%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV097+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 : n027.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 22:54:53 EDT 2023 % Result : Theorem 18.42s 3.25s % Output : Proof 23.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV097+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n027.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Aug 29 05:42:23 EDT 2023 % 0.16/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.93/1.38 Prover 4: Preprocessing ... % 3.93/1.38 Prover 1: Preprocessing ... % 3.93/1.41 Prover 2: Preprocessing ... % 3.93/1.41 Prover 6: Preprocessing ... % 3.93/1.41 Prover 5: Preprocessing ... % 3.93/1.41 Prover 0: Preprocessing ... % 3.93/1.41 Prover 3: Preprocessing ... % 11.73/2.34 Prover 1: Warning: ignoring some quantifiers % 11.73/2.35 Prover 3: Warning: ignoring some quantifiers % 12.02/2.38 Prover 6: Proving ... % 12.02/2.41 Prover 3: Constructing countermodel ... % 12.02/2.41 Prover 1: Constructing countermodel ... % 12.02/2.42 Prover 4: Warning: ignoring some quantifiers % 13.08/2.52 Prover 4: Constructing countermodel ... % 13.08/2.54 Prover 5: Proving ... % 13.33/2.63 Prover 0: Proving ... % 13.95/2.69 Prover 2: Proving ... % 18.42/3.25 Prover 3: proved (2591ms) % 18.42/3.25 % 18.42/3.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.42/3.25 % 18.42/3.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 18.42/3.26 Prover 5: stopped % 18.42/3.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.42/3.27 Prover 0: stopped % 18.42/3.27 Prover 6: stopped % 18.42/3.27 Prover 2: stopped % 18.42/3.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.42/3.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.42/3.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.42/3.43 Prover 7: Preprocessing ... % 20.04/3.49 Prover 8: Preprocessing ... % 20.04/3.50 Prover 10: Preprocessing ... % 20.69/3.55 Prover 11: Preprocessing ... % 20.69/3.56 Prover 13: Preprocessing ... % 21.87/3.70 Prover 7: Warning: ignoring some quantifiers % 21.87/3.72 Prover 7: Constructing countermodel ... % 21.87/3.75 Prover 10: Warning: ignoring some quantifiers % 22.32/3.75 Prover 1: Found proof (size 202) % 22.32/3.75 Prover 1: proved (3116ms) % 22.33/3.75 Prover 13: stopped % 22.33/3.76 Prover 7: stopped % 22.33/3.76 Prover 10: Constructing countermodel ... % 22.33/3.76 Prover 4: stopped % 22.33/3.78 Prover 8: Warning: ignoring some quantifiers % 22.33/3.78 Prover 10: stopped % 22.33/3.79 Prover 8: Constructing countermodel ... % 22.60/3.81 Prover 8: stopped % 22.78/3.87 Prover 11: Warning: ignoring some quantifiers % 22.78/3.89 Prover 11: Constructing countermodel ... % 22.78/3.90 Prover 11: stopped % 22.78/3.90 % 22.78/3.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.78/3.90 % 23.21/3.95 % SZS output start Proof for theBenchmark % 23.21/3.95 Assumptions after simplification: % 23.21/3.95 --------------------------------- % 23.21/3.95 % 23.21/3.96 (gt_3_0) % 23.21/3.98 gt(n3, n0) = 0 & $i(n3) & $i(n0) % 23.21/3.98 % 23.21/3.98 (gt_3_1) % 23.21/3.98 gt(n3, n1) = 0 & $i(n3) & $i(n1) % 23.21/3.98 % 23.21/3.98 (gt_3_2) % 23.21/3.98 gt(n3, n2) = 0 & $i(n3) & $i(n2) % 23.21/3.98 % 23.21/3.98 (gt_3_tptp_minus_1) % 23.21/3.98 gt(n3, tptp_minus_1) = 0 & $i(n3) & $i(tptp_minus_1) % 23.21/3.98 % 23.21/3.98 (leq_succ_gt) % 23.21/3.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2, % 23.21/3.98 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 23.21/3.98 % 23.21/3.98 (leq_succ_gt_equiv) % 23.21/3.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.21/3.98 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 23.21/3.98 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 23.21/3.98 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 23.21/3.98 leq(v0, v1) = 0) % 23.21/3.98 % 23.21/3.98 (pred_minus_1) % 23.21/3.98 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 23.21/3.98 (pred(v0) = v1 & $i(v1))) % 23.21/3.98 % 23.21/3.98 (quaternion_ds1_inuse_0009) % 23.21/3.99 $i(z_defuse) & $i(n999) & $i(pv5) & $i(xinit_noise_defuse) & % 23.21/3.99 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) & % 23.21/3.99 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) % 23.21/3.99 & ? [v0: $i] : ? [v1: $i] : (minus(n999, n1) = v0 & minus(pv5, n1) = v1 & % 23.21/3.99 a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use & % 23.21/3.99 a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use % 23.21/3.99 & a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse, % 23.21/3.99 n3) = use & a_select2(xinit_noise_defuse, n2) = use & % 23.21/3.99 a_select2(xinit_noise_defuse, n1) = use & a_select2(xinit_noise_defuse, n0) % 23.21/3.99 = use & a_select2(xinit_mean_defuse, n5) = use & % 23.21/3.99 a_select2(xinit_mean_defuse, n4) = use & a_select2(xinit_mean_defuse, n3) = % 23.21/3.99 use & a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse, % 23.21/3.99 n1) = use & a_select2(xinit_mean_defuse, n0) = use & % 23.21/3.99 a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use & % 23.21/3.99 a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use & % 23.21/3.99 a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use & % 23.21/3.99 a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use & % 23.21/3.99 a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use & % 23.21/3.99 a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use & leq(pv5, % 23.21/3.99 v0) = 0 & leq(n0, pv5) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : % 23.21/3.99 ! [v4: $i] : ( ~ (a_select3(z_defuse, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) % 23.21/3.99 | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] % 23.21/3.99 : (a_select3(u_defuse, v2, v3) = v9 & leq(v3, pv5) = v8 & leq(v2, n2) = v7 % 23.21/3.99 & leq(n0, v3) = v6 & leq(n0, v2) = v5 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = % 23.21/3.99 0) | ~ (v6 = 0) | ~ (v5 = 0) | (v9 = use & v4 = use)))) & ! [v2: % 23.21/3.99 $i] : ! [v3: $i] : ( ~ (leq(v3, v1) = 0) | ~ (leq(v2, n2) = 0) | ~ % 23.21/3.99 $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: % 23.21/3.99 $i] : (a_select3(z_defuse, v2, v3) = v7 & a_select3(u_defuse, v2, v3) = % 23.21/3.99 v6 & leq(n0, v3) = v5 & leq(n0, v2) = v4 & $i(v7) & $i(v6) & ( ~ (v5 = % 23.21/3.99 0) | ~ (v4 = 0) | (v7 = use & v6 = use)))) & ( ? [v2: $i] : ? [v3: % 23.21/3.99 $i] : ? [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v2, v3) = v5 & % 23.21/3.99 a_select3(u_defuse, v2, v3) = v4 & leq(v3, v1) = 0 & leq(v2, n2) = 0 & % 23.21/3.99 leq(n0, v3) = 0 & leq(n0, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 23.21/3.99 ( ~ (v5 = use) | ~ (v4 = use))) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 23.21/3.99 $i] : ? [v5: $i] : (a_select3(z_defuse, v2, v3) = v5 & % 23.21/3.99 a_select3(u_defuse, v2, v3) = v4 & leq(v3, pv5) = 0 & leq(v2, n2) = 0 & % 23.21/3.99 leq(n0, v3) = 0 & leq(n0, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 23.21/3.99 ( ~ (v5 = use) | ~ (v4 = use))))) % 23.21/3.99 % 23.21/3.99 (succ_pred) % 23.21/3.99 ! [v0: $i] : ! [v1: $i] : ( ~ (pred(v0) = v1) | ~ $i(v0) | succ(v1) = v0) % 23.21/3.99 % 23.21/3.99 (succ_tptp_minus_1) % 23.21/3.99 succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0) % 23.21/3.99 % 23.21/3.99 (successor_1) % 23.21/3.99 succ(n0) = n1 & $i(n1) & $i(n0) % 23.21/3.99 % 23.21/3.99 (successor_2) % 23.21/3.99 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 23.21/3.99 % 23.21/3.99 (successor_3) % 23.21/3.99 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 23.21/4.00 succ(n0) = v0 & $i(v1) & $i(v0)) % 23.21/4.00 % 23.47/4.00 (successor_4) % 23.47/4.00 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 23.47/4.00 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 23.47/4.00 % 23.47/4.00 (successor_5) % 23.47/4.00 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 23.47/4.00 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 23.47/4.00 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 23.47/4.00 % 23.47/4.00 (function-axioms) % 23.47/4.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 23.47/4.00 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 23.47/4.00 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.47/4.00 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 23.47/4.00 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.47/4.00 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 23.47/4.00 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 23.47/4.00 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 23.47/4.00 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.47/4.00 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 23.47/4.00 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.47/4.00 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 23.47/4.00 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 23.47/4.00 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 23.47/4.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 23.47/4.00 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.47/4.00 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 23.47/4.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.47/4.00 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 23.47/4.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 23.47/4.00 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 23.47/4.00 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 23.47/4.00 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 23.47/4.00 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 23.47/4.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.47/4.00 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 23.47/4.00 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 23.47/4.00 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 23.47/4.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.47/4.00 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 23.47/4.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.47/4.00 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 23.47/4.00 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.47/4.00 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 23.47/4.00 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 23.47/4.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 23.47/4.00 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.47/4.00 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.47/4.00 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 23.47/4.00 % 23.47/4.00 Further assumptions not needed in the proof: % 23.47/4.00 -------------------------------------------- % 23.47/4.00 const_array1_select, const_array2_select, defuse, finite_domain_0, % 23.47/4.00 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4, % 23.47/4.00 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, % 23.47/4.00 gt_2_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, % 23.47/4.00 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2, % 23.47/4.00 gt_999_3, gt_999_4, gt_999_5, gt_999_tptp_minus_1, gt_succ, irreflexivity_gt, % 23.47/4.00 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_succ, % 23.47/4.00 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, % 23.47/4.00 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 23.47/4.00 matrix_symm_update_diagonal, pred_succ, reflexivity_leq, sel2_update_1, % 23.47/4.00 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, % 23.47/4.00 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, % 23.47/4.00 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, % 23.47/4.00 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq, % 23.47/4.00 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo % 23.47/4.00 % 23.47/4.00 Those formulas are unsatisfiable: % 23.47/4.00 --------------------------------- % 23.47/4.00 % 23.47/4.00 Begin of proof % 23.47/4.01 | % 23.47/4.01 | ALPHA: (leq_succ_gt_equiv) implies: % 23.47/4.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 23.47/4.01 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0) % 23.47/4.01 | % 23.47/4.01 | ALPHA: (succ_tptp_minus_1) implies: % 23.47/4.01 | (2) succ(tptp_minus_1) = n0 % 23.47/4.01 | % 23.47/4.01 | ALPHA: (pred_minus_1) implies: % 23.47/4.01 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) | % 23.47/4.01 | (pred(v0) = v1 & $i(v1))) % 23.47/4.01 | % 23.47/4.01 | ALPHA: (gt_3_tptp_minus_1) implies: % 23.47/4.01 | (4) $i(tptp_minus_1) % 23.47/4.01 | (5) gt(n3, tptp_minus_1) = 0 % 23.47/4.01 | % 23.47/4.01 | ALPHA: (gt_3_0) implies: % 23.47/4.01 | (6) gt(n3, n0) = 0 % 23.47/4.01 | % 23.47/4.01 | ALPHA: (gt_3_1) implies: % 23.47/4.01 | (7) gt(n3, n1) = 0 % 23.47/4.01 | % 23.47/4.01 | ALPHA: (gt_3_2) implies: % 23.47/4.01 | (8) gt(n3, n2) = 0 % 23.47/4.01 | % 23.47/4.01 | ALPHA: (successor_4) implies: % 23.47/4.01 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 23.47/4.01 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 23.47/4.01 | % 23.47/4.01 | ALPHA: (successor_5) implies: % 23.47/4.01 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 23.47/4.01 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 23.47/4.01 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 23.47/4.01 | % 23.47/4.01 | ALPHA: (successor_1) implies: % 23.47/4.01 | (11) succ(n0) = n1 % 23.47/4.01 | % 23.47/4.01 | ALPHA: (successor_2) implies: % 23.47/4.01 | (12) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 23.47/4.01 | % 23.47/4.01 | ALPHA: (successor_3) implies: % 23.47/4.01 | (13) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) % 23.47/4.01 | = v0 & $i(v1) & $i(v0)) % 23.47/4.01 | % 23.47/4.01 | ALPHA: (quaternion_ds1_inuse_0009) implies: % 23.47/4.01 | (14) $i(n0) % 23.47/4.01 | (15) $i(pv5) % 23.47/4.02 | (16) ? [v0: $i] : ? [v1: $i] : (minus(n999, n1) = v0 & minus(pv5, n1) = % 23.47/4.02 | v1 & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) % 23.47/4.02 | = use & a_select3(u_defuse, n0, n0) = use & % 23.47/4.02 | a_select2(xinit_noise_defuse, n5) = use & % 23.47/4.02 | a_select2(xinit_noise_defuse, n4) = use & % 23.47/4.02 | a_select2(xinit_noise_defuse, n3) = use & % 23.47/4.02 | a_select2(xinit_noise_defuse, n2) = use & % 23.47/4.02 | a_select2(xinit_noise_defuse, n1) = use & % 23.47/4.02 | a_select2(xinit_noise_defuse, n0) = use & % 23.47/4.02 | a_select2(xinit_mean_defuse, n5) = use & % 23.47/4.02 | a_select2(xinit_mean_defuse, n4) = use & % 23.47/4.02 | a_select2(xinit_mean_defuse, n3) = use & % 23.47/4.02 | a_select2(xinit_mean_defuse, n2) = use & % 23.47/4.02 | a_select2(xinit_mean_defuse, n1) = use & % 23.47/4.02 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) % 23.47/4.02 | = use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, % 23.47/4.02 | n3) = use & a_select2(sigma_defuse, n5) = use & % 23.47/4.02 | a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = % 23.47/4.02 | use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, % 23.47/4.02 | n1) = use & a_select2(sigma_defuse, n0) = use & % 23.47/4.02 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 23.47/4.02 | a_select2(rho_defuse, n0) = use & leq(pv5, v0) = 0 & leq(n0, pv5) = % 23.47/4.02 | 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 23.47/4.02 | (a_select3(z_defuse, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? % 23.47/4.02 | [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 23.47/4.02 | $i] : (a_select3(u_defuse, v2, v3) = v9 & leq(v3, pv5) = v8 & % 23.47/4.02 | leq(v2, n2) = v7 & leq(n0, v3) = v6 & leq(n0, v2) = v5 & $i(v9) % 23.47/4.02 | & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | (v9 = % 23.47/4.02 | use & v4 = use)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 23.47/4.02 | (leq(v3, v1) = 0) | ~ (leq(v2, n2) = 0) | ~ $i(v3) | ~ $i(v2) | % 23.47/4.02 | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 23.47/4.02 | (a_select3(z_defuse, v2, v3) = v7 & a_select3(u_defuse, v2, v3) = % 23.47/4.02 | v6 & leq(n0, v3) = v5 & leq(n0, v2) = v4 & $i(v7) & $i(v6) & ( ~ % 23.47/4.02 | (v5 = 0) | ~ (v4 = 0) | (v7 = use & v6 = use)))) & ( ? [v2: % 23.47/4.02 | $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 23.47/4.02 | (a_select3(z_defuse, v2, v3) = v5 & a_select3(u_defuse, v2, v3) = % 23.47/4.02 | v4 & leq(v3, v1) = 0 & leq(v2, n2) = 0 & leq(n0, v3) = 0 & % 23.47/4.02 | leq(n0, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v5 = % 23.47/4.02 | use) | ~ (v4 = use))) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 23.47/4.02 | $i] : ? [v5: $i] : (a_select3(z_defuse, v2, v3) = v5 & % 23.47/4.02 | a_select3(u_defuse, v2, v3) = v4 & leq(v3, pv5) = 0 & leq(v2, % 23.47/4.02 | n2) = 0 & leq(n0, v3) = 0 & leq(n0, v2) = 0 & $i(v5) & $i(v4) % 23.47/4.02 | & $i(v3) & $i(v2) & ( ~ (v5 = use) | ~ (v4 = use))))) % 23.47/4.02 | % 23.47/4.02 | ALPHA: (function-axioms) implies: % 23.47/4.02 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 23.47/4.02 | v1) | ~ (succ(v2) = v0)) % 23.47/4.02 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.47/4.02 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 23.47/4.02 | v0)) % 23.47/4.02 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.47/4.02 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) % 23.47/4.02 | = v0)) % 23.47/4.02 | % 23.47/4.02 | DELTA: instantiating (12) with fresh symbol all_49_0 gives: % 23.47/4.02 | (20) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0) % 23.47/4.02 | % 23.47/4.02 | ALPHA: (20) implies: % 23.47/4.02 | (21) $i(all_49_0) % 23.47/4.02 | (22) succ(n0) = all_49_0 % 23.47/4.02 | (23) succ(all_49_0) = n2 % 23.47/4.02 | % 23.47/4.02 | DELTA: instantiating (13) with fresh symbols all_51_0, all_51_1 gives: % 23.47/4.02 | (24) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1 % 23.47/4.02 | & $i(all_51_0) & $i(all_51_1) % 23.47/4.02 | % 23.47/4.02 | ALPHA: (24) implies: % 23.47/4.02 | (25) $i(all_51_0) % 23.47/4.02 | (26) succ(n0) = all_51_1 % 23.47/4.02 | (27) succ(all_51_1) = all_51_0 % 23.47/4.02 | (28) succ(all_51_0) = n3 % 23.47/4.02 | % 23.47/4.02 | DELTA: instantiating (9) with fresh symbols all_53_0, all_53_1, all_53_2 % 23.47/4.02 | gives: % 23.47/4.02 | (29) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) = % 23.47/4.02 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) & % 23.47/4.02 | $i(all_53_2) % 23.47/4.02 | % 23.47/4.02 | ALPHA: (29) implies: % 23.47/4.02 | (30) succ(n0) = all_53_2 % 23.47/4.02 | (31) succ(all_53_2) = all_53_1 % 23.47/4.02 | (32) succ(all_53_1) = all_53_0 % 23.47/4.02 | % 23.47/4.02 | DELTA: instantiating (10) with fresh symbols all_55_0, all_55_1, all_55_2, % 23.47/4.02 | all_55_3 gives: % 23.47/4.02 | (33) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) = % 23.47/4.02 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 & % 23.47/4.02 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) % 23.47/4.02 | % 23.47/4.02 | ALPHA: (33) implies: % 23.47/4.02 | (34) succ(n0) = all_55_3 % 23.47/4.02 | (35) succ(all_55_3) = all_55_2 % 23.47/4.03 | (36) succ(all_55_2) = all_55_1 % 23.47/4.03 | % 23.47/4.03 | DELTA: instantiating (16) with fresh symbols all_76_0, all_76_1 gives: % 23.47/4.03 | (37) minus(n999, n1) = all_76_1 & minus(pv5, n1) = all_76_0 & % 23.47/4.03 | a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use % 23.47/4.03 | & a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, % 23.47/4.03 | n5) = use & a_select2(xinit_noise_defuse, n4) = use & % 23.47/4.03 | a_select2(xinit_noise_defuse, n3) = use & % 23.47/4.03 | a_select2(xinit_noise_defuse, n2) = use & % 23.47/4.03 | a_select2(xinit_noise_defuse, n1) = use & % 23.47/4.03 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse, % 23.47/4.03 | n5) = use & a_select2(xinit_mean_defuse, n4) = use & % 23.47/4.03 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 23.47/4.03 | n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 23.47/4.03 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = % 23.47/4.03 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) % 23.47/4.03 | = use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, % 23.47/4.03 | n4) = use & a_select2(sigma_defuse, n3) = use & % 23.47/4.03 | a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use % 23.47/4.03 | & a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use % 23.47/4.03 | & a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use & % 23.47/4.03 | leq(pv5, all_76_1) = 0 & leq(n0, pv5) = 0 & $i(all_76_0) & % 23.47/4.03 | $i(all_76_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.47/4.03 | (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 23.47/4.03 | any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] : % 23.47/4.03 | (a_select3(u_defuse, v0, v1) = v7 & leq(v1, pv5) = v6 & leq(v0, n2) % 23.47/4.03 | = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3 & $i(v7) & ( ~ (v6 = 0) % 23.47/4.03 | | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v7 = use & v2 = % 23.47/4.03 | use)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = % 23.47/4.03 | 0) | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : % 23.47/4.03 | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v0, % 23.47/4.03 | v1) = v5 & a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & % 23.47/4.03 | leq(n0, v0) = v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | % 23.47/4.03 | (v5 = use & v4 = use)))) & ( ? [v0: $i] : ? [v1: $i] : ? [v2: % 23.47/4.03 | $i] : ? [v3: $i] : (a_select3(z_defuse, v0, v1) = v3 & % 23.47/4.03 | a_select3(u_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 & leq(v0, % 23.47/4.03 | n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v3) & $i(v2) & % 23.47/4.03 | $i(v1) & $i(v0) & ( ~ (v3 = use) | ~ (v2 = use))) | ? [v0: $i] : % 23.47/4.03 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (a_select3(z_defuse, v0, % 23.47/4.03 | v1) = v3 & a_select3(u_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 & % 23.47/4.03 | leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v3) & % 23.47/4.03 | $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) | ~ (v2 = use)))) % 23.47/4.03 | % 23.47/4.03 | ALPHA: (37) implies: % 23.47/4.03 | (38) leq(n0, pv5) = 0 % 23.47/4.03 | (39) minus(pv5, n1) = all_76_0 % 23.47/4.03 | (40) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 23.47/4.03 | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = v2 & % 23.47/4.03 | leq(v1, all_76_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, % 23.47/4.03 | v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) | ~ % 23.47/4.03 | (v2 = use))) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 23.47/4.03 | $i] : (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, % 23.47/4.03 | v1) = v2 & leq(v1, pv5) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & % 23.47/4.03 | leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) % 23.47/4.03 | | ~ (v2 = use))) % 23.47/4.03 | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0, % 23.47/4.03 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 23.47/4.03 | ? [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v0, v1) = v5 & % 23.47/4.03 | a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) % 23.47/4.04 | = v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = use & % 23.47/4.04 | v4 = use)))) % 23.47/4.04 | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a_select3(z_defuse, v0, % 23.47/4.04 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] % 23.47/4.04 | : ? [v5: any] : ? [v6: any] : ? [v7: $i] : (a_select3(u_defuse, % 23.47/4.04 | v0, v1) = v7 & leq(v1, pv5) = v6 & leq(v0, n2) = v5 & leq(n0, % 23.47/4.04 | v1) = v4 & leq(n0, v0) = v3 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = % 23.47/4.04 | 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v7 = use & v2 = use)))) % 23.47/4.04 | % 23.47/4.04 | GROUND_INST: instantiating (17) with all_51_1, all_53_2, n0, simplifying with % 23.47/4.04 | (26), (30) gives: % 23.47/4.04 | (43) all_53_2 = all_51_1 % 23.47/4.04 | % 23.47/4.04 | GROUND_INST: instantiating (17) with all_49_0, all_53_2, n0, simplifying with % 23.47/4.04 | (22), (30) gives: % 23.47/4.04 | (44) all_53_2 = all_49_0 % 23.47/4.04 | % 23.47/4.04 | GROUND_INST: instantiating (17) with all_51_1, all_55_3, n0, simplifying with % 23.47/4.04 | (26), (34) gives: % 23.47/4.04 | (45) all_55_3 = all_51_1 % 23.47/4.04 | % 23.47/4.04 | GROUND_INST: instantiating (17) with n1, all_55_3, n0, simplifying with (11), % 23.47/4.04 | (34) gives: % 23.47/4.04 | (46) all_55_3 = n1 % 23.47/4.04 | % 23.47/4.04 | COMBINE_EQS: (45), (46) imply: % 23.47/4.04 | (47) all_51_1 = n1 % 23.47/4.04 | % 23.47/4.04 | SIMP: (47) implies: % 23.47/4.04 | (48) all_51_1 = n1 % 23.47/4.04 | % 23.47/4.04 | COMBINE_EQS: (43), (44) imply: % 23.47/4.04 | (49) all_51_1 = all_49_0 % 23.47/4.04 | % 23.47/4.04 | SIMP: (49) implies: % 23.47/4.04 | (50) all_51_1 = all_49_0 % 23.47/4.04 | % 23.47/4.04 | COMBINE_EQS: (48), (50) imply: % 23.47/4.04 | (51) all_49_0 = n1 % 23.47/4.04 | % 23.47/4.04 | COMBINE_EQS: (44), (51) imply: % 23.47/4.04 | (52) all_53_2 = n1 % 23.47/4.04 | % 23.47/4.04 | REDUCE: (35), (46) imply: % 23.47/4.04 | (53) succ(n1) = all_55_2 % 23.47/4.04 | % 23.47/4.04 | REDUCE: (31), (52) imply: % 23.47/4.04 | (54) succ(n1) = all_53_1 % 23.47/4.04 | % 23.47/4.04 | REDUCE: (27), (48) imply: % 23.47/4.04 | (55) succ(n1) = all_51_0 % 23.47/4.04 | % 23.47/4.04 | REDUCE: (23), (51) imply: % 23.47/4.04 | (56) succ(n1) = n2 % 23.47/4.04 | % 23.47/4.04 | REDUCE: (21), (51) imply: % 23.47/4.04 | (57) $i(n1) % 23.47/4.04 | % 23.47/4.04 | GROUND_INST: instantiating (17) with all_51_0, all_53_1, n1, simplifying with % 23.47/4.04 | (54), (55) gives: % 23.47/4.04 | (58) all_53_1 = all_51_0 % 23.47/4.04 | % 23.47/4.04 | GROUND_INST: instantiating (17) with all_53_1, all_55_2, n1, simplifying with % 23.47/4.04 | (53), (54) gives: % 23.47/4.04 | (59) all_55_2 = all_53_1 % 23.47/4.04 | % 23.47/4.04 | GROUND_INST: instantiating (17) with n2, all_55_2, n1, simplifying with (53), % 23.47/4.04 | (56) gives: % 23.47/4.04 | (60) all_55_2 = n2 % 23.47/4.04 | % 23.47/4.04 | COMBINE_EQS: (59), (60) imply: % 23.47/4.04 | (61) all_53_1 = n2 % 23.47/4.04 | % 23.47/4.04 | SIMP: (61) implies: % 23.47/4.04 | (62) all_53_1 = n2 % 23.47/4.04 | % 23.47/4.04 | COMBINE_EQS: (58), (62) imply: % 23.47/4.04 | (63) all_51_0 = n2 % 23.47/4.04 | % 23.47/4.04 | SIMP: (63) implies: % 23.47/4.04 | (64) all_51_0 = n2 % 23.47/4.04 | % 23.47/4.04 | REDUCE: (36), (60) imply: % 23.47/4.04 | (65) succ(n2) = all_55_1 % 23.47/4.04 | % 23.47/4.04 | REDUCE: (32), (62) imply: % 23.47/4.04 | (66) succ(n2) = all_53_0 % 23.47/4.04 | % 23.47/4.04 | REDUCE: (28), (64) imply: % 23.47/4.04 | (67) succ(n2) = n3 % 23.47/4.04 | % 23.47/4.04 | REDUCE: (25), (64) imply: % 23.47/4.04 | (68) $i(n2) % 23.47/4.04 | % 23.47/4.04 | GROUND_INST: instantiating (17) with all_53_0, all_55_1, n2, simplifying with % 23.47/4.04 | (65), (66) gives: % 23.47/4.04 | (69) all_55_1 = all_53_0 % 23.47/4.04 | % 23.47/4.04 | GROUND_INST: instantiating (17) with n3, all_55_1, n2, simplifying with (65), % 23.47/4.04 | (67) gives: % 23.47/4.04 | (70) all_55_1 = n3 % 23.47/4.04 | % 23.47/4.04 | COMBINE_EQS: (69), (70) imply: % 23.47/4.04 | (71) all_53_0 = n3 % 23.47/4.04 | % 23.47/4.04 | SIMP: (71) implies: % 23.47/4.04 | (72) all_53_0 = n3 % 23.47/4.04 | % 23.47/4.05 | GROUND_INST: instantiating (leq_succ_gt) with tptp_minus_1, pv5, n0, % 23.47/4.05 | simplifying with (2), (4), (15), (38) gives: % 23.47/4.05 | (73) gt(pv5, tptp_minus_1) = 0 % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (1) with n2, n2, n3, simplifying with (8), (67), % 23.47/4.05 | (68) gives: % 23.47/4.05 | (74) leq(n2, n2) = 0 % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (1) with n1, n2, n3, simplifying with (7), (57), % 23.47/4.05 | (67), (68) gives: % 23.47/4.05 | (75) leq(n1, n2) = 0 % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (1) with tptp_minus_1, n2, n3, simplifying with % 23.47/4.05 | (4), (5), (67), (68) gives: % 23.47/4.05 | (76) leq(tptp_minus_1, n2) = 0 % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (1) with n0, n2, n3, simplifying with (6), (14), % 23.47/4.05 | (67), (68) gives: % 23.47/4.05 | (77) leq(n0, n2) = 0 % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (3) with pv5, all_76_0, simplifying with (15), (39) % 23.47/4.05 | gives: % 23.47/4.05 | (78) pred(pv5) = all_76_0 & $i(all_76_0) % 23.47/4.05 | % 23.47/4.05 | ALPHA: (78) implies: % 23.47/4.05 | (79) $i(all_76_0) % 23.47/4.05 | (80) pred(pv5) = all_76_0 % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (succ_pred) with pv5, all_76_0, simplifying with % 23.47/4.05 | (15), (80) gives: % 23.47/4.05 | (81) succ(all_76_0) = pv5 % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (1) with tptp_minus_1, all_76_0, pv5, simplifying % 23.47/4.05 | with (4), (73), (79), (81) gives: % 23.47/4.05 | (82) leq(tptp_minus_1, all_76_0) = 0 % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (41) with n2, tptp_minus_1, simplifying with (4), % 23.47/4.05 | (68), (74), (82) gives: % 23.47/4.05 | (83) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.47/4.05 | (a_select3(z_defuse, n2, tptp_minus_1) = v3 & a_select3(u_defuse, n2, % 23.47/4.05 | tptp_minus_1) = v2 & leq(n0, n2) = v0 & leq(n0, tptp_minus_1) = v1 % 23.47/4.05 | & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = % 23.47/4.05 | use))) % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (41) with n1, tptp_minus_1, simplifying with (4), % 23.47/4.05 | (57), (75), (82) gives: % 23.47/4.05 | (84) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.47/4.05 | (a_select3(z_defuse, n1, tptp_minus_1) = v3 & a_select3(u_defuse, n1, % 23.47/4.05 | tptp_minus_1) = v2 & leq(n0, n1) = v0 & leq(n0, tptp_minus_1) = v1 % 23.47/4.05 | & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = % 23.47/4.05 | use))) % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (41) with tptp_minus_1, tptp_minus_1, simplifying % 23.47/4.05 | with (4), (76), (82) gives: % 23.47/4.05 | (85) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.47/4.05 | (a_select3(z_defuse, tptp_minus_1, tptp_minus_1) = v3 & % 23.47/4.05 | a_select3(u_defuse, tptp_minus_1, tptp_minus_1) = v2 & leq(n0, % 23.47/4.05 | tptp_minus_1) = v1 & leq(n0, tptp_minus_1) = v0 & $i(v3) & $i(v2) % 23.47/4.05 | & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use))) % 23.47/4.05 | % 23.47/4.05 | GROUND_INST: instantiating (41) with n0, tptp_minus_1, simplifying with (4), % 23.47/4.05 | (14), (77), (82) gives: % 23.47/4.05 | (86) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.47/4.05 | (a_select3(z_defuse, n0, tptp_minus_1) = v3 & a_select3(u_defuse, n0, % 23.47/4.05 | tptp_minus_1) = v2 & leq(n0, tptp_minus_1) = v1 & leq(n0, n0) = v0 % 23.47/4.05 | & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = % 23.47/4.05 | use))) % 23.47/4.05 | % 23.47/4.05 | DELTA: instantiating (85) with fresh symbols all_119_0, all_119_1, all_119_2, % 23.47/4.05 | all_119_3 gives: % 23.47/4.05 | (87) a_select3(z_defuse, tptp_minus_1, tptp_minus_1) = all_119_0 & % 23.47/4.05 | a_select3(u_defuse, tptp_minus_1, tptp_minus_1) = all_119_1 & leq(n0, % 23.47/4.05 | tptp_minus_1) = all_119_2 & leq(n0, tptp_minus_1) = all_119_3 & % 23.47/4.05 | $i(all_119_0) & $i(all_119_1) & ( ~ (all_119_2 = 0) | ~ (all_119_3 = % 23.47/4.05 | 0) | (all_119_0 = use & all_119_1 = use)) % 23.47/4.05 | % 23.47/4.05 | ALPHA: (87) implies: % 23.47/4.05 | (88) a_select3(z_defuse, tptp_minus_1, tptp_minus_1) = all_119_0 % 23.47/4.05 | % 23.47/4.05 | DELTA: instantiating (84) with fresh symbols all_121_0, all_121_1, all_121_2, % 23.47/4.05 | all_121_3 gives: % 23.76/4.05 | (89) a_select3(z_defuse, n1, tptp_minus_1) = all_121_0 & % 23.76/4.05 | a_select3(u_defuse, n1, tptp_minus_1) = all_121_1 & leq(n0, n1) = % 23.76/4.05 | all_121_3 & leq(n0, tptp_minus_1) = all_121_2 & $i(all_121_0) & % 23.76/4.05 | $i(all_121_1) & ( ~ (all_121_2 = 0) | ~ (all_121_3 = 0) | (all_121_0 % 23.76/4.05 | = use & all_121_1 = use)) % 23.76/4.05 | % 23.76/4.05 | ALPHA: (89) implies: % 23.76/4.05 | (90) a_select3(z_defuse, n1, tptp_minus_1) = all_121_0 % 23.76/4.05 | % 23.76/4.05 | DELTA: instantiating (83) with fresh symbols all_123_0, all_123_1, all_123_2, % 23.76/4.05 | all_123_3 gives: % 23.76/4.06 | (91) a_select3(z_defuse, n2, tptp_minus_1) = all_123_0 & % 23.76/4.06 | a_select3(u_defuse, n2, tptp_minus_1) = all_123_1 & leq(n0, n2) = % 23.76/4.06 | all_123_3 & leq(n0, tptp_minus_1) = all_123_2 & $i(all_123_0) & % 23.76/4.06 | $i(all_123_1) & ( ~ (all_123_2 = 0) | ~ (all_123_3 = 0) | (all_123_0 % 23.76/4.06 | = use & all_123_1 = use)) % 23.76/4.06 | % 23.76/4.06 | ALPHA: (91) implies: % 23.76/4.06 | (92) leq(n0, n2) = all_123_3 % 23.76/4.06 | (93) a_select3(z_defuse, n2, tptp_minus_1) = all_123_0 % 23.76/4.06 | % 23.76/4.06 | DELTA: instantiating (86) with fresh symbols all_125_0, all_125_1, all_125_2, % 23.76/4.06 | all_125_3 gives: % 23.76/4.06 | (94) a_select3(z_defuse, n0, tptp_minus_1) = all_125_0 & % 23.76/4.06 | a_select3(u_defuse, n0, tptp_minus_1) = all_125_1 & leq(n0, % 23.76/4.06 | tptp_minus_1) = all_125_2 & leq(n0, n0) = all_125_3 & $i(all_125_0) % 23.76/4.06 | & $i(all_125_1) & ( ~ (all_125_2 = 0) | ~ (all_125_3 = 0) | % 23.76/4.06 | (all_125_0 = use & all_125_1 = use)) % 23.76/4.06 | % 23.76/4.06 | ALPHA: (94) implies: % 23.76/4.06 | (95) a_select3(z_defuse, n0, tptp_minus_1) = all_125_0 % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (18) with 0, all_123_3, n2, n0, simplifying with % 23.76/4.06 | (77), (92) gives: % 23.76/4.06 | (96) all_123_3 = 0 % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (42) with n0, tptp_minus_1, all_125_0, simplifying % 23.76/4.06 | with (4), (14), (95) gives: % 23.76/4.06 | (97) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 23.76/4.06 | $i] : (a_select3(u_defuse, n0, tptp_minus_1) = v4 & % 23.76/4.06 | leq(tptp_minus_1, pv5) = v3 & leq(n0, n2) = v2 & leq(n0, % 23.76/4.06 | tptp_minus_1) = v1 & leq(n0, n0) = v0 & $i(v4) & ( ~ (v3 = 0) | ~ % 23.76/4.06 | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v4 = use & all_125_0 = % 23.76/4.06 | use))) % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (42) with tptp_minus_1, tptp_minus_1, all_119_0, % 23.76/4.06 | simplifying with (4), (88) gives: % 23.76/4.06 | (98) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 23.76/4.06 | $i] : (a_select3(u_defuse, tptp_minus_1, tptp_minus_1) = v4 & % 23.76/4.06 | leq(tptp_minus_1, pv5) = v3 & leq(tptp_minus_1, n2) = v2 & leq(n0, % 23.76/4.06 | tptp_minus_1) = v1 & leq(n0, tptp_minus_1) = v0 & $i(v4) & ( ~ (v3 % 23.76/4.06 | = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v4 = use & % 23.76/4.06 | all_119_0 = use))) % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (42) with n1, tptp_minus_1, all_121_0, simplifying % 23.76/4.06 | with (4), (57), (90) gives: % 23.76/4.06 | (99) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 23.76/4.06 | $i] : (a_select3(u_defuse, n1, tptp_minus_1) = v4 & leq(n1, n2) = v2 % 23.76/4.06 | & leq(tptp_minus_1, pv5) = v3 & leq(n0, n1) = v0 & leq(n0, % 23.76/4.06 | tptp_minus_1) = v1 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 % 23.76/4.06 | = 0) | ~ (v0 = 0) | (v4 = use & all_121_0 = use))) % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (42) with n2, tptp_minus_1, all_123_0, simplifying % 23.76/4.06 | with (4), (68), (93) gives: % 23.76/4.06 | (100) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 23.76/4.06 | $i] : (a_select3(u_defuse, n2, tptp_minus_1) = v4 & leq(n2, n2) = % 23.76/4.06 | v2 & leq(tptp_minus_1, pv5) = v3 & leq(n0, n2) = v0 & leq(n0, % 23.76/4.06 | tptp_minus_1) = v1 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 % 23.76/4.06 | = 0) | ~ (v0 = 0) | (v4 = use & all_123_0 = use))) % 23.76/4.06 | % 23.76/4.06 | DELTA: instantiating (100) with fresh symbols all_137_0, all_137_1, all_137_2, % 23.76/4.06 | all_137_3, all_137_4 gives: % 23.76/4.06 | (101) a_select3(u_defuse, n2, tptp_minus_1) = all_137_0 & leq(n2, n2) = % 23.76/4.06 | all_137_2 & leq(tptp_minus_1, pv5) = all_137_1 & leq(n0, n2) = % 23.76/4.06 | all_137_4 & leq(n0, tptp_minus_1) = all_137_3 & $i(all_137_0) & ( ~ % 23.76/4.06 | (all_137_1 = 0) | ~ (all_137_2 = 0) | ~ (all_137_3 = 0) | ~ % 23.76/4.06 | (all_137_4 = 0) | (all_137_0 = use & all_123_0 = use)) % 23.76/4.06 | % 23.76/4.06 | ALPHA: (101) implies: % 23.76/4.06 | (102) leq(n0, n2) = all_137_4 % 23.76/4.06 | (103) leq(n2, n2) = all_137_2 % 23.76/4.06 | % 23.76/4.06 | DELTA: instantiating (98) with fresh symbols all_139_0, all_139_1, all_139_2, % 23.76/4.06 | all_139_3, all_139_4 gives: % 23.76/4.06 | (104) a_select3(u_defuse, tptp_minus_1, tptp_minus_1) = all_139_0 & % 23.76/4.06 | leq(tptp_minus_1, pv5) = all_139_1 & leq(tptp_minus_1, n2) = % 23.76/4.06 | all_139_2 & leq(n0, tptp_minus_1) = all_139_3 & leq(n0, tptp_minus_1) % 23.76/4.06 | = all_139_4 & $i(all_139_0) & ( ~ (all_139_1 = 0) | ~ (all_139_2 = % 23.76/4.06 | 0) | ~ (all_139_3 = 0) | ~ (all_139_4 = 0) | (all_139_0 = use & % 23.76/4.06 | all_119_0 = use)) % 23.76/4.06 | % 23.76/4.06 | ALPHA: (104) implies: % 23.76/4.06 | (105) leq(tptp_minus_1, n2) = all_139_2 % 23.76/4.06 | % 23.76/4.06 | DELTA: instantiating (99) with fresh symbols all_141_0, all_141_1, all_141_2, % 23.76/4.06 | all_141_3, all_141_4 gives: % 23.76/4.06 | (106) a_select3(u_defuse, n1, tptp_minus_1) = all_141_0 & leq(n1, n2) = % 23.76/4.06 | all_141_2 & leq(tptp_minus_1, pv5) = all_141_1 & leq(n0, n1) = % 23.76/4.06 | all_141_4 & leq(n0, tptp_minus_1) = all_141_3 & $i(all_141_0) & ( ~ % 23.76/4.06 | (all_141_1 = 0) | ~ (all_141_2 = 0) | ~ (all_141_3 = 0) | ~ % 23.76/4.06 | (all_141_4 = 0) | (all_141_0 = use & all_121_0 = use)) % 23.76/4.06 | % 23.76/4.06 | ALPHA: (106) implies: % 23.76/4.06 | (107) leq(n1, n2) = all_141_2 % 23.76/4.06 | % 23.76/4.06 | DELTA: instantiating (97) with fresh symbols all_143_0, all_143_1, all_143_2, % 23.76/4.06 | all_143_3, all_143_4 gives: % 23.76/4.06 | (108) a_select3(u_defuse, n0, tptp_minus_1) = all_143_0 & leq(tptp_minus_1, % 23.76/4.06 | pv5) = all_143_1 & leq(n0, n2) = all_143_2 & leq(n0, tptp_minus_1) % 23.76/4.06 | = all_143_3 & leq(n0, n0) = all_143_4 & $i(all_143_0) & ( ~ % 23.76/4.06 | (all_143_1 = 0) | ~ (all_143_2 = 0) | ~ (all_143_3 = 0) | ~ % 23.76/4.06 | (all_143_4 = 0) | (all_143_0 = use & all_125_0 = use)) % 23.76/4.06 | % 23.76/4.06 | ALPHA: (108) implies: % 23.76/4.06 | (109) leq(n0, n2) = all_143_2 % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (18) with 0, all_143_2, n2, n0, simplifying with % 23.76/4.06 | (77), (109) gives: % 23.76/4.06 | (110) all_143_2 = 0 % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (18) with all_137_4, all_143_2, n2, n0, simplifying % 23.76/4.06 | with (102), (109) gives: % 23.76/4.06 | (111) all_143_2 = all_137_4 % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (18) with 0, all_139_2, n2, tptp_minus_1, % 23.76/4.06 | simplifying with (76), (105) gives: % 23.76/4.06 | (112) all_139_2 = 0 % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (18) with 0, all_141_2, n2, n1, simplifying with % 23.76/4.06 | (75), (107) gives: % 23.76/4.06 | (113) all_141_2 = 0 % 23.76/4.06 | % 23.76/4.06 | GROUND_INST: instantiating (18) with 0, all_137_2, n2, n2, simplifying with % 23.76/4.06 | (74), (103) gives: % 23.76/4.06 | (114) all_137_2 = 0 % 23.76/4.06 | % 23.76/4.06 | COMBINE_EQS: (110), (111) imply: % 23.76/4.06 | (115) all_137_4 = 0 % 23.76/4.06 | % 23.76/4.06 | BETA: splitting (40) gives: % 23.76/4.06 | % 23.76/4.06 | Case 1: % 23.76/4.06 | | % 23.76/4.07 | | (116) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 23.76/4.07 | | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = % 23.76/4.07 | | v2 & leq(v1, all_76_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & % 23.76/4.07 | | leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = % 23.76/4.07 | | use) | ~ (v2 = use))) % 23.76/4.07 | | % 23.76/4.07 | | DELTA: instantiating (116) with fresh symbols all_162_0, all_162_1, % 23.76/4.07 | | all_162_2, all_162_3 gives: % 23.76/4.07 | | (117) a_select3(z_defuse, all_162_3, all_162_2) = all_162_0 & % 23.76/4.07 | | a_select3(u_defuse, all_162_3, all_162_2) = all_162_1 & % 23.76/4.07 | | leq(all_162_2, all_76_0) = 0 & leq(all_162_3, n2) = 0 & leq(n0, % 23.76/4.07 | | all_162_2) = 0 & leq(n0, all_162_3) = 0 & $i(all_162_0) & % 23.76/4.07 | | $i(all_162_1) & $i(all_162_2) & $i(all_162_3) & ( ~ (all_162_0 = % 23.76/4.07 | | use) | ~ (all_162_1 = use)) % 23.76/4.07 | | % 23.76/4.07 | | ALPHA: (117) implies: % 23.76/4.07 | | (118) $i(all_162_3) % 23.76/4.07 | | (119) $i(all_162_2) % 23.76/4.07 | | (120) leq(n0, all_162_3) = 0 % 23.76/4.07 | | (121) leq(n0, all_162_2) = 0 % 23.76/4.07 | | (122) leq(all_162_3, n2) = 0 % 23.76/4.07 | | (123) leq(all_162_2, all_76_0) = 0 % 23.76/4.07 | | (124) a_select3(u_defuse, all_162_3, all_162_2) = all_162_1 % 23.76/4.07 | | (125) a_select3(z_defuse, all_162_3, all_162_2) = all_162_0 % 23.76/4.07 | | (126) ~ (all_162_0 = use) | ~ (all_162_1 = use) % 23.76/4.07 | | % 23.76/4.07 | | GROUND_INST: instantiating (41) with all_162_3, tptp_minus_1, simplifying % 23.76/4.07 | | with (4), (82), (118), (122) gives: % 23.76/4.07 | | (127) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.76/4.07 | | (a_select3(z_defuse, all_162_3, tptp_minus_1) = v3 & % 23.76/4.07 | | a_select3(u_defuse, all_162_3, tptp_minus_1) = v2 & leq(n0, % 23.76/4.07 | | all_162_3) = v0 & leq(n0, tptp_minus_1) = v1 & $i(v3) & $i(v2) % 23.76/4.07 | | & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use))) % 23.76/4.07 | | % 23.76/4.07 | | GROUND_INST: instantiating (41) with n2, all_162_2, simplifying with (68), % 23.76/4.07 | | (74), (119), (123) gives: % 23.76/4.07 | | (128) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.76/4.07 | | (a_select3(z_defuse, n2, all_162_2) = v3 & a_select3(u_defuse, n2, % 23.76/4.07 | | all_162_2) = v2 & leq(n0, all_162_2) = v1 & leq(n0, n2) = v0 & % 23.76/4.07 | | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = % 23.76/4.07 | | use))) % 23.76/4.07 | | % 23.76/4.07 | | GROUND_INST: instantiating (41) with n1, all_162_2, simplifying with (57), % 23.76/4.07 | | (75), (119), (123) gives: % 23.76/4.07 | | (129) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.76/4.07 | | (a_select3(z_defuse, n1, all_162_2) = v3 & a_select3(u_defuse, n1, % 23.76/4.07 | | all_162_2) = v2 & leq(n0, all_162_2) = v1 & leq(n0, n1) = v0 & % 23.76/4.07 | | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = % 23.76/4.07 | | use))) % 23.76/4.07 | | % 23.76/4.07 | | GROUND_INST: instantiating (41) with tptp_minus_1, all_162_2, simplifying % 23.76/4.07 | | with (4), (76), (119), (123) gives: % 23.76/4.07 | | (130) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.76/4.07 | | (a_select3(z_defuse, tptp_minus_1, all_162_2) = v3 & % 23.76/4.07 | | a_select3(u_defuse, tptp_minus_1, all_162_2) = v2 & leq(n0, % 23.76/4.07 | | all_162_2) = v1 & leq(n0, tptp_minus_1) = v0 & $i(v3) & $i(v2) % 23.76/4.07 | | & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use))) % 23.76/4.07 | | % 23.76/4.07 | | GROUND_INST: instantiating (41) with n0, all_162_2, simplifying with (14), % 23.76/4.07 | | (77), (119), (123) gives: % 23.76/4.07 | | (131) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.76/4.07 | | (a_select3(z_defuse, n0, all_162_2) = v3 & a_select3(u_defuse, n0, % 23.76/4.07 | | all_162_2) = v2 & leq(n0, all_162_2) = v1 & leq(n0, n0) = v0 & % 23.76/4.07 | | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = % 23.76/4.07 | | use))) % 23.76/4.07 | | % 23.76/4.07 | | GROUND_INST: instantiating (41) with all_162_3, all_162_2, simplifying with % 23.76/4.07 | | (118), (119), (122), (123) gives: % 23.76/4.07 | | (132) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.76/4.07 | | (a_select3(z_defuse, all_162_3, all_162_2) = v3 & % 23.76/4.07 | | a_select3(u_defuse, all_162_3, all_162_2) = v2 & leq(n0, % 23.76/4.07 | | all_162_2) = v1 & leq(n0, all_162_3) = v0 & $i(v3) & $i(v2) & ( % 23.76/4.07 | | ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use))) % 23.76/4.07 | | % 23.76/4.07 | | GROUND_INST: instantiating (42) with all_162_3, all_162_2, all_162_0, % 23.76/4.07 | | simplifying with (118), (119), (125) gives: % 23.76/4.07 | | (133) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 23.76/4.07 | | $i] : (a_select3(u_defuse, all_162_3, all_162_2) = v4 & % 23.76/4.07 | | leq(all_162_2, pv5) = v3 & leq(all_162_3, n2) = v2 & leq(n0, % 23.76/4.07 | | all_162_2) = v1 & leq(n0, all_162_3) = v0 & $i(v4) & ( ~ (v3 = % 23.76/4.07 | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v4 = use & % 23.76/4.07 | | all_162_0 = use))) % 23.76/4.07 | | % 23.76/4.07 | | DELTA: instantiating (132) with fresh symbols all_170_0, all_170_1, % 23.76/4.07 | | all_170_2, all_170_3 gives: % 23.76/4.07 | | (134) a_select3(z_defuse, all_162_3, all_162_2) = all_170_0 & % 23.76/4.07 | | a_select3(u_defuse, all_162_3, all_162_2) = all_170_1 & leq(n0, % 23.76/4.07 | | all_162_2) = all_170_2 & leq(n0, all_162_3) = all_170_3 & % 23.76/4.07 | | $i(all_170_0) & $i(all_170_1) & ( ~ (all_170_2 = 0) | ~ (all_170_3 % 23.76/4.07 | | = 0) | (all_170_0 = use & all_170_1 = use)) % 23.76/4.07 | | % 23.76/4.07 | | ALPHA: (134) implies: % 23.76/4.07 | | (135) leq(n0, all_162_3) = all_170_3 % 23.76/4.07 | | (136) leq(n0, all_162_2) = all_170_2 % 23.76/4.07 | | (137) a_select3(u_defuse, all_162_3, all_162_2) = all_170_1 % 23.76/4.07 | | (138) a_select3(z_defuse, all_162_3, all_162_2) = all_170_0 % 23.76/4.07 | | (139) ~ (all_170_2 = 0) | ~ (all_170_3 = 0) | (all_170_0 = use & % 23.76/4.07 | | all_170_1 = use) % 23.76/4.07 | | % 23.76/4.07 | | DELTA: instantiating (131) with fresh symbols all_172_0, all_172_1, % 23.76/4.07 | | all_172_2, all_172_3 gives: % 23.76/4.07 | | (140) a_select3(z_defuse, n0, all_162_2) = all_172_0 & % 23.76/4.07 | | a_select3(u_defuse, n0, all_162_2) = all_172_1 & leq(n0, all_162_2) % 23.76/4.07 | | = all_172_2 & leq(n0, n0) = all_172_3 & $i(all_172_0) & % 23.76/4.07 | | $i(all_172_1) & ( ~ (all_172_2 = 0) | ~ (all_172_3 = 0) | % 23.76/4.07 | | (all_172_0 = use & all_172_1 = use)) % 23.76/4.07 | | % 23.76/4.07 | | ALPHA: (140) implies: % 23.76/4.07 | | (141) leq(n0, all_162_2) = all_172_2 % 23.76/4.07 | | % 23.76/4.07 | | DELTA: instantiating (130) with fresh symbols all_174_0, all_174_1, % 23.76/4.07 | | all_174_2, all_174_3 gives: % 23.76/4.07 | | (142) a_select3(z_defuse, tptp_minus_1, all_162_2) = all_174_0 & % 23.76/4.07 | | a_select3(u_defuse, tptp_minus_1, all_162_2) = all_174_1 & leq(n0, % 23.76/4.07 | | all_162_2) = all_174_2 & leq(n0, tptp_minus_1) = all_174_3 & % 23.76/4.07 | | $i(all_174_0) & $i(all_174_1) & ( ~ (all_174_2 = 0) | ~ (all_174_3 % 23.76/4.07 | | = 0) | (all_174_0 = use & all_174_1 = use)) % 23.76/4.07 | | % 23.76/4.07 | | ALPHA: (142) implies: % 23.76/4.07 | | (143) leq(n0, all_162_2) = all_174_2 % 23.76/4.07 | | % 23.76/4.07 | | DELTA: instantiating (129) with fresh symbols all_176_0, all_176_1, % 23.76/4.07 | | all_176_2, all_176_3 gives: % 23.76/4.07 | | (144) a_select3(z_defuse, n1, all_162_2) = all_176_0 & % 23.76/4.07 | | a_select3(u_defuse, n1, all_162_2) = all_176_1 & leq(n0, all_162_2) % 23.76/4.07 | | = all_176_2 & leq(n0, n1) = all_176_3 & $i(all_176_0) & % 23.76/4.07 | | $i(all_176_1) & ( ~ (all_176_2 = 0) | ~ (all_176_3 = 0) | % 23.76/4.07 | | (all_176_0 = use & all_176_1 = use)) % 23.76/4.07 | | % 23.76/4.07 | | ALPHA: (144) implies: % 23.76/4.07 | | (145) leq(n0, all_162_2) = all_176_2 % 23.76/4.07 | | % 23.76/4.07 | | DELTA: instantiating (127) with fresh symbols all_178_0, all_178_1, % 23.76/4.07 | | all_178_2, all_178_3 gives: % 23.76/4.08 | | (146) a_select3(z_defuse, all_162_3, tptp_minus_1) = all_178_0 & % 23.76/4.08 | | a_select3(u_defuse, all_162_3, tptp_minus_1) = all_178_1 & leq(n0, % 23.76/4.08 | | all_162_3) = all_178_3 & leq(n0, tptp_minus_1) = all_178_2 & % 23.76/4.08 | | $i(all_178_0) & $i(all_178_1) & ( ~ (all_178_2 = 0) | ~ (all_178_3 % 23.76/4.08 | | = 0) | (all_178_0 = use & all_178_1 = use)) % 23.76/4.08 | | % 23.76/4.08 | | ALPHA: (146) implies: % 23.76/4.08 | | (147) leq(n0, all_162_3) = all_178_3 % 23.76/4.08 | | % 23.76/4.08 | | DELTA: instantiating (128) with fresh symbols all_180_0, all_180_1, % 23.76/4.08 | | all_180_2, all_180_3 gives: % 23.76/4.08 | | (148) a_select3(z_defuse, n2, all_162_2) = all_180_0 & % 23.76/4.08 | | a_select3(u_defuse, n2, all_162_2) = all_180_1 & leq(n0, all_162_2) % 23.76/4.08 | | = all_180_2 & leq(n0, n2) = all_180_3 & $i(all_180_0) & % 23.76/4.08 | | $i(all_180_1) & ( ~ (all_180_2 = 0) | ~ (all_180_3 = 0) | % 23.76/4.08 | | (all_180_0 = use & all_180_1 = use)) % 23.76/4.08 | | % 23.76/4.08 | | ALPHA: (148) implies: % 23.76/4.08 | | (149) leq(n0, all_162_2) = all_180_2 % 23.76/4.08 | | % 23.76/4.08 | | DELTA: instantiating (133) with fresh symbols all_182_0, all_182_1, % 23.76/4.08 | | all_182_2, all_182_3, all_182_4 gives: % 23.76/4.08 | | (150) a_select3(u_defuse, all_162_3, all_162_2) = all_182_0 & % 23.76/4.08 | | leq(all_162_2, pv5) = all_182_1 & leq(all_162_3, n2) = all_182_2 & % 23.76/4.08 | | leq(n0, all_162_2) = all_182_3 & leq(n0, all_162_3) = all_182_4 & % 23.76/4.08 | | $i(all_182_0) & ( ~ (all_182_1 = 0) | ~ (all_182_2 = 0) | ~ % 23.76/4.08 | | (all_182_3 = 0) | ~ (all_182_4 = 0) | (all_182_0 = use & % 23.76/4.08 | | all_162_0 = use)) % 23.76/4.08 | | % 23.76/4.08 | | ALPHA: (150) implies: % 23.76/4.08 | | (151) leq(n0, all_162_3) = all_182_4 % 23.76/4.08 | | (152) leq(n0, all_162_2) = all_182_3 % 23.76/4.08 | | (153) a_select3(u_defuse, all_162_3, all_162_2) = all_182_0 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (18) with 0, all_178_3, all_162_3, n0, % 23.76/4.08 | | simplifying with (120), (147) gives: % 23.76/4.08 | | (154) all_178_3 = 0 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (18) with all_178_3, all_182_4, all_162_3, n0, % 23.76/4.08 | | simplifying with (147), (151) gives: % 23.76/4.08 | | (155) all_182_4 = all_178_3 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (18) with all_170_3, all_182_4, all_162_3, n0, % 23.76/4.08 | | simplifying with (135), (151) gives: % 23.76/4.08 | | (156) all_182_4 = all_170_3 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (18) with all_172_2, all_174_2, all_162_2, n0, % 23.76/4.08 | | simplifying with (141), (143) gives: % 23.76/4.08 | | (157) all_174_2 = all_172_2 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (18) with all_172_2, all_180_2, all_162_2, n0, % 23.76/4.08 | | simplifying with (141), (149) gives: % 23.76/4.08 | | (158) all_180_2 = all_172_2 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (18) with all_170_2, all_180_2, all_162_2, n0, % 23.76/4.08 | | simplifying with (136), (149) gives: % 23.76/4.08 | | (159) all_180_2 = all_170_2 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (18) with 0, all_182_3, all_162_2, n0, % 23.76/4.08 | | simplifying with (121), (152) gives: % 23.76/4.08 | | (160) all_182_3 = 0 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (18) with all_176_2, all_182_3, all_162_2, n0, % 23.76/4.08 | | simplifying with (145), (152) gives: % 23.76/4.08 | | (161) all_182_3 = all_176_2 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (18) with all_174_2, all_182_3, all_162_2, n0, % 23.76/4.08 | | simplifying with (143), (152) gives: % 23.76/4.08 | | (162) all_182_3 = all_174_2 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (19) with all_162_1, all_182_0, all_162_2, % 23.76/4.08 | | all_162_3, u_defuse, simplifying with (124), (153) gives: % 23.76/4.08 | | (163) all_182_0 = all_162_1 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (19) with all_170_1, all_182_0, all_162_2, % 23.76/4.08 | | all_162_3, u_defuse, simplifying with (137), (153) gives: % 23.76/4.08 | | (164) all_182_0 = all_170_1 % 23.76/4.08 | | % 23.76/4.08 | | GROUND_INST: instantiating (19) with all_162_0, all_170_0, all_162_2, % 23.76/4.08 | | all_162_3, z_defuse, simplifying with (125), (138) gives: % 23.76/4.08 | | (165) all_170_0 = all_162_0 % 23.76/4.08 | | % 23.76/4.08 | | COMBINE_EQS: (163), (164) imply: % 23.76/4.08 | | (166) all_170_1 = all_162_1 % 23.76/4.08 | | % 23.76/4.08 | | COMBINE_EQS: (160), (161) imply: % 23.76/4.08 | | (167) all_176_2 = 0 % 23.76/4.08 | | % 23.76/4.08 | | COMBINE_EQS: (161), (162) imply: % 23.76/4.08 | | (168) all_176_2 = all_174_2 % 23.76/4.08 | | % 23.76/4.08 | | COMBINE_EQS: (155), (156) imply: % 23.76/4.08 | | (169) all_178_3 = all_170_3 % 23.76/4.08 | | % 23.76/4.08 | | SIMP: (169) implies: % 23.76/4.08 | | (170) all_178_3 = all_170_3 % 23.76/4.08 | | % 23.76/4.08 | | COMBINE_EQS: (158), (159) imply: % 23.76/4.08 | | (171) all_172_2 = all_170_2 % 23.76/4.08 | | % 23.76/4.08 | | SIMP: (171) implies: % 23.76/4.08 | | (172) all_172_2 = all_170_2 % 23.76/4.08 | | % 23.76/4.08 | | COMBINE_EQS: (154), (170) imply: % 23.76/4.08 | | (173) all_170_3 = 0 % 23.76/4.08 | | % 23.76/4.08 | | COMBINE_EQS: (167), (168) imply: % 23.76/4.08 | | (174) all_174_2 = 0 % 23.76/4.08 | | % 23.76/4.08 | | SIMP: (174) implies: % 23.76/4.08 | | (175) all_174_2 = 0 % 23.76/4.08 | | % 23.76/4.08 | | COMBINE_EQS: (157), (175) imply: % 23.76/4.08 | | (176) all_172_2 = 0 % 23.76/4.08 | | % 23.76/4.08 | | SIMP: (176) implies: % 23.76/4.08 | | (177) all_172_2 = 0 % 23.76/4.08 | | % 23.76/4.08 | | COMBINE_EQS: (172), (177) imply: % 23.76/4.08 | | (178) all_170_2 = 0 % 23.76/4.08 | | % 23.76/4.08 | | BETA: splitting (139) gives: % 23.76/4.08 | | % 23.76/4.08 | | Case 1: % 23.76/4.08 | | | % 23.76/4.08 | | | (179) ~ (all_170_2 = 0) % 23.76/4.08 | | | % 23.76/4.08 | | | REDUCE: (178), (179) imply: % 23.76/4.08 | | | (180) $false % 23.76/4.08 | | | % 23.76/4.08 | | | CLOSE: (180) is inconsistent. % 23.76/4.08 | | | % 23.76/4.08 | | Case 2: % 23.76/4.08 | | | % 23.76/4.08 | | | (181) ~ (all_170_3 = 0) | (all_170_0 = use & all_170_1 = use) % 23.76/4.08 | | | % 23.76/4.08 | | | BETA: splitting (181) gives: % 23.76/4.08 | | | % 23.76/4.08 | | | Case 1: % 23.76/4.08 | | | | % 23.76/4.08 | | | | (182) ~ (all_170_3 = 0) % 23.76/4.08 | | | | % 23.76/4.08 | | | | REDUCE: (173), (182) imply: % 23.76/4.08 | | | | (183) $false % 23.76/4.08 | | | | % 23.76/4.08 | | | | CLOSE: (183) is inconsistent. % 23.76/4.08 | | | | % 23.76/4.08 | | | Case 2: % 23.76/4.08 | | | | % 23.76/4.08 | | | | (184) all_170_0 = use & all_170_1 = use % 23.76/4.08 | | | | % 23.76/4.08 | | | | ALPHA: (184) implies: % 23.76/4.08 | | | | (185) all_170_1 = use % 23.76/4.08 | | | | (186) all_170_0 = use % 23.76/4.08 | | | | % 23.76/4.08 | | | | COMBINE_EQS: (165), (186) imply: % 23.76/4.08 | | | | (187) all_162_0 = use % 23.76/4.08 | | | | % 23.76/4.08 | | | | COMBINE_EQS: (166), (185) imply: % 23.76/4.08 | | | | (188) all_162_1 = use % 23.76/4.08 | | | | % 23.76/4.08 | | | | BETA: splitting (126) gives: % 23.76/4.08 | | | | % 23.76/4.08 | | | | Case 1: % 23.76/4.08 | | | | | % 23.76/4.08 | | | | | (189) ~ (all_162_0 = use) % 23.76/4.08 | | | | | % 23.76/4.08 | | | | | REDUCE: (187), (189) imply: % 23.76/4.08 | | | | | (190) $false % 23.76/4.08 | | | | | % 23.76/4.08 | | | | | CLOSE: (190) is inconsistent. % 23.76/4.08 | | | | | % 23.76/4.08 | | | | Case 2: % 23.76/4.08 | | | | | % 23.76/4.08 | | | | | (191) ~ (all_162_1 = use) % 23.76/4.08 | | | | | % 23.76/4.08 | | | | | REDUCE: (188), (191) imply: % 23.76/4.08 | | | | | (192) $false % 23.76/4.08 | | | | | % 23.76/4.08 | | | | | CLOSE: (192) is inconsistent. % 23.76/4.08 | | | | | % 23.76/4.08 | | | | End of split % 23.76/4.08 | | | | % 23.76/4.08 | | | End of split % 23.76/4.08 | | | % 23.76/4.08 | | End of split % 23.76/4.08 | | % 23.76/4.09 | Case 2: % 23.76/4.09 | | % 23.76/4.09 | | (193) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 23.76/4.09 | | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = % 23.76/4.09 | | v2 & leq(v1, pv5) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & % 23.76/4.09 | | leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = % 23.76/4.09 | | use) | ~ (v2 = use))) % 23.76/4.09 | | % 23.76/4.09 | | DELTA: instantiating (193) with fresh symbols all_162_0, all_162_1, % 23.76/4.09 | | all_162_2, all_162_3 gives: % 23.76/4.09 | | (194) a_select3(z_defuse, all_162_3, all_162_2) = all_162_0 & % 23.76/4.09 | | a_select3(u_defuse, all_162_3, all_162_2) = all_162_1 & % 23.76/4.09 | | leq(all_162_2, pv5) = 0 & leq(all_162_3, n2) = 0 & leq(n0, % 23.76/4.09 | | all_162_2) = 0 & leq(n0, all_162_3) = 0 & $i(all_162_0) & % 23.76/4.09 | | $i(all_162_1) & $i(all_162_2) & $i(all_162_3) & ( ~ (all_162_0 = % 23.76/4.09 | | use) | ~ (all_162_1 = use)) % 23.76/4.09 | | % 23.76/4.09 | | ALPHA: (194) implies: % 23.76/4.09 | | (195) $i(all_162_3) % 23.76/4.09 | | (196) $i(all_162_2) % 23.76/4.09 | | (197) leq(n0, all_162_3) = 0 % 23.76/4.09 | | (198) leq(n0, all_162_2) = 0 % 23.76/4.09 | | (199) leq(all_162_3, n2) = 0 % 23.76/4.09 | | (200) leq(all_162_2, pv5) = 0 % 23.76/4.09 | | (201) a_select3(u_defuse, all_162_3, all_162_2) = all_162_1 % 23.76/4.09 | | (202) a_select3(z_defuse, all_162_3, all_162_2) = all_162_0 % 23.76/4.09 | | (203) ~ (all_162_0 = use) | ~ (all_162_1 = use) % 23.76/4.09 | | % 23.76/4.09 | | GROUND_INST: instantiating (41) with all_162_3, tptp_minus_1, simplifying % 23.76/4.09 | | with (4), (82), (195), (199) gives: % 23.76/4.09 | | (204) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.76/4.09 | | (a_select3(z_defuse, all_162_3, tptp_minus_1) = v3 & % 23.76/4.09 | | a_select3(u_defuse, all_162_3, tptp_minus_1) = v2 & leq(n0, % 23.76/4.09 | | all_162_3) = v0 & leq(n0, tptp_minus_1) = v1 & $i(v3) & $i(v2) % 23.76/4.09 | | & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = use & v2 = use))) % 23.76/4.09 | | % 23.76/4.09 | | GROUND_INST: instantiating (42) with all_162_3, all_162_2, all_162_0, % 23.76/4.09 | | simplifying with (195), (196), (202) gives: % 23.76/4.09 | | (205) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 23.76/4.09 | | $i] : (a_select3(u_defuse, all_162_3, all_162_2) = v4 & % 23.76/4.09 | | leq(all_162_2, pv5) = v3 & leq(all_162_3, n2) = v2 & leq(n0, % 23.76/4.09 | | all_162_2) = v1 & leq(n0, all_162_3) = v0 & $i(v4) & ( ~ (v3 = % 23.76/4.09 | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v4 = use & % 23.76/4.09 | | all_162_0 = use))) % 23.76/4.09 | | % 23.76/4.09 | | DELTA: instantiating (204) with fresh symbols all_170_0, all_170_1, % 23.76/4.09 | | all_170_2, all_170_3 gives: % 23.76/4.09 | | (206) a_select3(z_defuse, all_162_3, tptp_minus_1) = all_170_0 & % 23.76/4.09 | | a_select3(u_defuse, all_162_3, tptp_minus_1) = all_170_1 & leq(n0, % 23.76/4.09 | | all_162_3) = all_170_3 & leq(n0, tptp_minus_1) = all_170_2 & % 23.76/4.09 | | $i(all_170_0) & $i(all_170_1) & ( ~ (all_170_2 = 0) | ~ (all_170_3 % 23.76/4.09 | | = 0) | (all_170_0 = use & all_170_1 = use)) % 23.76/4.09 | | % 23.76/4.09 | | ALPHA: (206) implies: % 23.76/4.09 | | (207) leq(n0, all_162_3) = all_170_3 % 23.76/4.09 | | % 23.76/4.09 | | DELTA: instantiating (205) with fresh symbols all_172_0, all_172_1, % 23.76/4.09 | | all_172_2, all_172_3, all_172_4 gives: % 23.76/4.09 | | (208) a_select3(u_defuse, all_162_3, all_162_2) = all_172_0 & % 23.76/4.09 | | leq(all_162_2, pv5) = all_172_1 & leq(all_162_3, n2) = all_172_2 & % 23.76/4.09 | | leq(n0, all_162_2) = all_172_3 & leq(n0, all_162_3) = all_172_4 & % 23.76/4.09 | | $i(all_172_0) & ( ~ (all_172_1 = 0) | ~ (all_172_2 = 0) | ~ % 23.76/4.09 | | (all_172_3 = 0) | ~ (all_172_4 = 0) | (all_172_0 = use & % 23.76/4.09 | | all_162_0 = use)) % 23.76/4.09 | | % 23.76/4.09 | | ALPHA: (208) implies: % 23.76/4.09 | | (209) leq(n0, all_162_3) = all_172_4 % 23.76/4.09 | | (210) leq(n0, all_162_2) = all_172_3 % 23.76/4.09 | | (211) leq(all_162_3, n2) = all_172_2 % 23.76/4.09 | | (212) leq(all_162_2, pv5) = all_172_1 % 23.76/4.09 | | (213) a_select3(u_defuse, all_162_3, all_162_2) = all_172_0 % 23.76/4.09 | | (214) ~ (all_172_1 = 0) | ~ (all_172_2 = 0) | ~ (all_172_3 = 0) | ~ % 23.76/4.09 | | (all_172_4 = 0) | (all_172_0 = use & all_162_0 = use) % 23.76/4.09 | | % 23.76/4.09 | | GROUND_INST: instantiating (18) with 0, all_172_4, all_162_3, n0, % 23.76/4.09 | | simplifying with (197), (209) gives: % 23.76/4.09 | | (215) all_172_4 = 0 % 23.76/4.09 | | % 23.76/4.09 | | GROUND_INST: instantiating (18) with all_170_3, all_172_4, all_162_3, n0, % 23.76/4.09 | | simplifying with (207), (209) gives: % 23.76/4.09 | | (216) all_172_4 = all_170_3 % 23.76/4.09 | | % 23.76/4.09 | | GROUND_INST: instantiating (18) with 0, all_172_3, all_162_2, n0, % 23.76/4.09 | | simplifying with (198), (210) gives: % 23.76/4.09 | | (217) all_172_3 = 0 % 23.76/4.09 | | % 23.76/4.09 | | GROUND_INST: instantiating (18) with 0, all_172_2, n2, all_162_3, % 23.76/4.09 | | simplifying with (199), (211) gives: % 23.76/4.09 | | (218) all_172_2 = 0 % 23.76/4.09 | | % 23.76/4.09 | | GROUND_INST: instantiating (18) with 0, all_172_1, pv5, all_162_2, % 23.76/4.09 | | simplifying with (200), (212) gives: % 23.76/4.09 | | (219) all_172_1 = 0 % 23.76/4.09 | | % 23.76/4.09 | | GROUND_INST: instantiating (19) with all_162_1, all_172_0, all_162_2, % 23.76/4.09 | | all_162_3, u_defuse, simplifying with (201), (213) gives: % 23.76/4.09 | | (220) all_172_0 = all_162_1 % 23.76/4.09 | | % 23.76/4.09 | | COMBINE_EQS: (215), (216) imply: % 23.76/4.09 | | (221) all_170_3 = 0 % 23.76/4.09 | | % 23.76/4.09 | | BETA: splitting (214) gives: % 23.76/4.09 | | % 23.76/4.09 | | Case 1: % 23.76/4.09 | | | % 23.76/4.09 | | | (222) ~ (all_172_1 = 0) % 23.76/4.09 | | | % 23.76/4.09 | | | REDUCE: (219), (222) imply: % 23.76/4.09 | | | (223) $false % 23.76/4.09 | | | % 23.76/4.09 | | | CLOSE: (223) is inconsistent. % 23.76/4.09 | | | % 23.76/4.09 | | Case 2: % 23.76/4.09 | | | % 23.76/4.09 | | | (224) ~ (all_172_2 = 0) | ~ (all_172_3 = 0) | ~ (all_172_4 = 0) | % 23.76/4.09 | | | (all_172_0 = use & all_162_0 = use) % 23.76/4.09 | | | % 23.76/4.09 | | | BETA: splitting (224) gives: % 23.76/4.09 | | | % 23.76/4.09 | | | Case 1: % 23.76/4.09 | | | | % 23.76/4.09 | | | | (225) ~ (all_172_2 = 0) % 23.76/4.09 | | | | % 23.76/4.09 | | | | REDUCE: (218), (225) imply: % 23.76/4.09 | | | | (226) $false % 23.76/4.09 | | | | % 23.76/4.09 | | | | CLOSE: (226) is inconsistent. % 23.76/4.09 | | | | % 23.76/4.09 | | | Case 2: % 23.76/4.09 | | | | % 23.76/4.09 | | | | (227) ~ (all_172_3 = 0) | ~ (all_172_4 = 0) | (all_172_0 = use & % 23.76/4.09 | | | | all_162_0 = use) % 23.76/4.09 | | | | % 23.76/4.09 | | | | BETA: splitting (227) gives: % 23.76/4.09 | | | | % 23.76/4.09 | | | | Case 1: % 23.76/4.09 | | | | | % 23.76/4.09 | | | | | (228) ~ (all_172_3 = 0) % 23.76/4.09 | | | | | % 23.76/4.09 | | | | | REDUCE: (217), (228) imply: % 23.76/4.09 | | | | | (229) $false % 23.76/4.09 | | | | | % 23.76/4.09 | | | | | CLOSE: (229) is inconsistent. % 23.76/4.09 | | | | | % 23.76/4.09 | | | | Case 2: % 23.76/4.09 | | | | | % 23.76/4.09 | | | | | (230) ~ (all_172_4 = 0) | (all_172_0 = use & all_162_0 = use) % 23.76/4.09 | | | | | % 23.76/4.09 | | | | | BETA: splitting (230) gives: % 23.76/4.09 | | | | | % 23.76/4.09 | | | | | Case 1: % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | | (231) ~ (all_172_4 = 0) % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | | REDUCE: (215), (231) imply: % 23.76/4.09 | | | | | | (232) $false % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | | CLOSE: (232) is inconsistent. % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | Case 2: % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | | (233) all_172_0 = use & all_162_0 = use % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | | ALPHA: (233) implies: % 23.76/4.09 | | | | | | (234) all_162_0 = use % 23.76/4.09 | | | | | | (235) all_172_0 = use % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | | COMBINE_EQS: (220), (235) imply: % 23.76/4.09 | | | | | | (236) all_162_1 = use % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | | BETA: splitting (203) gives: % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | | Case 1: % 23.76/4.09 | | | | | | | % 23.76/4.09 | | | | | | | (237) ~ (all_162_0 = use) % 23.76/4.09 | | | | | | | % 23.76/4.09 | | | | | | | REDUCE: (234), (237) imply: % 23.76/4.09 | | | | | | | (238) $false % 23.76/4.09 | | | | | | | % 23.76/4.09 | | | | | | | CLOSE: (238) is inconsistent. % 23.76/4.09 | | | | | | | % 23.76/4.09 | | | | | | Case 2: % 23.76/4.09 | | | | | | | % 23.76/4.09 | | | | | | | (239) ~ (all_162_1 = use) % 23.76/4.09 | | | | | | | % 23.76/4.09 | | | | | | | REDUCE: (236), (239) imply: % 23.76/4.09 | | | | | | | (240) $false % 23.76/4.09 | | | | | | | % 23.76/4.09 | | | | | | | CLOSE: (240) is inconsistent. % 23.76/4.09 | | | | | | | % 23.76/4.09 | | | | | | End of split % 23.76/4.09 | | | | | | % 23.76/4.09 | | | | | End of split % 23.76/4.09 | | | | | % 23.76/4.09 | | | | End of split % 23.76/4.09 | | | | % 23.76/4.09 | | | End of split % 23.76/4.09 | | | % 23.76/4.09 | | End of split % 23.76/4.09 | | % 23.76/4.10 | End of split % 23.76/4.10 | % 23.76/4.10 End of proof % 23.76/4.10 % SZS output end Proof for theBenchmark % 23.76/4.10 % 23.76/4.10 3478ms %------------------------------------------------------------------------------