.60/8.01 | | | | GROUND_INST: instantiating (2) with 0, all_1020_1, all_992_1, n0, % 53.60/8.01 | | | | simplifying with (44), (52) gives: % 53.60/8.01 | | | | (55) all_1020_1 = 0 % 53.60/8.01 | | | | % 53.60/8.01 | | | | GROUND_INST: instantiating (2) with 0, all_1020_0, n3, all_992_1, % 53.60/8.01 | | | | simplifying with (45), (53) gives: % 53.60/8.01 | | | | (56) all_1020_0 = 0 % 53.60/8.01 | | | | % 53.60/8.01 | | | | BETA: splitting (54) gives: % 53.60/8.01 | | | | % 53.60/8.01 | | | | Case 1: % 53.60/8.01 | | | | | % 53.60/8.01 | | | | | (57) ~ (all_1020_0 = 0) % 53.60/8.01 | | | | | % 53.60/8.01 | | | | | REDUCE: (56), (57) imply: % 53.60/8.01 | | | | | (58) $false % 53.60/8.01 | | | | | % 53.60/8.01 | | | | | CLOSE: (58) is inconsistent. % 53.60/8.01 | | | | | % 53.60/8.01 | | | | Case 2: % 53.60/8.01 | | | | | % 53.60/8.01 | | | | | (59) ~ (all_1020_1 = 0) % 53.60/8.01 | | | | | % 53.60/8.01 | | | | | REDUCE: (55), (59) imply: % 53.60/8.01 | | | | | (60) $false % 53.60/8.01 | | | | | % 53.60/8.01 | | | | | CLOSE: (60) is inconsistent. % 53.60/8.01 | | | | | % 53.60/8.01 | | | | End of split % 53.60/8.01 | | | | % 53.60/8.01 | | | End of split % 53.60/8.01 | | | % 53.60/8.01 | | End of split % 53.60/8.01 | | % 53.60/8.01 | Case 2: % 53.60/8.01 | | % 53.60/8.01 | | (61) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? [v1: % 53.60/8.01 | | $i] : ? [v2: $i] : ( ~ (v2 = init) & a_select3(simplex7_init, % 53.60/8.01 | | v1, v0) = v2 & leq(v1, n3) = 0 & leq(n0, v1) = 0 & $i(v2) & % 53.60/8.01 | | $i(v1))) | (all_76_12 = 0 & ( ~ (pvar1402_init = init) | ~ % 53.60/8.01 | | (pvar1401_init = init) | ~ (pvar1400_init = init))) % 53.60/8.01 | | % 53.60/8.01 | | BETA: splitting (61) gives: % 53.60/8.01 | | % 53.60/8.01 | | Case 1: % 53.60/8.01 | | | % 53.60/8.01 | | | (62) ? [v0: $i] : (leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v0) & ? % 53.60/8.01 | | | [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & % 53.60/8.01 | | | a_select3(simplex7_init, v1, v0) = v2 & leq(v1, n3) = 0 & % 53.60/8.01 | | | leq(n0, v1) = 0 & $i(v2) & $i(v1))) % 53.60/8.01 | | | % 53.60/8.01 | | | DELTA: instantiating (62) with fresh symbol all_992_0 gives: % 53.60/8.01 | | | (63) leq(all_992_0, n2) = 0 & leq(n0, all_992_0) = 0 & $i(all_992_0) & % 53.60/8.01 | | | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/8.01 | | | a_select3(simplex7_init, v0, all_992_0) = v1 & leq(v0, n3) = 0 & % 53.60/8.01 | | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/8.01 | | | % 53.60/8.01 | | | ALPHA: (63) implies: % 53.60/8.01 | | | (64) $i(all_992_0) % 53.60/8.01 | | | (65) leq(n0, all_992_0) = 0 % 53.60/8.01 | | | (66) leq(all_992_0, n2) = 0 % 53.60/8.01 | | | (67) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 53.60/8.01 | | | a_select3(simplex7_init, v0, all_992_0) = v1 & leq(v0, n3) = 0 & % 53.60/8.01 | | | leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 53.60/8.01 | | | % 53.60/8.01 | | | DELTA: instantiating (67) with fresh symbols all_994_0, all_994_1 gives: % 53.60/8.01 | | | (68) ~ (all_994_0 = init) & a_select3(simplex7_init, all_994_1, % 53.60/8.01 | | | all_992_0) = all_994_0 & leq(all_994_1, n3) = 0 & leq(n0, % 53.60/8.01 | | | all_994_1) = 0 & $i(all_994_0) & $i(all_994_1) % 53.60/8.01 | | | % 53.60/8.01 | | | ALPHA: (68) implies: % 53.60/8.01 | | | (69) ~ (all_994_0 = init) % 53.60/8.01 | | | (70) $i(all_994_1) % 53.60/8.01 | | | (71) leq(n0, all_994_1) = 0 % 53.60/8.01 | | | (72) leq(all_994_1, n3) = 0 % 53.60/8.01 | | | (73) a_select3(simplex7_init, all_994_1, all_992_0) = all_994_0 % 53.60/8.01 | | | % 53.60/8.01 | | | GROUND_INST: instantiating (1) with all_992_0, simplifying with (64), (66) % 53.60/8.01 | | | gives: % 53.60/8.01 | | | (74) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_992_0) = v0) | ! [v0: % 53.60/8.01 | | | $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(simplex7_init, % 53.60/8.01 | | | v0, all_992_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 53.60/8.01 | | | any] : (leq(v0, n3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | % 53.60/8.01 | | | ~ (v2 = 0)))) % 53.60/8.01 | | | % 53.60/8.01 | | | BETA: splitting (74) gives: % 53.60/8.01 | | | % 53.60/8.01 | | | Case 1: % 53.60/8.01 | | | | % 53.60/8.01 | | | | (75) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_992_0) = v0) % 53.60/8.01 | | | | % 53.60/8.01 | | | | DELTA: instantiating (75) with fresh symbol all_1021_0 gives: % 53.60/8.01 | | | | (76) ~ (all_1021_0 = 0) & leq(n0, all_992_0) = all_1021_0 % 53.60/8.01 | | | | % 53.60/8.01 | | | | ALPHA: (76) implies: % 53.60/8.01 | | | | (77) ~ (all_1021_0 = 0) % 53.60/8.01 | | | | (78) leq(n0, all_992_0) = all_1021_0 % 53.60/8.01 | | | | % 53.60/8.01 | | | | GROUND_INST: instantiating (2) with 0, all_1021_0, all_992_0, n0, % 53.60/8.01 | | | | simplifying with (65), (78) gives: % 53.60/8.01 | | | | (79) all_1021_0 = 0 % 53.60/8.01 | | | | % 53.60/8.01 | | | | REDUCE: (77), (79) imply: % 53.60/8.01 | | | | (80) $false % 53.60/8.01 | | | | % 53.60/8.01 | | | | CLOSE: (80) is inconsistent. % 53.60/8.01 | | | | % 53.60/8.01 | | | Case 2: % 53.60/8.01 | | | | % 53.60/8.01 | | | | (81) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 53.60/8.01 | | | | (a_select3(simplex7_init, v0, all_992_0) = v1) | ~ $i(v0) | % 53.60/8.01 | | | | ? [v2: any] : ? [v3: any] : (leq(v0, n3) = v3 & leq(n0, v0) = % 53.60/8.01 | | | | v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) % 53.60/8.01 | | | | % 53.60/8.01 | | | | GROUND_INST: instantiating (81) with all_994_1, all_994_0, simplifying % 53.60/8.01 | | | | with (70), (73) gives: % 53.60/8.02 | | | | (82) all_994_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_994_1, % 53.60/8.02 | | | | n3) = v1 & leq(n0, all_994_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 53.60/8.02 | | | | 0))) % 53.60/8.02 | | | | % 53.60/8.02 | | | | BETA: splitting (82) gives: % 53.60/8.02 | | | | % 53.60/8.02 | | | | Case 1: % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | (83) all_994_0 = init % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | REDUCE: (69), (83) imply: % 53.60/8.02 | | | | | (84) $false % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | CLOSE: (84) is inconsistent. % 53.60/8.02 | | | | | % 53.60/8.02 | | | | Case 2: % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | (85) ? [v0: any] : ? [v1: any] : (leq(all_994_1, n3) = v1 & % 53.60/8.02 | | | | | leq(n0, all_994_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | DELTA: instantiating (85) with fresh symbols all_1050_0, all_1050_1 % 53.60/8.02 | | | | | gives: % 53.60/8.02 | | | | | (86) leq(all_994_1, n3) = all_1050_0 & leq(n0, all_994_1) = % 53.60/8.02 | | | | | all_1050_1 & ( ~ (all_1050_0 = 0) | ~ (all_1050_1 = 0)) % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | ALPHA: (86) implies: % 53.60/8.02 | | | | | (87) leq(n0, all_994_1) = all_1050_1 % 53.60/8.02 | | | | | (88) leq(all_994_1, n3) = all_1050_0 % 53.60/8.02 | | | | | (89) ~ (all_1050_0 = 0) | ~ (all_1050_1 = 0) % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | GROUND_INST: instantiating (2) with 0, all_1050_1, all_994_1, n0, % 53.60/8.02 | | | | | simplifying with (71), (87) gives: % 53.60/8.02 | | | | | (90) all_1050_1 = 0 % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | GROUND_INST: instantiating (2) with 0, all_1050_0, n3, all_994_1, % 53.60/8.02 | | | | | simplifying with (72), (88) gives: % 53.60/8.02 | | | | | (91) all_1050_0 = 0 % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | BETA: splitting (89) gives: % 53.60/8.02 | | | | | % 53.60/8.02 | | | | | Case 1: % 53.60/8.02 | | | | | | % 53.60/8.02 | | | | | | (92) ~ (all_1050_0 = 0) % 53.60/8.02 | | | | | | % 53.60/8.02 | | | | | | REDUCE: (91), (92) imply: % 53.60/8.02 | | | | | | (93) $false % 53.60/8.02 | | | | | | % 53.60/8.02 | | | | | | CLOSE: (93) is inconsistent. % 53.60/8.02 | | | | | | % 53.60/8.02 | | | | | Case 2: % 53.60/8.02 | | | | | | % 53.60/8.02 | | | | | | (94) ~ (all_1050_1 = 0) % 53.60/8.02 | | | | | | % 53.60/8.02 | | | | | | REDUCE: (90), (94) imply: % 53.60/8.02 | | | | | | (95) $false % 53.60/8.02 | | | | | | % 53.60/8.02 | | | | | | CLOSE: (95) is inconsistent. % 53.60/8.02 | | | | | | % 53.60/8.02 | | | | | End of split % 53.60/8.02 | | | | | % 53.60/8.02 | | | | End of split % 53.60/8.02 | | | | % 53.60/8.02 | | | End of split % 53.60/8.02 | | | % 53.60/8.02 | | Case 2: % 53.60/8.02 | | | % 53.60/8.02 | | | (96) all_76_12 = 0 & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = % 53.60/8.02 | | | init) | ~ (pvar1400_init = init)) % 53.60/8.02 | | | % 53.60/8.02 | | | ALPHA: (96) implies: % 53.60/8.02 | | | (97) all_76_12 = 0 % 53.60/8.02 | | | % 53.60/8.02 | | | REDUCE: (4), (97) imply: % 53.60/8.02 | | | (98) $false % 53.60/8.02 | | | % 53.60/8.02 | | | CLOSE: (98) is inconsistent. % 53.60/8.02 | | | % 53.60/8.02 | | End of split % 53.60/8.02 | | % 53.60/8.02 | End of split % 53.60/8.02 | % 53.60/8.02 End of proof % 53.60/8.02 % SZS output end Proof for theBenchmark % 53.86/8.02 % 53.86/8.02 7347ms %------------------------------------------------------------------------------