%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV208+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 : n028.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 22:55:21 EDT 2023 % Result : Theorem 16.97s 3.03s % Output : Proof 26.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV208+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n028.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 08:16:10 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.21/1.32 Prover 4: Preprocessing ... % 4.21/1.32 Prover 1: Preprocessing ... % 4.58/1.36 Prover 6: Preprocessing ... % 4.58/1.36 Prover 0: Preprocessing ... % 4.58/1.36 Prover 5: Preprocessing ... % 4.58/1.36 Prover 3: Preprocessing ... % 4.58/1.38 Prover 2: Preprocessing ... % 10.33/2.16 Prover 1: Warning: ignoring some quantifiers % 10.88/2.24 Prover 1: Constructing countermodel ... % 11.71/2.31 Prover 4: Warning: ignoring some quantifiers % 11.99/2.34 Prover 3: Warning: ignoring some quantifiers % 11.99/2.35 Prover 6: Proving ... % 11.99/2.39 Prover 3: Constructing countermodel ... % 11.99/2.41 Prover 4: Constructing countermodel ... % 13.12/2.55 Prover 0: Proving ... % 13.12/2.56 Prover 5: Proving ... % 13.74/2.62 Prover 2: Proving ... % 16.97/3.03 Prover 6: proved (2392ms) % 16.97/3.03 % 16.97/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.97/3.03 % 17.35/3.03 Prover 5: stopped % 17.35/3.03 Prover 0: stopped % 17.35/3.04 Prover 2: stopped % 17.35/3.05 Prover 3: stopped % 17.35/3.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.35/3.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.35/3.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.35/3.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.35/3.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.28/3.21 Prover 8: Preprocessing ... % 18.70/3.23 Prover 13: Preprocessing ... % 18.70/3.24 Prover 10: Preprocessing ... % 18.98/3.26 Prover 11: Preprocessing ... % 18.98/3.26 Prover 7: Preprocessing ... % 21.07/3.54 Prover 10: Warning: ignoring some quantifiers % 21.34/3.56 Prover 8: Warning: ignoring some quantifiers % 21.34/3.57 Prover 10: Constructing countermodel ... % 21.34/3.59 Prover 8: Constructing countermodel ... % 21.34/3.62 Prover 7: Warning: ignoring some quantifiers % 21.97/3.64 Prover 7: Constructing countermodel ... % 21.97/3.71 Prover 13: Warning: ignoring some quantifiers % 22.68/3.74 Prover 13: Constructing countermodel ... % 22.68/3.75 Prover 11: Warning: ignoring some quantifiers % 23.22/3.81 Prover 11: Constructing countermodel ... % 26.46/4.22 Prover 1: Found proof (size 98) % 26.46/4.22 Prover 1: proved (3604ms) % 26.46/4.22 Prover 13: stopped % 26.46/4.22 Prover 4: stopped % 26.46/4.22 Prover 8: stopped % 26.46/4.22 Prover 7: stopped % 26.46/4.23 Prover 10: stopped % 26.46/4.23 Prover 11: stopped % 26.46/4.23 % 26.46/4.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.46/4.23 % 26.46/4.24 % SZS output start Proof for theBenchmark % 26.46/4.24 Assumptions after simplification: % 26.46/4.24 --------------------------------- % 26.46/4.24 % 26.46/4.24 (finite_domain_0) % 26.46/4.27 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 26.46/4.27 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 26.46/4.27 % 26.46/4.27 (finite_domain_5) % 26.46/4.27 $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n5 | % 26.46/4.27 v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n5) = 0) | ~ % 26.46/4.27 $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) % 26.46/4.27 % 26.46/4.27 (leq_gt2) % 26.46/4.27 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (gt(v1, v0) % 26.46/4.27 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) % 26.46/4.27 = v3)) % 26.46/4.27 % 26.46/4.27 (leq_gt_pred) % 26.46/4.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.46/4.27 (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 26.46/4.27 int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 26.46/4.27 [v2: $i] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) % 26.46/4.27 | gt(v1, v0) = 0) % 26.46/4.27 % 26.46/4.27 (pred_succ) % 26.46/4.27 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0) % 26.46/4.27 % 26.46/4.27 (quaternion_ds1_inuse_0019) % 26.46/4.28 a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use & % 26.46/4.28 a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use & % 26.46/4.28 a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse, n3) = % 26.46/4.28 use & a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, % 26.46/4.28 n1) = use & a_select2(xinit_noise_defuse, n0) = use & % 26.46/4.28 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) = % 26.46/4.28 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse, % 26.46/4.28 n2) = use & a_select2(xinit_mean_defuse, n1) = use & % 26.46/4.28 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use & % 26.46/4.28 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use & % 26.46/4.28 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use & % 26.46/4.28 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use & % 26.46/4.28 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use & % 26.46/4.28 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use & % 26.46/4.28 a_select2(rho_defuse, n0) = use & $i(z_defuse) & $i(n998) & % 26.46/4.28 $i(xinit_noise_defuse) & $i(xinit_mean_defuse) & $i(xinit_defuse) & % 26.46/4.28 $i(u_defuse) & $i(sigma_defuse) & $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & % 26.46/4.28 $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.46/4.28 (v2 = use | ~ (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.46/4.28 [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : (leq(v1, n998) = v6 % 26.46/4.28 & leq(v0, n2) = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3 & ( ~ (v6 = 0) | % 26.46/4.28 ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 26.46/4.28 ! [v2: $i] : (v2 = use | ~ (a_select3(u_defuse, v0, v1) = v2) | ~ $i(v1) | % 26.46/4.28 ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : % 26.46/4.28 (leq(v1, n998) = v6 & leq(v0, n2) = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3 % 26.46/4.28 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ? [v0: $i] % 26.46/4.28 : ? [v1: $i] : ( ~ (v1 = use) & a_select2(xinit_mean_defuse, v0) = v1 & % 26.46/4.28 leq(v0, n5) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) % 26.46/4.28 % 26.46/4.28 (successor_1) % 26.46/4.28 succ(n0) = n1 & $i(n1) & $i(n0) % 26.46/4.28 % 26.46/4.28 (successor_2) % 26.46/4.28 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 26.46/4.28 % 26.46/4.28 (successor_3) % 26.46/4.29 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 26.46/4.29 succ(n0) = v0 & $i(v1) & $i(v0)) % 26.46/4.29 % 26.46/4.29 (successor_4) % 26.46/4.29 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 26.46/4.29 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 26.46/4.29 % 26.46/4.29 (successor_5) % 26.46/4.29 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 26.46/4.29 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 26.46/4.29 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 26.46/4.29 % 26.46/4.29 (function-axioms) % 26.46/4.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.46/4.29 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 26.46/4.30 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.46/4.30 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 26.46/4.30 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 26.46/4.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 26.46/4.30 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.46/4.30 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 26.46/4.30 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 26.87/4.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 26.87/4.30 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 26.87/4.30 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 26.87/4.30 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 26.87/4.30 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 26.87/4.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 26.87/4.30 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.87/4.30 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 26.87/4.30 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 26.87/4.30 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 26.87/4.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 26.87/4.30 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 26.87/4.30 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 26.87/4.30 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 26.87/4.30 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 26.87/4.30 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.87/4.30 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 26.87/4.30 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 26.87/4.30 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 26.87/4.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.87/4.30 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 26.87/4.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.87/4.30 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 26.87/4.30 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.87/4.30 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 26.87/4.30 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 26.87/4.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 26.87/4.30 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 26.87/4.30 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.87/4.30 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 26.87/4.30 % 26.87/4.30 Further assumptions not needed in the proof: % 26.87/4.30 -------------------------------------------- % 26.87/4.30 const_array1_select, const_array2_select, defuse, finite_domain_1, % 26.87/4.30 finite_domain_2, finite_domain_3, finite_domain_4, gt_0_tptp_minus_1, gt_1_0, % 26.87/4.30 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, % 26.87/4.30 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, % 26.87/4.30 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_998_0, gt_998_1, gt_998_2, % 26.87/4.30 gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, gt_succ, irreflexivity_gt, % 26.87/4.30 leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, % 26.87/4.30 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 26.87/4.30 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 26.87/4.30 matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1, % 26.87/4.30 sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, % 26.87/4.30 succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, % 26.87/4.30 succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, % 26.87/4.30 succ_pred, succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality, % 26.87/4.30 transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 26.87/4.30 uniform_int_rand_ranges_lo % 26.87/4.30 % 26.87/4.30 Those formulas are unsatisfiable: % 26.87/4.30 --------------------------------- % 26.87/4.30 % 26.87/4.30 Begin of proof % 26.87/4.30 | % 26.87/4.30 | ALPHA: (leq_gt_pred) implies: % 26.87/4.30 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.87/4.30 | (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 26.87/4.30 | [v4: int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) % 26.87/4.30 | % 26.87/4.30 | ALPHA: (finite_domain_5) implies: % 26.87/4.30 | (2) ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = % 26.87/4.30 | n0 | ~ (leq(v0, n5) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 26.87/4.30 | leq(n0, v0) = v1)) % 26.87/4.30 | % 26.87/4.30 | ALPHA: (finite_domain_0) implies: % 26.87/4.30 | (3) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 26.87/4.30 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 26.87/4.30 | % 26.87/4.30 | ALPHA: (successor_4) implies: % 26.87/4.30 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 26.87/4.30 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 26.87/4.30 | % 26.87/4.30 | ALPHA: (successor_5) implies: % 26.87/4.30 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 26.87/4.30 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 26.87/4.30 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 26.87/4.30 | % 26.87/4.30 | ALPHA: (successor_1) implies: % 26.87/4.30 | (6) succ(n0) = n1 % 26.87/4.30 | % 26.87/4.30 | ALPHA: (successor_2) implies: % 26.87/4.30 | (7) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 26.87/4.30 | % 26.87/4.30 | ALPHA: (successor_3) implies: % 26.87/4.31 | (8) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) = % 26.87/4.31 | v0 & $i(v1) & $i(v0)) % 26.87/4.31 | % 26.87/4.31 | ALPHA: (quaternion_ds1_inuse_0019) implies: % 26.87/4.31 | (9) $i(n0) % 26.87/4.31 | (10) a_select2(xinit_mean_defuse, n0) = use % 26.87/4.31 | (11) a_select2(xinit_mean_defuse, n1) = use % 26.87/4.31 | (12) a_select2(xinit_mean_defuse, n2) = use % 26.87/4.31 | (13) a_select2(xinit_mean_defuse, n3) = use % 26.87/4.31 | (14) a_select2(xinit_mean_defuse, n4) = use % 26.87/4.31 | (15) a_select2(xinit_mean_defuse, n5) = use % 26.87/4.31 | (16) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = use) & % 26.87/4.31 | a_select2(xinit_mean_defuse, v0) = v1 & leq(v0, n5) = 0 & leq(n0, % 26.87/4.31 | v0) = 0 & $i(v1) & $i(v0)) % 26.87/4.31 | % 26.87/4.31 | ALPHA: (function-axioms) implies: % 26.87/4.31 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 26.87/4.31 | v1) | ~ (succ(v2) = v0)) % 26.87/4.31 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.87/4.31 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 26.87/4.31 | v0)) % 26.87/4.31 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.87/4.31 | (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) % 26.87/4.31 | % 26.87/4.31 | DELTA: instantiating (7) with fresh symbol all_50_0 gives: % 26.87/4.31 | (20) succ(all_50_0) = n2 & succ(n0) = all_50_0 & $i(all_50_0) % 26.87/4.31 | % 26.87/4.31 | ALPHA: (20) implies: % 26.87/4.31 | (21) $i(all_50_0) % 26.87/4.31 | (22) succ(n0) = all_50_0 % 26.87/4.31 | % 26.87/4.31 | DELTA: instantiating (8) with fresh symbols all_52_0, all_52_1 gives: % 26.87/4.31 | (23) succ(all_52_0) = n3 & succ(all_52_1) = all_52_0 & succ(n0) = all_52_1 % 26.87/4.31 | & $i(all_52_0) & $i(all_52_1) % 26.87/4.31 | % 26.87/4.31 | ALPHA: (23) implies: % 26.87/4.31 | (24) succ(n0) = all_52_1 % 26.87/4.31 | % 26.87/4.31 | DELTA: instantiating (16) with fresh symbols all_54_0, all_54_1 gives: % 26.87/4.31 | (25) ~ (all_54_0 = use) & a_select2(xinit_mean_defuse, all_54_1) = % 26.87/4.31 | all_54_0 & leq(all_54_1, n5) = 0 & leq(n0, all_54_1) = 0 & % 26.87/4.31 | $i(all_54_0) & $i(all_54_1) % 26.87/4.31 | % 26.87/4.31 | ALPHA: (25) implies: % 26.87/4.31 | (26) ~ (all_54_0 = use) % 26.87/4.31 | (27) $i(all_54_1) % 26.87/4.31 | (28) leq(n0, all_54_1) = 0 % 26.87/4.31 | (29) leq(all_54_1, n5) = 0 % 26.87/4.31 | (30) a_select2(xinit_mean_defuse, all_54_1) = all_54_0 % 26.87/4.31 | % 26.87/4.31 | DELTA: instantiating (4) with fresh symbols all_56_0, all_56_1, all_56_2 % 26.87/4.31 | gives: % 26.87/4.31 | (31) succ(all_56_0) = n4 & succ(all_56_1) = all_56_0 & succ(all_56_2) = % 26.87/4.31 | all_56_1 & succ(n0) = all_56_2 & $i(all_56_0) & $i(all_56_1) & % 26.87/4.31 | $i(all_56_2) % 26.87/4.31 | % 26.87/4.31 | ALPHA: (31) implies: % 26.87/4.31 | (32) succ(n0) = all_56_2 % 26.87/4.31 | % 26.87/4.31 | DELTA: instantiating (5) with fresh symbols all_58_0, all_58_1, all_58_2, % 26.87/4.31 | all_58_3 gives: % 26.87/4.32 | (33) succ(all_58_0) = n5 & succ(all_58_1) = all_58_0 & succ(all_58_2) = % 26.87/4.32 | all_58_1 & succ(all_58_3) = all_58_2 & succ(n0) = all_58_3 & % 26.87/4.32 | $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) % 26.87/4.32 | % 26.87/4.32 | ALPHA: (33) implies: % 26.87/4.32 | (34) succ(n0) = all_58_3 % 26.87/4.32 | % 26.87/4.32 | GROUND_INST: instantiating (17) with all_52_1, all_56_2, n0, simplifying with % 26.87/4.32 | (24), (32) gives: % 26.87/4.32 | (35) all_56_2 = all_52_1 % 26.87/4.32 | % 26.87/4.32 | GROUND_INST: instantiating (17) with all_50_0, all_56_2, n0, simplifying with % 26.87/4.32 | (22), (32) gives: % 26.87/4.32 | (36) all_56_2 = all_50_0 % 26.87/4.32 | % 26.87/4.32 | GROUND_INST: instantiating (17) with all_52_1, all_58_3, n0, simplifying with % 26.87/4.32 | (24), (34) gives: % 26.87/4.32 | (37) all_58_3 = all_52_1 % 26.87/4.32 | % 26.87/4.32 | GROUND_INST: instantiating (17) with n1, all_58_3, n0, simplifying with (6), % 26.87/4.32 | (34) gives: % 26.87/4.32 | (38) all_58_3 = n1 % 26.87/4.32 | % 26.87/4.32 | COMBINE_EQS: (37), (38) imply: % 26.87/4.32 | (39) all_52_1 = n1 % 26.87/4.32 | % 26.87/4.32 | SIMP: (39) implies: % 26.87/4.32 | (40) all_52_1 = n1 % 26.87/4.32 | % 26.87/4.32 | COMBINE_EQS: (35), (36) imply: % 26.87/4.32 | (41) all_52_1 = all_50_0 % 26.87/4.32 | % 26.87/4.32 | SIMP: (41) implies: % 26.87/4.32 | (42) all_52_1 = all_50_0 % 26.87/4.32 | % 26.87/4.32 | COMBINE_EQS: (40), (42) imply: % 26.87/4.32 | (43) all_50_0 = n1 % 26.87/4.32 | % 26.87/4.32 | REDUCE: (21), (43) imply: % 26.87/4.32 | (44) $i(n1) % 26.87/4.32 | % 26.87/4.32 | GROUND_INST: instantiating (3) with all_54_1, simplifying with (27), (28) % 26.87/4.32 | gives: % 26.87/4.32 | (45) all_54_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_54_1, n0) = v0) % 26.87/4.32 | % 26.87/4.32 | GROUND_INST: instantiating (2) with all_54_1, simplifying with (27), (29) % 26.87/4.32 | gives: % 26.87/4.32 | (46) all_54_1 = n5 | all_54_1 = n4 | all_54_1 = n3 | all_54_1 = n2 | % 26.87/4.32 | all_54_1 = n1 | all_54_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0, % 26.87/4.32 | all_54_1) = v0) % 26.87/4.32 | % 26.87/4.32 | GROUND_INST: instantiating (pred_succ) with n0, n1, simplifying with (6), (9) % 26.87/4.32 | gives: % 26.87/4.32 | (47) pred(n1) = n0 % 26.87/4.32 | % 26.87/4.32 | BETA: splitting (45) gives: % 26.87/4.32 | % 26.87/4.32 | Case 1: % 26.87/4.32 | | % 26.87/4.32 | | (48) all_54_1 = n0 % 26.87/4.32 | | % 26.87/4.32 | | REDUCE: (30), (48) imply: % 26.87/4.32 | | (49) a_select2(xinit_mean_defuse, n0) = all_54_0 % 26.87/4.32 | | % 26.87/4.32 | | GROUND_INST: instantiating (19) with use, all_54_0, n0, xinit_mean_defuse, % 26.87/4.32 | | simplifying with (10), (49) gives: % 26.87/4.32 | | (50) all_54_0 = use % 26.87/4.32 | | % 26.87/4.32 | | REDUCE: (26), (50) imply: % 26.87/4.32 | | (51) $false % 26.87/4.32 | | % 26.87/4.32 | | CLOSE: (51) is inconsistent. % 26.87/4.32 | | % 26.87/4.32 | Case 2: % 26.87/4.32 | | % 26.87/4.32 | | (52) ~ (all_54_1 = n0) % 26.87/4.32 | | (53) ? [v0: int] : ( ~ (v0 = 0) & leq(all_54_1, n0) = v0) % 26.87/4.32 | | % 26.87/4.32 | | DELTA: instantiating (53) with fresh symbol all_121_0 gives: % 26.87/4.33 | | (54) ~ (all_121_0 = 0) & leq(all_54_1, n0) = all_121_0 % 26.87/4.33 | | % 26.87/4.33 | | ALPHA: (54) implies: % 26.87/4.33 | | (55) ~ (all_121_0 = 0) % 26.87/4.33 | | (56) leq(all_54_1, n0) = all_121_0 % 26.87/4.33 | | % 26.87/4.33 | | GROUND_INST: instantiating (1) with all_54_1, n1, n0, all_121_0, simplifying % 26.87/4.33 | | with (27), (44), (47), (56) gives: % 26.87/4.33 | | (57) all_121_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & gt(n1, all_54_1) = v0) % 26.87/4.33 | | % 26.87/4.33 | | BETA: splitting (57) gives: % 26.87/4.33 | | % 26.87/4.33 | | Case 1: % 26.87/4.33 | | | % 26.87/4.33 | | | (58) all_121_0 = 0 % 26.87/4.33 | | | % 26.87/4.33 | | | REDUCE: (55), (58) imply: % 26.87/4.33 | | | (59) $false % 26.87/4.33 | | | % 26.87/4.33 | | | CLOSE: (59) is inconsistent. % 26.87/4.33 | | | % 26.87/4.33 | | Case 2: % 26.87/4.33 | | | % 26.87/4.33 | | | (60) ? [v0: int] : ( ~ (v0 = 0) & gt(n1, all_54_1) = v0) % 26.87/4.33 | | | % 26.87/4.33 | | | DELTA: instantiating (60) with fresh symbol all_141_0 gives: % 26.87/4.33 | | | (61) ~ (all_141_0 = 0) & gt(n1, all_54_1) = all_141_0 % 26.87/4.33 | | | % 26.87/4.33 | | | ALPHA: (61) implies: % 26.87/4.33 | | | (62) ~ (all_141_0 = 0) % 26.87/4.33 | | | (63) gt(n1, all_54_1) = all_141_0 % 26.87/4.33 | | | % 26.87/4.33 | | | GROUND_INST: instantiating (leq_gt2) with all_54_1, n1, all_141_0, % 26.87/4.33 | | | simplifying with (27), (44), (63) gives: % 26.87/4.33 | | | (64) all_141_0 = 0 | all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) & % 26.87/4.33 | | | leq(all_54_1, n1) = v0) % 26.87/4.33 | | | % 26.87/4.33 | | | BETA: splitting (46) gives: % 26.87/4.33 | | | % 26.87/4.33 | | | Case 1: % 26.87/4.33 | | | | % 26.87/4.33 | | | | (65) all_54_1 = n0 % 26.87/4.33 | | | | % 26.87/4.33 | | | | REDUCE: (52), (65) imply: % 26.87/4.33 | | | | (66) $false % 26.87/4.33 | | | | % 26.87/4.33 | | | | CLOSE: (66) is inconsistent. % 26.87/4.33 | | | | % 26.87/4.33 | | | Case 2: % 26.87/4.33 | | | | % 26.87/4.33 | | | | (67) all_54_1 = n5 | all_54_1 = n4 | all_54_1 = n3 | all_54_1 = n2 | % 26.87/4.33 | | | | all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_54_1) % 26.87/4.33 | | | | = v0) % 26.87/4.33 | | | | % 26.87/4.33 | | | | BETA: splitting (64) gives: % 26.87/4.33 | | | | % 26.87/4.33 | | | | Case 1: % 26.87/4.33 | | | | | % 26.87/4.33 | | | | | (68) all_141_0 = 0 % 26.87/4.33 | | | | | % 26.87/4.33 | | | | | REDUCE: (62), (68) imply: % 26.87/4.33 | | | | | (69) $false % 26.87/4.33 | | | | | % 26.87/4.33 | | | | | CLOSE: (69) is inconsistent. % 26.87/4.33 | | | | | % 26.87/4.33 | | | | Case 2: % 26.87/4.33 | | | | | % 26.87/4.33 | | | | | (70) all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_54_1, % 26.87/4.33 | | | | | n1) = v0) % 26.87/4.33 | | | | | % 26.87/4.33 | | | | | BETA: splitting (67) gives: % 26.87/4.33 | | | | | % 26.87/4.33 | | | | | Case 1: % 26.87/4.33 | | | | | | % 26.87/4.33 | | | | | | (71) all_54_1 = n5 % 26.87/4.33 | | | | | | % 26.87/4.33 | | | | | | REDUCE: (30), (71) imply: % 26.87/4.33 | | | | | | (72) a_select2(xinit_mean_defuse, n5) = all_54_0 % 26.87/4.33 | | | | | | % 26.87/4.33 | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n5, % 26.87/4.33 | | | | | | xinit_mean_defuse, simplifying with (15), (72) gives: % 26.87/4.33 | | | | | | (73) all_54_0 = use % 26.87/4.33 | | | | | | % 26.87/4.33 | | | | | | REDUCE: (26), (73) imply: % 26.87/4.33 | | | | | | (74) $false % 26.87/4.33 | | | | | | % 26.87/4.33 | | | | | | CLOSE: (74) is inconsistent. % 26.87/4.33 | | | | | | % 26.87/4.33 | | | | | Case 2: % 26.87/4.33 | | | | | | % 26.87/4.33 | | | | | | (75) all_54_1 = n4 | all_54_1 = n3 | all_54_1 = n2 | all_54_1 = % 26.87/4.33 | | | | | | n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_54_1) = v0) % 26.87/4.33 | | | | | | % 26.87/4.33 | | | | | | BETA: splitting (70) gives: % 26.87/4.33 | | | | | | % 26.87/4.33 | | | | | | Case 1: % 26.87/4.33 | | | | | | | % 26.87/4.33 | | | | | | | (76) all_54_1 = n1 % 26.87/4.33 | | | | | | | % 26.87/4.33 | | | | | | | REDUCE: (30), (76) imply: % 26.87/4.33 | | | | | | | (77) a_select2(xinit_mean_defuse, n1) = all_54_0 % 26.87/4.33 | | | | | | | % 26.87/4.34 | | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n1, % 26.87/4.34 | | | | | | | xinit_mean_defuse, simplifying with (11), (77) gives: % 26.87/4.34 | | | | | | | (78) all_54_0 = use % 26.87/4.34 | | | | | | | % 26.87/4.34 | | | | | | | REDUCE: (26), (78) imply: % 26.87/4.34 | | | | | | | (79) $false % 26.87/4.34 | | | | | | | % 26.87/4.34 | | | | | | | CLOSE: (79) is inconsistent. % 26.87/4.34 | | | | | | | % 26.87/4.34 | | | | | | Case 2: % 26.87/4.34 | | | | | | | % 26.87/4.34 | | | | | | | (80) ~ (all_54_1 = n1) % 26.87/4.34 | | | | | | | % 26.87/4.34 | | | | | | | BETA: splitting (75) gives: % 26.87/4.34 | | | | | | | % 26.87/4.34 | | | | | | | Case 1: % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | | (81) all_54_1 = n4 % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | | REDUCE: (30), (81) imply: % 26.87/4.34 | | | | | | | | (82) a_select2(xinit_mean_defuse, n4) = all_54_0 % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n4, % 26.87/4.34 | | | | | | | | xinit_mean_defuse, simplifying with (14), (82) % 26.87/4.34 | | | | | | | | gives: % 26.87/4.34 | | | | | | | | (83) all_54_0 = use % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | | REDUCE: (26), (83) imply: % 26.87/4.34 | | | | | | | | (84) $false % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | | CLOSE: (84) is inconsistent. % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | Case 2: % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | | (85) all_54_1 = n3 | all_54_1 = n2 | all_54_1 = n1 | ? [v0: % 26.87/4.34 | | | | | | | | int] : ( ~ (v0 = 0) & leq(n0, all_54_1) = v0) % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | | BETA: splitting (85) gives: % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | | Case 1: % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | | (86) all_54_1 = n3 % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | | REDUCE: (30), (86) imply: % 26.87/4.34 | | | | | | | | | (87) a_select2(xinit_mean_defuse, n3) = all_54_0 % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n3, % 26.87/4.34 | | | | | | | | | xinit_mean_defuse, simplifying with (13), (87) % 26.87/4.34 | | | | | | | | | gives: % 26.87/4.34 | | | | | | | | | (88) all_54_0 = use % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | | REDUCE: (26), (88) imply: % 26.87/4.34 | | | | | | | | | (89) $false % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | | CLOSE: (89) is inconsistent. % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | Case 2: % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | | (90) all_54_1 = n2 | all_54_1 = n1 | ? [v0: int] : ( ~ (v0 % 26.87/4.34 | | | | | | | | | = 0) & leq(n0, all_54_1) = v0) % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | | BETA: splitting (90) gives: % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | | Case 1: % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | (91) all_54_1 = n2 % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | REDUCE: (30), (91) imply: % 26.87/4.34 | | | | | | | | | | (92) a_select2(xinit_mean_defuse, n2) = all_54_0 % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | GROUND_INST: instantiating (19) with use, all_54_0, n2, % 26.87/4.34 | | | | | | | | | | xinit_mean_defuse, simplifying with (12), (92) % 26.87/4.34 | | | | | | | | | | gives: % 26.87/4.34 | | | | | | | | | | (93) all_54_0 = use % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | REDUCE: (26), (93) imply: % 26.87/4.34 | | | | | | | | | | (94) $false % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | CLOSE: (94) is inconsistent. % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | Case 2: % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | (95) all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) & % 26.87/4.34 | | | | | | | | | | leq(n0, all_54_1) = v0) % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | BETA: splitting (95) gives: % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | Case 1: % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | | (96) all_54_1 = n1 % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | | REDUCE: (80), (96) imply: % 26.87/4.34 | | | | | | | | | | | (97) $false % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | | CLOSE: (97) is inconsistent. % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | Case 2: % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | | (98) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_54_1) = % 26.87/4.34 | | | | | | | | | | | v0) % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | | DELTA: instantiating (98) with fresh symbol all_613_0 % 26.87/4.34 | | | | | | | | | | | gives: % 26.87/4.34 | | | | | | | | | | | (99) ~ (all_613_0 = 0) & leq(n0, all_54_1) = all_613_0 % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | | ALPHA: (99) implies: % 26.87/4.34 | | | | | | | | | | | (100) ~ (all_613_0 = 0) % 26.87/4.34 | | | | | | | | | | | (101) leq(n0, all_54_1) = all_613_0 % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_613_0, all_54_1, % 26.87/4.34 | | | | | | | | | | | n0, simplifying with (28), (101) gives: % 26.87/4.34 | | | | | | | | | | | (102) all_613_0 = 0 % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | | REDUCE: (100), (102) imply: % 26.87/4.34 | | | | | | | | | | | (103) $false % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | | CLOSE: (103) is inconsistent. % 26.87/4.34 | | | | | | | | | | | % 26.87/4.34 | | | | | | | | | | End of split % 26.87/4.34 | | | | | | | | | | % 26.87/4.34 | | | | | | | | | End of split % 26.87/4.34 | | | | | | | | | % 26.87/4.34 | | | | | | | | End of split % 26.87/4.34 | | | | | | | | % 26.87/4.34 | | | | | | | End of split % 26.87/4.34 | | | | | | | % 26.87/4.34 | | | | | | End of split % 26.87/4.34 | | | | | | % 26.87/4.34 | | | | | End of split % 26.87/4.34 | | | | | % 26.87/4.34 | | | | End of split % 26.87/4.34 | | | | % 26.87/4.34 | | | End of split % 26.87/4.34 | | | % 26.87/4.34 | | End of split % 26.87/4.34 | | % 26.87/4.34 | End of split % 26.87/4.34 | % 26.87/4.34 End of proof % 26.87/4.34 % SZS output end Proof for theBenchmark % 26.87/4.34 % 26.87/4.34 3746ms %------------------------------------------------------------------------------