%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV026+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 : n013.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 22:54:37 EDT 2023 % Result : Theorem 164.53s 22.27s % Output : Proof 165.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV026+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n013.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 05:51:02 EDT 2023 % 0.13/0.34 % CPUTime : % 0.44/0.67 ________ _____ % 0.44/0.67 ___ __ \_________(_)________________________________ % 0.44/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.44/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.44/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.44/0.67 % 0.44/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.44/0.67 (2023-06-19) % 0.44/0.67 % 0.44/0.67 (c) Philipp Rümmer, 2009-2023 % 0.44/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.44/0.67 Amanda Stjerna. % 0.44/0.67 Free software under BSD-3-Clause. % 0.44/0.67 % 0.44/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.44/0.67 % 0.44/0.68 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.69 Running up to 7 provers in parallel. % 0.74/0.72 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.74/0.72 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.74/0.72 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.74/0.72 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.74/0.72 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.74/0.72 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.74/0.72 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 5.94/1.64 Prover 1: Preprocessing ... % 5.94/1.65 Prover 4: Preprocessing ... % 6.32/1.68 Prover 3: Preprocessing ... % 6.32/1.68 Prover 6: Preprocessing ... % 6.32/1.68 Prover 2: Preprocessing ... % 6.32/1.68 Prover 0: Preprocessing ... % 6.32/1.71 Prover 5: Preprocessing ... % 16.42/3.03 Prover 3: Warning: ignoring some quantifiers % 16.42/3.07 Prover 1: Warning: ignoring some quantifiers % 16.94/3.11 Prover 3: Constructing countermodel ... % 16.94/3.14 Prover 6: Proving ... % 16.94/3.20 Prover 1: Constructing countermodel ... % 16.94/3.23 Prover 4: Warning: ignoring some quantifiers % 18.79/3.36 Prover 4: Constructing countermodel ... % 18.79/3.39 Prover 5: Proving ... % 19.85/3.49 Prover 2: Proving ... % 19.85/3.56 Prover 0: Proving ... % 73.78/10.49 Prover 2: stopped % 73.78/10.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.78/10.65 Prover 7: Preprocessing ... % 77.52/10.98 Prover 7: Warning: ignoring some quantifiers % 77.89/11.03 Prover 7: Constructing countermodel ... % 101.48/14.06 Prover 5: stopped % 101.48/14.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 103.18/14.30 Prover 8: Preprocessing ... % 106.04/14.69 Prover 8: Warning: ignoring some quantifiers % 106.61/14.73 Prover 8: Constructing countermodel ... % 116.63/16.07 Prover 1: stopped % 116.63/16.07 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 117.97/16.26 Prover 9: Preprocessing ... % 121.45/16.68 Prover 9: Warning: ignoring some quantifiers % 121.45/16.70 Prover 9: Constructing countermodel ... % 130.96/17.96 Prover 6: stopped % 130.96/17.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.51/18.13 Prover 10: Preprocessing ... % 133.25/18.29 Prover 10: Warning: ignoring some quantifiers % 133.25/18.30 Prover 10: Constructing countermodel ... % 164.16/22.25 Prover 10: Found proof (size 304) % 164.16/22.26 Prover 10: proved (4284ms) % 164.16/22.26 Prover 0: stopped % 164.53/22.27 Prover 3: stopped % 164.53/22.27 Prover 7: stopped % 164.53/22.27 Prover 9: stopped % 164.53/22.27 Prover 4: stopped % 164.53/22.27 Prover 8: stopped % 164.53/22.27 % 164.53/22.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 164.53/22.27 % 164.53/22.30 % SZS output start Proof for theBenchmark % 164.53/22.30 Assumptions after simplification: % 164.53/22.30 --------------------------------- % 164.53/22.30 % 164.53/22.30 (finite_domain_1) % 164.53/22.31 $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, % 164.53/22.31 n1) | ~ leq(n0, v0)) % 164.53/22.31 % 164.53/22.31 (finite_domain_2) % 164.53/22.31 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ % 164.53/22.31 $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0)) % 164.53/22.31 % 164.53/22.31 (gauss_init_0017) % 164.53/22.37 $i(pvar1402_init) & $i(pvar1401_init) & $i(pvar1400_init) & $i(loopcounter) & % 164.53/22.37 $i(s_try7_init) & $i(s_center7_init) & $i(s_values7_init) & $i(simplex7_init) % 164.53/22.37 & $i(n330) & $i(n410) & $i(pv1376) & $i(pv20) & $i(pv19) & $i(pv9) & % 164.53/22.37 $i(s_worst7) & $i(s_sworst7) & $i(s_best7) & $i(s_worst7_init) & % 164.53/22.37 $i(s_sworst7_init) & $i(s_best7_init) & $i(init) & $i(n3) & $i(n2) & $i(n1) & % 164.53/22.37 $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 164.53/22.37 ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 164.53/22.37 $i] : ? [v11: $i] : (s_worst7_init = init & s_sworst7_init = init & % 164.53/22.37 s_best7_init = init & minus(n330, n1) = v1 & minus(n410, n1) = v0 & % 164.53/22.37 minus(n3, n1) = v2 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & $i(v3) & $i(v2) & % 164.53/22.37 $i(v1) & $i(v0) & leq(pv1376, n3) & leq(pv20, v1) & leq(pv19, v0) & leq(pv9, % 164.53/22.37 v0) & leq(s_worst7, n3) & leq(s_sworst7, n3) & leq(s_best7, n3) & leq(n0, % 164.53/22.37 pv1376) & leq(n0, pv20) & leq(n0, pv19) & leq(n0, pv9) & leq(n0, s_worst7) % 164.53/22.37 & leq(n0, s_sworst7) & leq(n0, s_best7) & ! [v12: $i] : ! [v13: $i] : ! % 164.53/22.37 [v14: $i] : (v14 = init | ~ (a_select3(simplex7_init, v13, v12) = v14) | ~ % 164.53/22.37 $i(v13) | ~ $i(v12) | ~ leq(v13, n3) | ~ leq(v12, n2) | ~ leq(n0, v13) % 164.53/22.37 | ~ leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] : (v13 = init | ~ % 164.53/22.37 (a_select2(s_try7_init, v12) = v13) | ~ $i(v12) | ~ leq(v12, v2) | ~ % 164.53/22.37 leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] : (v13 = init | ~ % 164.53/22.37 (a_select2(s_center7_init, v12) = v13) | ~ $i(v12) | ~ leq(v12, n2) | ~ % 164.53/22.37 leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] : (v13 = init | ~ % 164.53/22.37 (a_select2(s_values7_init, v12) = v13) | ~ $i(v12) | ~ leq(v12, n3) | ~ % 164.53/22.37 leq(n0, v12)) & ( ~ gt(loopcounter, n1) | (pvar1402_init = init & % 164.53/22.37 pvar1401_init = init & pvar1400_init = init)) & (( ~ (v11 = init) & % 164.53/22.37 a_select3(simplex7_init, v10, v9) = v11 & $i(v11) & leq(v10, n3) & % 164.53/22.37 leq(v9, n2) & leq(n0, v10) & leq(n0, v9)) | ( ~ (v8 = init) & % 164.53/22.37 a_select2(s_values7_init, v7) = v8 & $i(v8) & leq(v7, n3) & leq(n0, v7)) % 164.53/22.37 | ( ~ (v6 = init) & a_select2(s_center7_init, v5) = v6 & $i(v6) & leq(v5, % 164.53/22.37 n2) & leq(n0, v5)) | ( ~ (v4 = init) & a_select2(s_try7_init, v3) = v4 % 164.53/22.37 & $i(v4) & leq(v3, v2) & leq(n0, v3)) | (gt(loopcounter, n1) & ( ~ % 164.53/22.37 (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ (pvar1400_init % 164.53/22.37 = init))))) % 164.53/22.37 % 164.53/22.37 (irreflexivity_gt) % 164.53/22.37 ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 164.53/22.37 % 164.53/22.37 (leq_gt2) % 164.53/22.38 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) % 164.53/22.38 | gt(v1, v0)) % 164.53/22.38 % 164.53/22.38 (leq_gt_pred) % 164.53/22.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ % 164.53/22.38 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 164.53/22.38 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, % 164.53/22.38 v2)) % 164.53/22.38 % 164.53/22.38 (pred_minus_1) % 164.53/22.38 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 164.53/22.38 (pred(v0) = v1 & $i(v1))) % 164.53/22.38 % 164.53/22.38 (pred_succ) % 164.53/22.38 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 164.53/22.38 % 164.53/22.38 (successor_1) % 164.53/22.38 succ(n0) = n1 & $i(n1) & $i(n0) % 164.53/22.38 % 164.53/22.38 (successor_2) % 164.53/22.38 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 164.53/22.38 % 164.53/22.38 (successor_3) % 164.53/22.38 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 164.53/22.38 succ(n0) = v0 & $i(v1) & $i(v0)) % 164.53/22.38 % 164.53/22.38 (successor_4) % 164.53/22.39 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 164.53/22.39 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 164.53/22.39 % 164.53/22.39 (successor_5) % 164.53/22.39 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 164.53/22.39 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 164.53/22.39 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 164.53/22.39 % 164.53/22.39 (function-axioms) % 164.53/22.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 164.53/22.40 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 164.53/22.40 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 164.53/22.40 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 164.53/22.40 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 164.53/22.40 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 164.53/22.40 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 164.53/22.40 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 164.53/22.40 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 164.53/22.40 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 164.53/22.40 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 164.53/22.40 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 164.53/22.40 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 164.53/22.40 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 164.53/22.40 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 164.53/22.40 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 164.53/22.40 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 164.53/22.40 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 164.53/22.40 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 164.53/22.40 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 164.53/22.40 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 164.53/22.40 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 164.53/22.40 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 164.53/22.40 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 164.53/22.40 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 164.53/22.40 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 164.53/22.40 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ % 164.53/22.40 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 164.53/22.40 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 164.53/22.40 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : % 164.53/22.40 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = % 164.53/22.40 v0)) % 164.53/22.40 % 164.53/22.40 Further assumptions not needed in the proof: % 164.53/22.40 -------------------------------------------- % 164.53/22.40 const_array1_select, const_array2_select, defuse, finite_domain_0, % 164.53/22.40 finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0, % 164.53/22.40 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_330_0, gt_330_1, % 164.53/22.40 gt_330_2, gt_330_3, gt_330_4, gt_330_5, gt_330_tptp_minus_1, gt_3_0, gt_3_1, % 164.53/22.40 gt_3_2, gt_3_tptp_minus_1, gt_410_0, gt_410_1, gt_410_2, gt_410_3, gt_410_330, % 164.53/22.40 gt_410_4, gt_410_5, gt_410_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, % 164.53/22.40 gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, % 164.53/22.40 gt_succ, leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 164.53/22.40 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 164.53/22.40 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 164.53/22.40 matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2, % 164.53/22.40 sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, % 164.53/22.40 succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, % 164.53/22.40 succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, % 164.53/22.40 succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality, % 164.53/22.40 transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 164.53/22.40 uniform_int_rand_ranges_lo % 164.53/22.40 % 164.53/22.40 Those formulas are unsatisfiable: % 164.53/22.40 --------------------------------- % 164.53/22.40 % 164.53/22.40 Begin of proof % 164.53/22.40 | % 164.53/22.40 | ALPHA: (leq_gt_pred) implies: % 164.53/22.41 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 164.53/22.41 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 164.53/22.41 | % 164.53/22.41 | ALPHA: (pred_minus_1) implies: % 164.53/22.41 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 164.53/22.41 | (pred(v0) = v1 & $i(v1))) % 164.53/22.41 | % 164.53/22.41 | ALPHA: (finite_domain_1) implies: % 164.53/22.41 | (3) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 164.53/22.41 | leq(n0, v0)) % 164.53/22.41 | % 164.53/22.41 | ALPHA: (finite_domain_2) implies: % 164.53/22.41 | (4) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) % 164.53/22.41 | | ~ leq(n0, v0)) % 164.53/22.41 | % 164.53/22.41 | ALPHA: (successor_4) implies: % 164.53/22.41 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 164.53/22.41 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 164.53/22.41 | % 164.53/22.41 | ALPHA: (successor_5) implies: % 164.53/22.41 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 164.53/22.41 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 164.53/22.41 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 164.53/22.41 | % 164.53/22.41 | ALPHA: (successor_1) implies: % 164.53/22.41 | (7) succ(n0) = n1 % 164.53/22.41 | % 164.53/22.41 | ALPHA: (successor_2) implies: % 164.53/22.41 | (8) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 164.53/22.42 | % 164.53/22.42 | ALPHA: (successor_3) implies: % 164.53/22.42 | (9) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) = % 164.53/22.42 | v0 & $i(v1) & $i(v0)) % 164.53/22.42 | % 164.53/22.42 | ALPHA: (gauss_init_0017) implies: % 164.53/22.42 | (10) $i(n0) % 164.53/22.43 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 164.53/22.43 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 164.53/22.43 | ? [v10: $i] : ? [v11: $i] : (s_worst7_init = init & s_sworst7_init = % 164.53/22.43 | init & s_best7_init = init & minus(n330, n1) = v1 & minus(n410, n1) % 164.53/22.43 | = v0 & minus(n3, n1) = v2 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & % 164.53/22.43 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(pv1376, n3) & leq(pv20, v1) % 164.53/22.43 | & leq(pv19, v0) & leq(pv9, v0) & leq(s_worst7, n3) & leq(s_sworst7, % 164.53/22.43 | n3) & leq(s_best7, n3) & leq(n0, pv1376) & leq(n0, pv20) & leq(n0, % 164.53/22.43 | pv19) & leq(n0, pv9) & leq(n0, s_worst7) & leq(n0, s_sworst7) & % 164.53/22.43 | leq(n0, s_best7) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : (v14 % 164.53/22.43 | = init | ~ (a_select3(simplex7_init, v13, v12) = v14) | ~ % 164.53/22.43 | $i(v13) | ~ $i(v12) | ~ leq(v13, n3) | ~ leq(v12, n2) | ~ % 164.53/22.43 | leq(n0, v13) | ~ leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] : % 164.53/22.43 | (v13 = init | ~ (a_select2(s_try7_init, v12) = v13) | ~ $i(v12) | % 164.53/22.43 | ~ leq(v12, v2) | ~ leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] : % 164.53/22.43 | (v13 = init | ~ (a_select2(s_center7_init, v12) = v13) | ~ $i(v12) % 164.53/22.43 | | ~ leq(v12, n2) | ~ leq(n0, v12)) & ! [v12: $i] : ! [v13: $i] % 164.53/22.43 | : (v13 = init | ~ (a_select2(s_values7_init, v12) = v13) | ~ % 164.53/22.43 | $i(v12) | ~ leq(v12, n3) | ~ leq(n0, v12)) & ( ~ gt(loopcounter, % 164.53/22.43 | n1) | (pvar1402_init = init & pvar1401_init = init & % 164.53/22.43 | pvar1400_init = init)) & (( ~ (v11 = init) & % 164.53/22.43 | a_select3(simplex7_init, v10, v9) = v11 & $i(v11) & leq(v10, n3) % 164.53/22.43 | & leq(v9, n2) & leq(n0, v10) & leq(n0, v9)) | ( ~ (v8 = init) & % 164.53/22.43 | a_select2(s_values7_init, v7) = v8 & $i(v8) & leq(v7, n3) & % 164.53/22.43 | leq(n0, v7)) | ( ~ (v6 = init) & a_select2(s_center7_init, v5) = % 164.53/22.43 | v6 & $i(v6) & leq(v5, n2) & leq(n0, v5)) | ( ~ (v4 = init) & % 164.53/22.43 | a_select2(s_try7_init, v3) = v4 & $i(v4) & leq(v3, v2) & leq(n0, % 164.53/22.43 | v3)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~ % 164.53/22.43 | (pvar1401_init = init) | ~ (pvar1400_init = init))))) % 164.53/22.43 | % 165.00/22.43 | ALPHA: (function-axioms) implies: % 165.00/22.43 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = % 165.00/22.43 | v1) | ~ (pred(v2) = v0)) % 165.00/22.43 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 165.00/22.43 | v1) | ~ (succ(v2) = v0)) % 165.00/22.43 | % 165.00/22.43 | DELTA: instantiating (8) with fresh symbol all_54_0 gives: % 165.00/22.43 | (14) succ(all_54_0) = n2 & succ(n0) = all_54_0 & $i(all_54_0) % 165.00/22.43 | % 165.00/22.43 | ALPHA: (14) implies: % 165.00/22.43 | (15) $i(all_54_0) % 165.00/22.43 | (16) succ(n0) = all_54_0 % 165.00/22.43 | (17) succ(all_54_0) = n2 % 165.00/22.43 | % 165.00/22.43 | DELTA: instantiating (9) with fresh symbols all_57_0, all_57_1 gives: % 165.00/22.44 | (18) succ(all_57_0) = n3 & succ(all_57_1) = all_57_0 & succ(n0) = all_57_1 % 165.00/22.44 | & $i(all_57_0) & $i(all_57_1) % 165.00/22.44 | % 165.00/22.44 | ALPHA: (18) implies: % 165.00/22.44 | (19) $i(all_57_0) % 165.00/22.44 | (20) succ(n0) = all_57_1 % 165.00/22.44 | (21) succ(all_57_1) = all_57_0 % 165.00/22.44 | (22) succ(all_57_0) = n3 % 165.00/22.44 | % 165.00/22.44 | DELTA: instantiating (5) with fresh symbols all_59_0, all_59_1, all_59_2 % 165.00/22.44 | gives: % 165.00/22.44 | (23) succ(all_59_0) = n4 & succ(all_59_1) = all_59_0 & succ(all_59_2) = % 165.00/22.44 | all_59_1 & succ(n0) = all_59_2 & $i(all_59_0) & $i(all_59_1) & % 165.00/22.44 | $i(all_59_2) % 165.00/22.44 | % 165.00/22.44 | ALPHA: (23) implies: % 165.00/22.44 | (24) $i(all_59_0) % 165.00/22.44 | (25) succ(n0) = all_59_2 % 165.00/22.44 | (26) succ(all_59_2) = all_59_1 % 165.00/22.44 | (27) succ(all_59_1) = all_59_0 % 165.00/22.44 | % 165.00/22.44 | DELTA: instantiating (6) with fresh symbols all_61_0, all_61_1, all_61_2, % 165.00/22.44 | all_61_3 gives: % 165.00/22.44 | (28) succ(all_61_0) = n5 & succ(all_61_1) = all_61_0 & succ(all_61_2) = % 165.00/22.44 | all_61_1 & succ(all_61_3) = all_61_2 & succ(n0) = all_61_3 & % 165.00/22.44 | $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3) % 165.00/22.44 | % 165.00/22.44 | ALPHA: (28) implies: % 165.00/22.44 | (29) succ(n0) = all_61_3 % 165.00/22.44 | (30) succ(all_61_3) = all_61_2 % 165.00/22.44 | (31) succ(all_61_2) = all_61_1 % 165.00/22.44 | % 165.00/22.44 | DELTA: instantiating (11) with fresh symbols all_71_0, all_71_1, all_71_2, % 165.00/22.44 | all_71_3, all_71_4, all_71_5, all_71_6, all_71_7, all_71_8, all_71_9, % 165.00/22.44 | all_71_10, all_71_11 gives: % 165.00/22.45 | (32) s_worst7_init = init & s_sworst7_init = init & s_best7_init = init & % 165.00/22.45 | minus(n330, n1) = all_71_10 & minus(n410, n1) = all_71_11 & minus(n3, % 165.00/22.45 | n1) = all_71_9 & $i(all_71_1) & $i(all_71_2) & $i(all_71_4) & % 165.00/22.45 | $i(all_71_6) & $i(all_71_8) & $i(all_71_9) & $i(all_71_10) & % 165.00/22.45 | $i(all_71_11) & leq(pv1376, n3) & leq(pv20, all_71_10) & leq(pv19, % 165.00/22.45 | all_71_11) & leq(pv9, all_71_11) & leq(s_worst7, n3) & % 165.00/22.45 | leq(s_sworst7, n3) & leq(s_best7, n3) & leq(n0, pv1376) & leq(n0, % 165.00/22.45 | pv20) & leq(n0, pv19) & leq(n0, pv9) & leq(n0, s_worst7) & leq(n0, % 165.00/22.45 | s_sworst7) & leq(n0, s_best7) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 165.00/22.45 | $i] : (v2 = init | ~ (a_select3(simplex7_init, v1, v0) = v2) | ~ % 165.00/22.45 | $i(v1) | ~ $i(v0) | ~ leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0, % 165.00/22.45 | v1) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = init | % 165.00/22.45 | ~ (a_select2(s_try7_init, v0) = v1) | ~ $i(v0) | ~ leq(v0, % 165.00/22.45 | all_71_9) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = % 165.00/22.45 | init | ~ (a_select2(s_center7_init, v0) = v1) | ~ $i(v0) | ~ % 165.00/22.45 | leq(v0, n2) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = % 165.00/22.45 | init | ~ (a_select2(s_values7_init, v0) = v1) | ~ $i(v0) | ~ % 165.00/22.45 | leq(v0, n3) | ~ leq(n0, v0)) & ( ~ gt(loopcounter, n1) | % 165.00/22.45 | (pvar1402_init = init & pvar1401_init = init & pvar1400_init = % 165.00/22.45 | init)) & (( ~ (all_71_0 = init) & a_select3(simplex7_init, % 165.00/22.45 | all_71_1, all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, % 165.00/22.45 | n3) & leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) % 165.00/22.45 | | ( ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) = % 165.00/22.45 | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4)) | % 165.00/22.45 | ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) = % 165.00/22.45 | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0, all_71_6)) | % 165.00/22.45 | ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = all_71_7 % 165.00/22.45 | & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, all_71_8)) | % 165.00/22.46 | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~ % 165.00/22.46 | (pvar1401_init = init) | ~ (pvar1400_init = init)))) % 165.00/22.46 | % 165.00/22.46 | ALPHA: (32) implies: % 165.00/22.46 | (33) $i(all_71_8) % 165.00/22.46 | (34) $i(all_71_6) % 165.00/22.46 | (35) $i(all_71_4) % 165.00/22.46 | (36) $i(all_71_2) % 165.00/22.46 | (37) $i(all_71_1) % 165.00/22.46 | (38) minus(n3, n1) = all_71_9 % 165.00/22.46 | (39) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, all_71_2) = % 165.00/22.46 | all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & leq(all_71_2, n2) & % 165.00/22.46 | leq(n0, all_71_1) & leq(n0, all_71_2)) | ( ~ (all_71_3 = init) & % 165.00/22.46 | a_select2(s_values7_init, all_71_4) = all_71_3 & $i(all_71_3) & % 165.00/22.46 | leq(all_71_4, n3) & leq(n0, all_71_4)) | ( ~ (all_71_5 = init) & % 165.00/22.46 | a_select2(s_center7_init, all_71_6) = all_71_5 & $i(all_71_5) & % 165.00/22.46 | leq(all_71_6, n2) & leq(n0, all_71_6)) | ( ~ (all_71_7 = init) & % 165.00/22.46 | a_select2(s_try7_init, all_71_8) = all_71_7 & $i(all_71_7) & % 165.00/22.46 | leq(all_71_8, all_71_9) & leq(n0, all_71_8)) | (gt(loopcounter, n1) % 165.00/22.46 | & ( ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 165.00/22.46 | (pvar1400_init = init))) % 165.00/22.46 | (40) ~ gt(loopcounter, n1) | (pvar1402_init = init & pvar1401_init = init % 165.00/22.46 | & pvar1400_init = init) % 165.39/22.46 | (41) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_values7_init, % 165.39/22.46 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n3) | ~ leq(n0, v0)) % 165.39/22.46 | (42) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_center7_init, % 165.39/22.46 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n2) | ~ leq(n0, v0)) % 165.39/22.47 | (43) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, % 165.39/22.47 | v0) = v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0)) % 165.39/22.47 | (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 165.39/22.47 | (a_select3(simplex7_init, v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 165.39/22.47 | leq(v1, n3) | ~ leq(v0, n2) | ~ leq(n0, v1) | ~ leq(n0, v0)) % 165.39/22.47 | % 165.39/22.47 | GROUND_INST: instantiating (13) with all_54_0, all_57_1, n0, simplifying with % 165.39/22.47 | (16), (20) gives: % 165.39/22.47 | (45) all_57_1 = all_54_0 % 165.39/22.47 | % 165.39/22.47 | GROUND_INST: instantiating (13) with all_57_1, all_59_2, n0, simplifying with % 165.39/22.47 | (20), (25) gives: % 165.39/22.47 | (46) all_59_2 = all_57_1 % 165.39/22.47 | % 165.39/22.47 | GROUND_INST: instantiating (13) with all_59_2, all_61_3, n0, simplifying with % 165.39/22.47 | (25), (29) gives: % 165.39/22.47 | (47) all_61_3 = all_59_2 % 165.39/22.47 | % 165.39/22.47 | GROUND_INST: instantiating (13) with n1, all_61_3, n0, simplifying with (7), % 165.39/22.47 | (29) gives: % 165.39/22.47 | (48) all_61_3 = n1 % 165.39/22.47 | % 165.39/22.47 | COMBINE_EQS: (47), (48) imply: % 165.39/22.47 | (49) all_59_2 = n1 % 165.39/22.47 | % 165.39/22.47 | SIMP: (49) implies: % 165.39/22.47 | (50) all_59_2 = n1 % 165.39/22.47 | % 165.39/22.47 | COMBINE_EQS: (46), (50) imply: % 165.39/22.47 | (51) all_57_1 = n1 % 165.39/22.47 | % 165.39/22.47 | SIMP: (51) implies: % 165.39/22.47 | (52) all_57_1 = n1 % 165.39/22.47 | % 165.39/22.47 | COMBINE_EQS: (45), (52) imply: % 165.39/22.47 | (53) all_54_0 = n1 % 165.39/22.47 | % 165.39/22.47 | SIMP: (53) implies: % 165.39/22.47 | (54) all_54_0 = n1 % 165.39/22.47 | % 165.39/22.47 | REDUCE: (30), (48) imply: % 165.39/22.47 | (55) succ(n1) = all_61_2 % 165.39/22.47 | % 165.39/22.47 | REDUCE: (26), (50) imply: % 165.39/22.47 | (56) succ(n1) = all_59_1 % 165.39/22.47 | % 165.39/22.48 | REDUCE: (21), (52) imply: % 165.39/22.48 | (57) succ(n1) = all_57_0 % 165.39/22.48 | % 165.39/22.48 | REDUCE: (17), (54) imply: % 165.39/22.48 | (58) succ(n1) = n2 % 165.39/22.48 | % 165.39/22.48 | REDUCE: (15), (54) imply: % 165.39/22.48 | (59) $i(n1) % 165.39/22.48 | % 165.39/22.48 | GROUND_INST: instantiating (13) with all_57_0, all_59_1, n1, simplifying with % 165.39/22.48 | (56), (57) gives: % 165.39/22.48 | (60) all_59_1 = all_57_0 % 165.39/22.48 | % 165.39/22.48 | GROUND_INST: instantiating (13) with all_59_1, all_61_2, n1, simplifying with % 165.39/22.48 | (55), (56) gives: % 165.39/22.48 | (61) all_61_2 = all_59_1 % 165.39/22.48 | % 165.39/22.48 | GROUND_INST: instantiating (13) with n2, all_61_2, n1, simplifying with (55), % 165.39/22.48 | (58) gives: % 165.39/22.48 | (62) all_61_2 = n2 % 165.39/22.48 | % 165.39/22.48 | COMBINE_EQS: (61), (62) imply: % 165.39/22.48 | (63) all_59_1 = n2 % 165.39/22.48 | % 165.39/22.48 | SIMP: (63) implies: % 165.39/22.48 | (64) all_59_1 = n2 % 165.39/22.48 | % 165.39/22.48 | COMBINE_EQS: (60), (64) imply: % 165.39/22.48 | (65) all_57_0 = n2 % 165.39/22.48 | % 165.39/22.48 | REDUCE: (31), (62) imply: % 165.39/22.48 | (66) succ(n2) = all_61_1 % 165.39/22.48 | % 165.39/22.48 | REDUCE: (27), (64) imply: % 165.39/22.48 | (67) succ(n2) = all_59_0 % 165.39/22.48 | % 165.39/22.48 | REDUCE: (22), (65) imply: % 165.39/22.48 | (68) succ(n2) = n3 % 165.39/22.48 | % 165.39/22.48 | REDUCE: (19), (65) imply: % 165.39/22.48 | (69) $i(n2) % 165.39/22.48 | % 165.39/22.48 | GROUND_INST: instantiating (13) with all_59_0, all_61_1, n2, simplifying with % 165.39/22.48 | (66), (67) gives: % 165.39/22.48 | (70) all_61_1 = all_59_0 % 165.39/22.48 | % 165.39/22.48 | GROUND_INST: instantiating (13) with n3, all_61_1, n2, simplifying with (66), % 165.39/22.48 | (68) gives: % 165.39/22.48 | (71) all_61_1 = n3 % 165.39/22.48 | % 165.39/22.48 | COMBINE_EQS: (70), (71) imply: % 165.39/22.48 | (72) all_59_0 = n3 % 165.39/22.48 | % 165.39/22.48 | SIMP: (72) implies: % 165.39/22.48 | (73) all_59_0 = n3 % 165.39/22.48 | % 165.39/22.48 | REDUCE: (24), (73) imply: % 165.39/22.48 | (74) $i(n3) % 165.39/22.48 | % 165.39/22.49 | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (58), % 165.39/22.49 | (59) gives: % 165.39/22.49 | (75) pred(n2) = n1 % 165.39/22.49 | % 165.39/22.49 | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (68), % 165.39/22.49 | (69) gives: % 165.39/22.49 | (76) pred(n3) = n2 % 165.39/22.49 | % 165.39/22.49 | GROUND_INST: instantiating (2) with n3, all_71_9, simplifying with (38), (74) % 165.39/22.49 | gives: % 165.39/22.49 | (77) pred(n3) = all_71_9 & $i(all_71_9) % 165.39/22.49 | % 165.39/22.49 | ALPHA: (77) implies: % 165.39/22.49 | (78) $i(all_71_9) % 165.39/22.49 | (79) pred(n3) = all_71_9 % 165.39/22.49 | % 165.39/22.49 | GROUND_INST: instantiating (12) with n2, all_71_9, n3, simplifying with (76), % 165.39/22.49 | (79) gives: % 165.39/22.49 | (80) all_71_9 = n2 % 165.39/22.49 | % 165.39/22.49 | BETA: splitting (40) gives: % 165.39/22.49 | % 165.39/22.49 | Case 1: % 165.39/22.49 | | % 165.39/22.49 | | (81) ~ gt(loopcounter, n1) % 165.39/22.49 | | % 165.39/22.49 | | BETA: splitting (39) gives: % 165.39/22.49 | | % 165.39/22.49 | | Case 1: % 165.39/22.49 | | | % 165.39/22.49 | | | (82) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, % 165.39/22.49 | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & % 165.39/22.49 | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) | ( ~ % 165.39/22.49 | | | (all_71_3 = init) & a_select2(s_values7_init, all_71_4) = % 165.39/22.49 | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4)) % 165.39/22.49 | | | % 165.39/22.49 | | | BETA: splitting (82) gives: % 165.39/22.49 | | | % 165.39/22.49 | | | Case 1: % 165.39/22.49 | | | | % 165.39/22.49 | | | | (83) ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, % 165.39/22.49 | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & % 165.39/22.49 | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2) % 165.39/22.49 | | | | % 165.39/22.49 | | | | ALPHA: (83) implies: % 165.39/22.49 | | | | (84) ~ (all_71_0 = init) % 165.39/22.49 | | | | (85) leq(n0, all_71_2) % 165.39/22.49 | | | | (86) leq(n0, all_71_1) % 165.39/22.49 | | | | (87) leq(all_71_2, n2) % 165.39/22.50 | | | | (88) leq(all_71_1, n3) % 165.39/22.50 | | | | (89) a_select3(simplex7_init, all_71_1, all_71_2) = all_71_0 % 165.39/22.50 | | | | % 165.39/22.50 | | | | GROUND_INST: instantiating (44) with all_71_2, all_71_1, all_71_0, % 165.39/22.50 | | | | simplifying with (36), (37), (85), (86), (87), (88), (89) % 165.39/22.50 | | | | gives: % 165.39/22.50 | | | | (90) all_71_0 = init % 165.39/22.50 | | | | % 165.39/22.50 | | | | REDUCE: (84), (90) imply: % 165.39/22.50 | | | | (91) $false % 165.39/22.50 | | | | % 165.39/22.50 | | | | CLOSE: (91) is inconsistent. % 165.39/22.50 | | | | % 165.39/22.50 | | | Case 2: % 165.39/22.50 | | | | % 165.39/22.50 | | | | (92) ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) = % 165.39/22.50 | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4) % 165.39/22.50 | | | | % 165.39/22.50 | | | | ALPHA: (92) implies: % 165.39/22.50 | | | | (93) ~ (all_71_3 = init) % 165.39/22.50 | | | | (94) leq(n0, all_71_4) % 165.39/22.50 | | | | (95) leq(all_71_4, n3) % 165.39/22.50 | | | | (96) a_select2(s_values7_init, all_71_4) = all_71_3 % 165.39/22.50 | | | | % 165.39/22.50 | | | | GROUND_INST: instantiating (41) with all_71_4, all_71_3, simplifying % 165.39/22.50 | | | | with (35), (94), (95), (96) gives: % 165.39/22.50 | | | | (97) all_71_3 = init % 165.39/22.50 | | | | % 165.39/22.50 | | | | REDUCE: (93), (97) imply: % 165.39/22.50 | | | | (98) $false % 165.39/22.50 | | | | % 165.39/22.50 | | | | CLOSE: (98) is inconsistent. % 165.39/22.50 | | | | % 165.39/22.50 | | | End of split % 165.39/22.50 | | | % 165.39/22.50 | | Case 2: % 165.39/22.50 | | | % 165.39/22.50 | | | (99) ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) = % 165.39/22.50 | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0, all_71_6)) % 165.39/22.50 | | | | ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = % 165.39/22.50 | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, % 165.39/22.50 | | | all_71_8)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) % 165.39/22.50 | | | | ~ (pvar1401_init = init) | ~ (pvar1400_init = init))) % 165.39/22.50 | | | % 165.39/22.50 | | | BETA: splitting (99) gives: % 165.39/22.50 | | | % 165.39/22.50 | | | Case 1: % 165.39/22.50 | | | | % 165.39/22.50 | | | | (100) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) = % 165.39/22.50 | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0, all_71_6) % 165.39/22.50 | | | | % 165.39/22.50 | | | | ALPHA: (100) implies: % 165.39/22.51 | | | | (101) ~ (all_71_5 = init) % 165.39/22.51 | | | | (102) leq(n0, all_71_6) % 165.39/22.51 | | | | (103) leq(all_71_6, n2) % 165.39/22.51 | | | | (104) a_select2(s_center7_init, all_71_6) = all_71_5 % 165.39/22.51 | | | | % 165.39/22.51 | | | | GROUND_INST: instantiating (42) with all_71_6, all_71_5, simplifying % 165.39/22.51 | | | | with (34), (102), (103), (104) gives: % 165.39/22.51 | | | | (105) all_71_5 = init % 165.39/22.51 | | | | % 165.39/22.51 | | | | REDUCE: (101), (105) imply: % 165.39/22.51 | | | | (106) $false % 165.39/22.51 | | | | % 165.39/22.51 | | | | CLOSE: (106) is inconsistent. % 165.39/22.51 | | | | % 165.39/22.51 | | | Case 2: % 165.39/22.51 | | | | % 165.39/22.51 | | | | (107) ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = % 165.39/22.51 | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, % 165.39/22.51 | | | | all_71_8)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = % 165.39/22.51 | | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init = % 165.39/22.51 | | | | init))) % 165.39/22.51 | | | | % 165.39/22.51 | | | | BETA: splitting (107) gives: % 165.39/22.51 | | | | % 165.39/22.51 | | | | Case 1: % 165.39/22.51 | | | | | % 165.39/22.51 | | | | | (108) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = % 165.39/22.51 | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, % 165.39/22.51 | | | | | all_71_8) % 165.39/22.51 | | | | | % 165.39/22.51 | | | | | REF_CLOSE: (1), (3), (4), (10), (33), (43), (69), (75), (80), (108), % 165.39/22.51 | | | | | (irreflexivity_gt), (leq_gt2) are inconsistent by sub-proof % 165.39/22.51 | | | | | #1. % 165.39/22.51 | | | | | % 165.39/22.51 | | | | Case 2: % 165.39/22.51 | | | | | % 165.39/22.51 | | | | | (109) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~ % 165.39/22.51 | | | | | (pvar1401_init = init) | ~ (pvar1400_init = init)) % 165.39/22.51 | | | | | % 165.39/22.51 | | | | | ALPHA: (109) implies: % 165.39/22.51 | | | | | (110) gt(loopcounter, n1) % 165.39/22.51 | | | | | % 165.39/22.51 | | | | | PRED_UNIFY: (81), (110) imply: % 165.39/22.51 | | | | | (111) $false % 165.39/22.51 | | | | | % 165.39/22.51 | | | | | CLOSE: (111) is inconsistent. % 165.39/22.51 | | | | | % 165.39/22.51 | | | | End of split % 165.39/22.51 | | | | % 165.39/22.51 | | | End of split % 165.39/22.51 | | | % 165.39/22.51 | | End of split % 165.39/22.51 | | % 165.39/22.51 | Case 2: % 165.39/22.51 | | % 165.39/22.51 | | (112) pvar1402_init = init & pvar1401_init = init & pvar1400_init = init % 165.39/22.51 | | % 165.39/22.51 | | ALPHA: (112) implies: % 165.39/22.51 | | (113) pvar1400_init = init % 165.39/22.51 | | (114) pvar1401_init = init % 165.65/22.51 | | (115) pvar1402_init = init % 165.65/22.51 | | % 165.65/22.51 | | BETA: splitting (39) gives: % 165.65/22.51 | | % 165.65/22.51 | | Case 1: % 165.65/22.51 | | | % 165.65/22.52 | | | (116) ( ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, % 165.65/22.52 | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & % 165.65/22.52 | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2)) | ( % 165.65/22.52 | | | ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) = % 165.65/22.52 | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, % 165.65/22.52 | | | all_71_4)) % 165.65/22.52 | | | % 165.65/22.52 | | | BETA: splitting (116) gives: % 165.65/22.52 | | | % 165.65/22.52 | | | Case 1: % 165.65/22.52 | | | | % 165.65/22.52 | | | | (117) ~ (all_71_0 = init) & a_select3(simplex7_init, all_71_1, % 165.65/22.52 | | | | all_71_2) = all_71_0 & $i(all_71_0) & leq(all_71_1, n3) & % 165.65/22.52 | | | | leq(all_71_2, n2) & leq(n0, all_71_1) & leq(n0, all_71_2) % 165.65/22.52 | | | | % 165.65/22.52 | | | | ALPHA: (117) implies: % 165.65/22.52 | | | | (118) ~ (all_71_0 = init) % 165.65/22.52 | | | | (119) leq(n0, all_71_2) % 165.65/22.52 | | | | (120) leq(n0, all_71_1) % 165.65/22.52 | | | | (121) leq(all_71_2, n2) % 165.65/22.52 | | | | (122) leq(all_71_1, n3) % 165.65/22.52 | | | | (123) a_select3(simplex7_init, all_71_1, all_71_2) = all_71_0 % 165.65/22.52 | | | | % 165.65/22.52 | | | | GROUND_INST: instantiating (44) with all_71_2, all_71_1, all_71_0, % 165.65/22.52 | | | | simplifying with (36), (37), (119), (120), (121), (122), % 165.65/22.52 | | | | (123) gives: % 165.65/22.52 | | | | (124) all_71_0 = init % 165.65/22.52 | | | | % 165.65/22.52 | | | | REDUCE: (118), (124) imply: % 165.65/22.52 | | | | (125) $false % 165.65/22.52 | | | | % 165.65/22.52 | | | | CLOSE: (125) is inconsistent. % 165.65/22.52 | | | | % 165.65/22.52 | | | Case 2: % 165.65/22.52 | | | | % 165.65/22.52 | | | | (126) ~ (all_71_3 = init) & a_select2(s_values7_init, all_71_4) = % 165.65/22.52 | | | | all_71_3 & $i(all_71_3) & leq(all_71_4, n3) & leq(n0, all_71_4) % 165.65/22.52 | | | | % 165.65/22.52 | | | | ALPHA: (126) implies: % 165.65/22.52 | | | | (127) ~ (all_71_3 = init) % 165.65/22.52 | | | | (128) leq(n0, all_71_4) % 165.65/22.52 | | | | (129) leq(all_71_4, n3) % 165.65/22.52 | | | | (130) a_select2(s_values7_init, all_71_4) = all_71_3 % 165.65/22.52 | | | | % 165.65/22.52 | | | | GROUND_INST: instantiating (41) with all_71_4, all_71_3, simplifying % 165.65/22.52 | | | | with (35), (128), (129), (130) gives: % 165.65/22.52 | | | | (131) all_71_3 = init % 165.65/22.52 | | | | % 165.65/22.52 | | | | REDUCE: (127), (131) imply: % 165.65/22.53 | | | | (132) $false % 165.65/22.53 | | | | % 165.65/22.53 | | | | CLOSE: (132) is inconsistent. % 165.65/22.53 | | | | % 165.65/22.53 | | | End of split % 165.65/22.53 | | | % 165.65/22.53 | | Case 2: % 165.65/22.53 | | | % 165.65/22.53 | | | (133) ( ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) = % 165.65/22.53 | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0, % 165.65/22.53 | | | all_71_6)) | ( ~ (all_71_7 = init) & a_select2(s_try7_init, % 165.65/22.53 | | | all_71_8) = all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) % 165.65/22.53 | | | & leq(n0, all_71_8)) | (gt(loopcounter, n1) & ( ~ % 165.65/22.53 | | | (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 165.65/22.53 | | | (pvar1400_init = init))) % 165.65/22.53 | | | % 165.65/22.53 | | | BETA: splitting (133) gives: % 165.65/22.53 | | | % 165.65/22.53 | | | Case 1: % 165.65/22.53 | | | | % 165.65/22.53 | | | | (134) ~ (all_71_5 = init) & a_select2(s_center7_init, all_71_6) = % 165.65/22.53 | | | | all_71_5 & $i(all_71_5) & leq(all_71_6, n2) & leq(n0, all_71_6) % 165.65/22.53 | | | | % 165.65/22.53 | | | | ALPHA: (134) implies: % 165.65/22.53 | | | | (135) ~ (all_71_5 = init) % 165.65/22.53 | | | | (136) leq(n0, all_71_6) % 165.65/22.53 | | | | (137) leq(all_71_6, n2) % 165.65/22.53 | | | | (138) a_select2(s_center7_init, all_71_6) = all_71_5 % 165.65/22.53 | | | | % 165.65/22.53 | | | | GROUND_INST: instantiating (42) with all_71_6, all_71_5, simplifying % 165.65/22.53 | | | | with (34), (136), (137), (138) gives: % 165.65/22.53 | | | | (139) all_71_5 = init % 165.65/22.53 | | | | % 165.65/22.53 | | | | REDUCE: (135), (139) imply: % 165.65/22.53 | | | | (140) $false % 165.65/22.53 | | | | % 165.65/22.53 | | | | CLOSE: (140) is inconsistent. % 165.65/22.53 | | | | % 165.65/22.53 | | | Case 2: % 165.65/22.53 | | | | % 165.65/22.53 | | | | (141) ( ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = % 165.65/22.53 | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, % 165.65/22.53 | | | | all_71_8)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = % 165.65/22.53 | | | | init) | ~ (pvar1401_init = init) | ~ (pvar1400_init = % 165.65/22.53 | | | | init))) % 165.65/22.53 | | | | % 165.65/22.53 | | | | BETA: splitting (141) gives: % 165.65/22.53 | | | | % 165.65/22.53 | | | | Case 1: % 165.65/22.53 | | | | | % 165.65/22.53 | | | | | (142) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = % 165.65/22.53 | | | | | all_71_7 & $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, % 165.65/22.53 | | | | | all_71_8) % 165.65/22.53 | | | | | % 165.65/22.53 | | | | | REF_CLOSE: (1), (3), (4), (10), (33), (43), (69), (75), (80), (142), % 165.65/22.53 | | | | | (irreflexivity_gt), (leq_gt2) are inconsistent by sub-proof % 165.65/22.53 | | | | | #1. % 165.65/22.53 | | | | | % 165.65/22.53 | | | | Case 2: % 165.65/22.53 | | | | | % 165.65/22.54 | | | | | (143) gt(loopcounter, n1) & ( ~ (pvar1402_init = init) | ~ % 165.65/22.54 | | | | | (pvar1401_init = init) | ~ (pvar1400_init = init)) % 165.65/22.54 | | | | | % 165.65/22.54 | | | | | ALPHA: (143) implies: % 165.65/22.54 | | | | | (144) ~ (pvar1402_init = init) | ~ (pvar1401_init = init) | ~ % 165.65/22.54 | | | | | (pvar1400_init = init) % 165.65/22.54 | | | | | % 165.65/22.54 | | | | | BETA: splitting (144) gives: % 165.65/22.54 | | | | | % 165.65/22.54 | | | | | Case 1: % 165.65/22.54 | | | | | | % 165.65/22.54 | | | | | | (145) ~ (pvar1402_init = init) % 165.65/22.54 | | | | | | % 165.65/22.54 | | | | | | REDUCE: (115), (145) imply: % 165.65/22.54 | | | | | | (146) $false % 165.65/22.54 | | | | | | % 165.65/22.54 | | | | | | CLOSE: (146) is inconsistent. % 165.65/22.54 | | | | | | % 165.65/22.54 | | | | | Case 2: % 165.65/22.54 | | | | | | % 165.65/22.54 | | | | | | (147) ~ (pvar1401_init = init) | ~ (pvar1400_init = init) % 165.65/22.54 | | | | | | % 165.65/22.54 | | | | | | BETA: splitting (147) gives: % 165.65/22.54 | | | | | | % 165.65/22.54 | | | | | | Case 1: % 165.65/22.54 | | | | | | | % 165.65/22.54 | | | | | | | (148) ~ (pvar1401_init = init) % 165.65/22.54 | | | | | | | % 165.65/22.54 | | | | | | | REDUCE: (114), (148) imply: % 165.65/22.54 | | | | | | | (149) $false % 165.65/22.54 | | | | | | | % 165.65/22.54 | | | | | | | CLOSE: (149) is inconsistent. % 165.65/22.54 | | | | | | | % 165.65/22.54 | | | | | | Case 2: % 165.65/22.54 | | | | | | | % 165.65/22.54 | | | | | | | (150) ~ (pvar1400_init = init) % 165.65/22.54 | | | | | | | % 165.65/22.54 | | | | | | | REDUCE: (113), (150) imply: % 165.65/22.54 | | | | | | | (151) $false % 165.65/22.54 | | | | | | | % 165.65/22.54 | | | | | | | CLOSE: (151) is inconsistent. % 165.65/22.54 | | | | | | | % 165.65/22.54 | | | | | | End of split % 165.65/22.54 | | | | | | % 165.65/22.54 | | | | | End of split % 165.65/22.54 | | | | | % 165.65/22.54 | | | | End of split % 165.65/22.54 | | | | % 165.65/22.54 | | | End of split % 165.65/22.54 | | | % 165.65/22.54 | | End of split % 165.65/22.54 | | % 165.65/22.54 | End of split % 165.65/22.54 | % 165.65/22.54 End of proof % 165.65/22.54 % 165.65/22.54 Sub-proof #1 shows that the following formulas are inconsistent: % 165.65/22.54 ---------------------------------------------------------------- % 165.65/22.54 (1) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n2) | % 165.65/22.54 ~ leq(n0, v0)) % 165.65/22.54 (2) $i(n0) % 165.65/22.54 (3) $i(n2) % 165.65/22.54 (4) all_71_9 = n2 % 165.65/22.54 (5) pred(n2) = n1 % 165.65/22.54 (6) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) = % 165.65/22.54 v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0)) % 165.65/22.54 (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, % 165.65/22.54 v1) | gt(v1, v0)) % 165.65/22.54 (8) ! [v0: $i] : ( ~ $i(v0) | ~ gt(v0, v0)) % 165.65/22.54 (9) ~ (all_71_7 = init) & a_select2(s_try7_init, all_71_8) = all_71_7 & % 165.65/22.55 $i(all_71_7) & leq(all_71_8, all_71_9) & leq(n0, all_71_8) % 165.65/22.55 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ % 165.65/22.55 $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 165.65/22.55 (11) $i(all_71_8) % 165.65/22.55 (12) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 165.65/22.55 leq(n0, v0)) % 165.65/22.55 % 165.65/22.55 Begin of proof % 165.65/22.55 | % 165.65/22.55 | ALPHA: (9) implies: % 165.65/22.55 | (13) ~ (all_71_7 = init) % 165.65/22.55 | (14) leq(n0, all_71_8) % 165.65/22.55 | (15) leq(all_71_8, all_71_9) % 165.65/22.55 | (16) a_select2(s_try7_init, all_71_8) = all_71_7 % 165.65/22.55 | % 165.65/22.55 | REDUCE: (4), (15) imply: % 165.82/22.55 | (17) leq(all_71_8, n2) % 165.82/22.55 | % 165.82/22.55 | GROUND_INST: instantiating (7) with n0, all_71_8, simplifying with (2), (11), % 165.82/22.55 | (14) gives: % 165.82/22.55 | (18) all_71_8 = n0 | gt(all_71_8, n0) % 165.82/22.55 | % 165.82/22.55 | GROUND_INST: instantiating (1) with all_71_8, simplifying with (11), (14), % 165.82/22.55 | (17) gives: % 165.82/22.55 | (19) all_71_8 = n2 | all_71_8 = n1 | all_71_8 = n0 % 165.82/22.55 | % 165.82/22.55 | GROUND_INST: instantiating (7) with all_71_8, n2, simplifying with (3), (11), % 165.82/22.55 | (17) gives: % 165.82/22.55 | (20) all_71_8 = n2 | gt(n2, all_71_8) % 165.82/22.55 | % 165.82/22.55 | BETA: splitting (18) gives: % 165.82/22.55 | % 165.82/22.55 | Case 1: % 165.82/22.55 | | % 165.82/22.55 | | (21) gt(all_71_8, n0) % 165.82/22.55 | | % 165.82/22.55 | | BETA: splitting (20) gives: % 165.82/22.55 | | % 165.82/22.55 | | Case 1: % 165.82/22.55 | | | % 165.82/22.55 | | | (22) gt(n2, all_71_8) % 165.82/22.55 | | | % 165.82/22.55 | | | BETA: splitting (19) gives: % 165.82/22.55 | | | % 165.82/22.55 | | | Case 1: % 165.82/22.55 | | | | % 165.82/22.55 | | | | (23) all_71_8 = n0 % 165.82/22.55 | | | | % 165.82/22.55 | | | | REDUCE: (21), (23) imply: % 165.82/22.55 | | | | (24) gt(n0, n0) % 165.82/22.55 | | | | % 165.82/22.55 | | | | GROUND_INST: instantiating (8) with n0, simplifying with (2), (24) % 165.82/22.55 | | | | gives: % 165.82/22.55 | | | | (25) $false % 165.82/22.55 | | | | % 165.82/22.55 | | | | CLOSE: (25) is inconsistent. % 165.82/22.55 | | | | % 165.82/22.55 | | | Case 2: % 165.82/22.55 | | | | % 165.82/22.55 | | | | (26) ~ (all_71_8 = n0) % 165.82/22.55 | | | | % 165.82/22.56 | | | | REF_CLOSE: (3), (4), (5), (6), (10), (11), (12), (13), (14), (16), (17), % 165.82/22.56 | | | | (22), (26) are inconsistent by sub-proof #3. % 165.82/22.56 | | | | % 165.82/22.56 | | | End of split % 165.82/22.56 | | | % 165.82/22.56 | | Case 2: % 165.82/22.56 | | | % 165.82/22.56 | | | (27) all_71_8 = n2 % 165.82/22.56 | | | % 165.82/22.56 | | | REF_CLOSE: (4), (6), (11), (13), (14), (16), (17), (27) are inconsistent % 165.82/22.56 | | | by sub-proof #2. % 165.82/22.56 | | | % 165.82/22.56 | | End of split % 165.82/22.56 | | % 165.82/22.56 | Case 2: % 165.82/22.56 | | % 165.82/22.56 | | (28) all_71_8 = n0 % 165.82/22.56 | | (29) ~ gt(all_71_8, n0) % 165.82/22.56 | | % 165.82/22.56 | | REDUCE: (28), (29) imply: % 165.82/22.56 | | (30) ~ gt(n0, n0) % 165.82/22.56 | | % 165.82/22.56 | | BETA: splitting (18) gives: % 165.82/22.56 | | % 165.82/22.56 | | Case 1: % 165.82/22.56 | | | % 165.82/22.56 | | | (31) gt(all_71_8, n0) % 165.82/22.56 | | | % 165.82/22.56 | | | BETA: splitting (20) gives: % 165.82/22.56 | | | % 165.82/22.56 | | | Case 1: % 165.82/22.56 | | | | % 165.82/22.56 | | | | (32) gt(n2, all_71_8) % 165.82/22.56 | | | | % 165.82/22.56 | | | | BETA: splitting (19) gives: % 165.82/22.56 | | | | % 165.82/22.56 | | | | Case 1: % 165.82/22.56 | | | | | % 165.82/22.56 | | | | | % 165.82/22.56 | | | | | REDUCE: (28), (31) imply: % 165.82/22.56 | | | | | (33) gt(n0, n0) % 165.82/22.56 | | | | | % 165.82/22.56 | | | | | PRED_UNIFY: (30), (33) imply: % 165.82/22.56 | | | | | (34) $false % 165.82/22.56 | | | | | % 165.82/22.56 | | | | | CLOSE: (34) is inconsistent. % 165.82/22.56 | | | | | % 165.82/22.56 | | | | Case 2: % 165.82/22.56 | | | | | % 165.82/22.56 | | | | | (35) ~ (all_71_8 = n0) % 165.82/22.56 | | | | | % 165.82/22.56 | | | | | REF_CLOSE: (3), (4), (5), (6), (10), (11), (12), (13), (14), (16), % 165.82/22.56 | | | | | (17), (32), (35) are inconsistent by sub-proof #3. % 165.82/22.56 | | | | | % 165.82/22.56 | | | | End of split % 165.82/22.56 | | | | % 165.82/22.56 | | | Case 2: % 165.82/22.56 | | | | % 165.82/22.56 | | | | (36) all_71_8 = n2 % 165.82/22.56 | | | | % 165.82/22.56 | | | | REF_CLOSE: (4), (6), (11), (13), (14), (16), (17), (36) are inconsistent % 165.82/22.56 | | | | by sub-proof #2. % 165.82/22.56 | | | | % 165.82/22.56 | | | End of split % 165.82/22.56 | | | % 165.82/22.56 | | Case 2: % 165.82/22.56 | | | % 165.82/22.56 | | | % 165.82/22.56 | | | REDUCE: (16), (28) imply: % 165.82/22.56 | | | (37) a_select2(s_try7_init, n0) = all_71_7 % 165.82/22.56 | | | % 165.82/22.56 | | | REDUCE: (17), (28) imply: % 165.82/22.56 | | | (38) leq(n0, n2) % 165.82/22.56 | | | % 165.82/22.56 | | | REDUCE: (14), (28) imply: % 165.82/22.56 | | | (39) leq(n0, n0) % 165.82/22.56 | | | % 165.82/22.56 | | | GROUND_INST: instantiating (6) with n0, all_71_7, simplifying with (2), % 165.82/22.56 | | | (37), (39) gives: % 165.82/22.56 | | | (40) all_71_7 = init | ~ leq(n0, all_71_9) % 165.82/22.56 | | | % 165.82/22.56 | | | BETA: splitting (40) gives: % 165.82/22.56 | | | % 165.82/22.56 | | | Case 1: % 165.82/22.56 | | | | % 165.82/22.56 | | | | (41) ~ leq(n0, all_71_9) % 165.82/22.56 | | | | % 165.82/22.56 | | | | REDUCE: (4), (41) imply: % 165.82/22.56 | | | | (42) ~ leq(n0, n2) % 165.82/22.56 | | | | % 165.82/22.56 | | | | PRED_UNIFY: (38), (42) imply: % 165.82/22.56 | | | | (43) $false % 165.82/22.56 | | | | % 165.82/22.56 | | | | CLOSE: (43) is inconsistent. % 165.82/22.56 | | | | % 165.82/22.56 | | | Case 2: % 165.82/22.56 | | | | % 165.82/22.56 | | | | (44) all_71_7 = init % 165.82/22.56 | | | | % 165.82/22.56 | | | | REDUCE: (13), (44) imply: % 165.82/22.56 | | | | (45) $false % 165.82/22.56 | | | | % 165.82/22.56 | | | | CLOSE: (45) is inconsistent. % 165.82/22.56 | | | | % 165.82/22.56 | | | End of split % 165.82/22.56 | | | % 165.82/22.56 | | End of split % 165.82/22.56 | | % 165.82/22.56 | End of split % 165.82/22.56 | % 165.82/22.56 End of proof % 165.82/22.56 % 165.82/22.56 Sub-proof #2 shows that the following formulas are inconsistent: % 165.82/22.56 ---------------------------------------------------------------- % 165.82/22.57 (1) leq(all_71_8, n2) % 165.82/22.57 (2) ~ (all_71_7 = init) % 165.82/22.57 (3) all_71_9 = n2 % 165.82/22.57 (4) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) = % 165.82/22.57 v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0)) % 165.82/22.57 (5) all_71_8 = n2 % 165.82/22.57 (6) leq(n0, all_71_8) % 165.82/22.57 (7) a_select2(s_try7_init, all_71_8) = all_71_7 % 165.82/22.57 (8) $i(all_71_8) % 165.82/22.57 % 165.82/22.57 Begin of proof % 165.82/22.57 | % 165.82/22.57 | REDUCE: (5), (7) imply: % 165.82/22.57 | (9) a_select2(s_try7_init, n2) = all_71_7 % 165.82/22.57 | % 165.82/22.57 | REDUCE: (5), (8) imply: % 165.82/22.57 | (10) $i(n2) % 165.82/22.57 | % 165.82/22.57 | REDUCE: (1), (5) imply: % 165.82/22.57 | (11) leq(n2, n2) % 165.82/22.57 | % 165.82/22.57 | REDUCE: (5), (6) imply: % 165.82/22.57 | (12) leq(n0, n2) % 165.82/22.57 | % 165.82/22.57 | GROUND_INST: instantiating (4) with n2, all_71_7, simplifying with (9), (10), % 165.82/22.57 | (12) gives: % 165.82/22.57 | (13) all_71_7 = init | ~ leq(n2, all_71_9) % 165.82/22.57 | % 165.82/22.57 | BETA: splitting (13) gives: % 165.82/22.57 | % 165.82/22.57 | Case 1: % 165.82/22.57 | | % 165.82/22.57 | | (14) ~ leq(n2, all_71_9) % 165.82/22.57 | | % 165.82/22.57 | | REDUCE: (3), (14) imply: % 165.82/22.57 | | (15) ~ leq(n2, n2) % 165.82/22.57 | | % 165.82/22.57 | | PRED_UNIFY: (11), (15) imply: % 165.82/22.57 | | (16) $false % 165.82/22.57 | | % 165.82/22.57 | | CLOSE: (16) is inconsistent. % 165.82/22.57 | | % 165.82/22.57 | Case 2: % 165.82/22.57 | | % 165.82/22.57 | | (17) all_71_7 = init % 165.82/22.57 | | % 165.82/22.57 | | REDUCE: (2), (17) imply: % 165.82/22.57 | | (18) $false % 165.82/22.57 | | % 165.82/22.57 | | CLOSE: (18) is inconsistent. % 165.82/22.57 | | % 165.82/22.57 | End of split % 165.82/22.57 | % 165.82/22.57 End of proof % 165.82/22.57 % 165.82/22.57 Sub-proof #3 shows that the following formulas are inconsistent: % 165.82/22.57 ---------------------------------------------------------------- % 165.82/22.57 (1) leq(all_71_8, n2) % 165.82/22.57 (2) ~ (all_71_7 = init) % 165.82/22.57 (3) $i(n2) % 165.82/22.57 (4) all_71_9 = n2 % 165.82/22.57 (5) pred(n2) = n1 % 165.82/22.57 (6) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(s_try7_init, v0) = % 165.82/22.57 v1) | ~ $i(v0) | ~ leq(v0, all_71_9) | ~ leq(n0, v0)) % 165.82/22.57 (7) ~ (all_71_8 = n0) % 165.82/22.57 (8) leq(n0, all_71_8) % 165.82/22.57 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) % 165.82/22.57 | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2)) % 165.82/22.57 (10) a_select2(s_try7_init, all_71_8) = all_71_7 % 165.82/22.57 (11) gt(n2, all_71_8) % 165.82/22.57 (12) $i(all_71_8) % 165.82/22.57 (13) ! [v0: $i] : (v0 = n1 | v0 = n0 | ~ $i(v0) | ~ leq(v0, n1) | ~ % 165.82/22.57 leq(n0, v0)) % 165.82/22.57 % 165.82/22.57 Begin of proof % 165.82/22.57 | % 165.82/22.57 | GROUND_INST: instantiating (9) with all_71_8, n2, n1, simplifying with (3), % 165.82/22.57 | (5), (11), (12) gives: % 165.82/22.57 | (14) leq(all_71_8, n1) % 165.82/22.57 | % 165.82/22.58 | GROUND_INST: instantiating (13) with all_71_8, simplifying with (8), (12), % 165.82/22.58 | (14) gives: % 165.82/22.58 | (15) all_71_8 = n1 | all_71_8 = n0 % 165.82/22.58 | % 165.82/22.58 | BETA: splitting (15) gives: % 165.82/22.58 | % 165.82/22.58 | Case 1: % 165.82/22.58 | | % 165.82/22.58 | | (16) all_71_8 = n0 % 165.82/22.58 | | % 165.82/22.58 | | REDUCE: (7), (16) imply: % 165.82/22.58 | | (17) $false % 165.82/22.58 | | % 165.82/22.58 | | CLOSE: (17) is inconsistent. % 165.82/22.58 | | % 165.82/22.58 | Case 2: % 165.82/22.58 | | % 165.82/22.58 | | (18) all_71_8 = n1 % 165.82/22.58 | | % 165.82/22.58 | | REDUCE: (10), (18) imply: % 165.82/22.58 | | (19) a_select2(s_try7_init, n1) = all_71_7 % 165.82/22.58 | | % 165.82/22.58 | | REDUCE: (12), (18) imply: % 165.82/22.58 | | (20) $i(n1) % 165.82/22.58 | | % 165.82/22.58 | | REDUCE: (1), (18) imply: % 165.82/22.58 | | (21) leq(n1, n2) % 165.82/22.58 | | % 165.82/22.58 | | REDUCE: (8), (18) imply: % 165.82/22.58 | | (22) leq(n0, n1) % 165.82/22.58 | | % 165.82/22.58 | | GROUND_INST: instantiating (6) with n1, all_71_7, simplifying with (19), % 165.82/22.58 | | (20), (22) gives: % 165.82/22.58 | | (23) all_71_7 = init | ~ leq(n1, all_71_9) % 165.82/22.58 | | % 165.82/22.58 | | BETA: splitting (23) gives: % 165.82/22.58 | | % 165.82/22.58 | | Case 1: % 165.82/22.58 | | | % 165.82/22.58 | | | (24) ~ leq(n1, all_71_9) % 165.82/22.58 | | | % 165.82/22.58 | | | REDUCE: (4), (24) imply: % 165.82/22.58 | | | (25) ~ leq(n1, n2) % 165.82/22.58 | | | % 165.82/22.58 | | | PRED_UNIFY: (21), (25) imply: % 165.82/22.58 | | | (26) $false % 165.82/22.58 | | | % 165.82/22.58 | | | CLOSE: (26) is inconsistent. % 165.82/22.58 | | | % 165.82/22.58 | | Case 2: % 165.82/22.58 | | | % 165.82/22.58 | | | (27) all_71_7 = init % 165.82/22.58 | | | % 165.82/22.58 | | | REDUCE: (2), (27) imply: % 165.82/22.58 | | | (28) $false % 165.82/22.58 | | | % 165.82/22.58 | | | CLOSE: (28) is inconsistent. % 165.82/22.58 | | | % 165.82/22.58 | | End of split % 165.82/22.58 | | % 165.82/22.58 | End of split % 165.82/22.58 | % 165.82/22.58 End of proof % 165.82/22.58 % SZS output end Proof for theBenchmark % 165.82/22.58 % 165.82/22.58 21902ms %------------------------------------------------------------------------------