%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 22:55:15 EDT 2023 % Result : Theorem 17.11s 3.01s % Output : Proof 20.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV181+1 : TPTP v8.1.2. Bugfixed v3.3.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n013.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 06:11:01 EDT 2023 % 0.13/0.34 % 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/sandbox2/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 % 5.48/1.43 Prover 4: Preprocessing ... % 5.48/1.45 Prover 1: Preprocessing ... % 5.48/1.47 Prover 0: Preprocessing ... % 5.48/1.47 Prover 5: Preprocessing ... % 5.48/1.47 Prover 3: Preprocessing ... % 5.48/1.47 Prover 2: Preprocessing ... % 5.48/1.47 Prover 6: Preprocessing ... % 10.93/2.21 Prover 1: Warning: ignoring some quantifiers % 11.72/2.29 Prover 3: Warning: ignoring some quantifiers % 12.15/2.34 Prover 1: Constructing countermodel ... % 12.15/2.35 Prover 3: Constructing countermodel ... % 12.33/2.35 Prover 6: Proving ... % 12.33/2.37 Prover 4: Warning: ignoring some quantifiers % 13.16/2.53 Prover 4: Constructing countermodel ... % 13.16/2.54 Prover 5: Proving ... % 13.16/2.58 Prover 2: Proving ... % 13.16/2.59 Prover 0: Proving ... % 17.11/3.01 Prover 3: proved (2383ms) % 17.11/3.01 % 17.11/3.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.11/3.01 % 17.11/3.02 Prover 5: stopped % 17.11/3.02 Prover 2: stopped % 17.11/3.04 Prover 0: stopped % 17.11/3.05 Prover 6: stopped % 17.66/3.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.66/3.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.66/3.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.66/3.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.66/3.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.66/3.19 Prover 7: Preprocessing ... % 18.95/3.25 Prover 10: Preprocessing ... % 18.95/3.27 Prover 13: Preprocessing ... % 18.95/3.27 Prover 8: Preprocessing ... % 18.95/3.28 Prover 1: Found proof (size 104) % 18.95/3.28 Prover 1: proved (2656ms) % 18.95/3.28 Prover 7: stopped % 18.95/3.28 Prover 4: stopped % 18.95/3.29 Prover 11: Preprocessing ... % 18.95/3.30 Prover 10: stopped % 19.61/3.36 Prover 11: stopped % 19.61/3.36 Prover 13: stopped % 19.98/3.44 Prover 8: Warning: ignoring some quantifiers % 19.98/3.46 Prover 8: Constructing countermodel ... % 20.35/3.47 Prover 8: stopped % 20.35/3.47 % 20.35/3.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.35/3.47 % 20.35/3.50 % SZS output start Proof for theBenchmark % 20.52/3.51 Assumptions after simplification: % 20.52/3.51 --------------------------------- % 20.52/3.51 % 20.52/3.51 (cl5_nebula_init_0081) % 20.66/3.55 $i(muold_init) & $i(sigma_init) & $i(rho_init) & $i(mu_init) & $i(center_init) % 20.66/3.55 & $i(init) & $i(q_init) & $i(n135299) & $i(loopcounter) & $i(pv76) & % 20.66/3.55 $i(tptp_float_0_001) & $i(n4) & $i(n1) & $i(n0) & ? [v0: any] : % 20.66/3.55 (leq(tptp_float_0_001, pv76) = 0 & leq(n1, loopcounter) = 0 & gt(loopcounter, % 20.66/3.55 n0) = v0 & gt(n1, loopcounter) = 0 & ! [v1: $i] : ! [v2: $i] : (v2 = % 20.66/3.55 init | ~ (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) | ? [v3: any] % 20.66/3.55 : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ % 20.66/3.55 (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, n135299) = 0) | ~ $i(v1) | % 20.66/3.55 ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] % 20.66/3.55 : (v3 = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4: % 20.66/3.55 any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = % 20.66/3.55 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) % 20.66/3.55 & a_select2(muold_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = 0 & % 20.66/3.55 $i(v2) & $i(v1)) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 20.66/3.55 ~ (a_select2(sigma_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 20.66/3.55 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 20.66/3.55 0))))) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 20.66/3.55 ~ (a_select2(rho_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 20.66/3.55 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 20.66/3.55 0))))) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init | % 20.66/3.55 ~ (a_select2(mu_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: % 20.66/3.55 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 20.66/3.55 0)))))) % 20.66/3.55 % 20.66/3.55 (finite_domain_0) % 20.66/3.55 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 20.66/3.55 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 20.66/3.55 % 20.66/3.55 (gt_2_0) % 20.66/3.55 gt(n2, n0) = 0 & $i(n2) & $i(n0) % 20.66/3.55 % 20.66/3.55 (gt_5_4) % 20.66/3.55 gt(n5, n4) = 0 & $i(n5) & $i(n4) % 20.66/3.55 % 20.66/3.55 (irreflexivity_gt) % 20.66/3.55 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0)) % 20.66/3.55 % 20.66/3.55 (leq_gt1) % 20.66/3.55 ! [v0: $i] : ! [v1: $i] : ( ~ (gt(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 20.66/3.55 leq(v0, v1) = 0) % 20.66/3.55 % 20.66/3.55 (leq_succ_gt) % 20.66/3.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v0) = v2) | ~ (leq(v2, % 20.66/3.55 v1) = 0) | ~ $i(v1) | ~ $i(v0) | gt(v1, v0) = 0) % 20.66/3.55 % 20.66/3.55 (leq_succ_gt_equiv) % 20.66/3.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.66/3.55 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 20.66/3.55 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! % 20.66/3.55 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 20.66/3.55 leq(v0, v1) = 0) % 20.66/3.55 % 20.66/3.55 (successor_1) % 20.66/3.55 succ(n0) = n1 & $i(n1) & $i(n0) % 20.66/3.55 % 20.66/3.55 (successor_2) % 20.66/3.56 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 20.66/3.56 % 20.66/3.56 (successor_3) % 20.66/3.56 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & % 20.66/3.56 succ(n0) = v0 & $i(v1) & $i(v0)) % 20.66/3.56 % 20.66/3.56 (successor_4) % 20.66/3.56 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & % 20.66/3.56 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 20.66/3.56 % 20.66/3.56 (successor_5) % 20.66/3.56 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 20.66/3.56 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 % 20.66/3.56 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.66/3.56 % 20.66/3.56 (function-axioms) % 20.66/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.66/3.56 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ % 20.66/3.56 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.66/3.56 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = % 20.66/3.56 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.66/3.56 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | % 20.66/3.56 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.66/3.56 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | % 20.66/3.56 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.66/3.56 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = % 20.66/3.56 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 20.66/3.56 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, % 20.66/3.56 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 20.66/3.56 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : ! % 20.66/3.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) % 20.66/3.56 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.66/3.56 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = % 20.66/3.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 20.66/3.56 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : ! % 20.66/3.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ % 20.66/3.56 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 20.66/3.56 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, % 20.66/3.56 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 20.66/3.56 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0: % 20.66/3.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.66/3.56 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! % 20.66/3.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.66/3.56 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 20.66/3.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.66/3.56 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 20.66/3.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.66/3.56 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 20.66/3.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.66/3.56 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : ! % 20.66/3.56 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & % 20.66/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~ % 20.66/3.56 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.66/3.56 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.66/3.56 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 20.66/3.56 % 20.66/3.56 Further assumptions not needed in the proof: % 20.66/3.56 -------------------------------------------- % 20.66/3.57 const_array1_select, const_array2_select, defuse, finite_domain_1, % 20.66/3.57 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 20.66/3.57 gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2, gt_135299_3, % 20.66/3.57 gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, % 20.66/3.57 gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, % 20.66/3.57 gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, % 20.66/3.57 gt_5_tptp_minus_1, gt_succ, leq_geq, leq_gt2, leq_gt_pred, leq_minus, leq_succ, % 20.66/3.57 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, % 20.66/3.57 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans, % 20.66/3.57 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq, % 20.66/3.57 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, % 20.66/3.57 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, % 20.66/3.57 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, % 20.66/3.57 succ_plus_5_r, succ_pred, succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, % 20.66/3.57 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 20.66/3.57 uniform_int_rand_ranges_lo % 20.66/3.57 % 20.66/3.57 Those formulas are unsatisfiable: % 20.66/3.57 --------------------------------- % 20.66/3.57 % 20.66/3.57 Begin of proof % 20.66/3.57 | % 20.66/3.57 | ALPHA: (leq_succ_gt_equiv) implies: % 20.66/3.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~ % 20.66/3.57 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0) % 20.66/3.57 | % 20.66/3.57 | ALPHA: (gt_5_4) implies: % 20.66/3.57 | (2) gt(n5, n4) = 0 % 20.66/3.57 | % 20.66/3.57 | ALPHA: (gt_2_0) implies: % 20.66/3.57 | (3) gt(n2, n0) = 0 % 20.66/3.57 | % 20.66/3.57 | ALPHA: (finite_domain_0) implies: % 20.66/3.57 | (4) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1: % 20.66/3.57 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 20.66/3.57 | % 20.66/3.57 | ALPHA: (successor_4) implies: % 20.66/3.57 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) = % 20.66/3.57 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 20.66/3.57 | % 20.66/3.57 | ALPHA: (successor_5) implies: % 20.66/3.57 | (6) $i(n5) % 20.66/3.57 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5 % 20.66/3.57 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & % 20.66/3.57 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.66/3.57 | % 20.66/3.57 | ALPHA: (successor_1) implies: % 20.66/3.57 | (8) succ(n0) = n1 % 20.66/3.57 | % 20.66/3.57 | ALPHA: (successor_2) implies: % 20.66/3.57 | (9) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0)) % 20.66/3.57 | % 20.66/3.57 | ALPHA: (successor_3) implies: % 20.66/3.57 | (10) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) % 20.66/3.57 | = v0 & $i(v1) & $i(v0)) % 20.66/3.57 | % 20.66/3.57 | ALPHA: (cl5_nebula_init_0081) implies: % 20.66/3.57 | (11) $i(n0) % 20.66/3.57 | (12) $i(loopcounter) % 20.66/3.58 | (13) ? [v0: any] : (leq(tptp_float_0_001, pv76) = 0 & leq(n1, loopcounter) % 20.66/3.58 | = 0 & gt(loopcounter, n0) = v0 & gt(n1, loopcounter) = 0 & ! [v1: % 20.66/3.58 | $i] : ! [v2: $i] : (v2 = init | ~ (a_select3(center_init, v1, % 20.66/3.58 | n0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, % 20.66/3.58 | n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & % 20.66/3.58 | ! [v1: $i] : ( ~ (leq(v1, n135299) = 0) | ~ $i(v1) | ? [v2: int] : % 20.66/3.58 | ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] : (v3 % 20.66/3.58 | = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? % 20.66/3.58 | [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 % 20.66/3.58 | & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : % 20.66/3.58 | ( ~ (v2 = init) & a_select2(muold_init, v1) = v2 & leq(v1, n4) = 0 & % 20.66/3.58 | leq(n0, v1) = 0 & $i(v2) & $i(v1)) & ( ~ (v0 = 0) | ! [v1: $i] : % 20.66/3.58 | ! [v2: $i] : (v2 = init | ~ (a_select2(sigma_init, v1) = v2) | ~ % 20.66/3.58 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & % 20.66/3.58 | leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ( ~ (v0 = % 20.66/3.58 | 0) | ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 20.66/3.58 | (a_select2(rho_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 20.66/3.58 | [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) % 20.66/3.58 | | ~ (v3 = 0))))) & ( ~ (v0 = 0) | ! [v1: $i] : ! [v2: $i] % 20.66/3.58 | : (v2 = init | ~ (a_select2(mu_init, v1) = v2) | ~ $i(v1) | ? % 20.66/3.58 | [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 % 20.66/3.58 | & ( ~ (v4 = 0) | ~ (v3 = 0)))))) % 20.66/3.58 | % 20.66/3.58 | ALPHA: (function-axioms) implies: % 20.66/3.58 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = % 20.66/3.58 | v1) | ~ (succ(v2) = v0)) % 20.66/3.58 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.66/3.58 | : ! [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = % 20.66/3.58 | v0)) % 20.66/3.58 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.66/3.58 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 20.66/3.58 | v0)) % 20.66/3.58 | % 20.66/3.58 | DELTA: instantiating (9) with fresh symbol all_49_0 gives: % 20.66/3.58 | (17) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0) % 20.66/3.58 | % 20.66/3.58 | ALPHA: (17) implies: % 20.66/3.58 | (18) $i(all_49_0) % 20.66/3.58 | (19) succ(n0) = all_49_0 % 20.66/3.58 | (20) succ(all_49_0) = n2 % 20.66/3.58 | % 20.66/3.58 | DELTA: instantiating (10) with fresh symbols all_51_0, all_51_1 gives: % 20.66/3.58 | (21) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1 % 20.66/3.58 | & $i(all_51_0) & $i(all_51_1) % 20.66/3.58 | % 20.66/3.58 | ALPHA: (21) implies: % 20.66/3.58 | (22) succ(n0) = all_51_1 % 20.66/3.58 | (23) succ(all_51_1) = all_51_0 % 20.66/3.58 | (24) succ(all_51_0) = n3 % 20.66/3.58 | % 20.66/3.58 | DELTA: instantiating (5) with fresh symbols all_53_0, all_53_1, all_53_2 % 20.66/3.58 | gives: % 20.66/3.58 | (25) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) = % 20.66/3.58 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) & % 20.66/3.58 | $i(all_53_2) % 20.66/3.58 | % 20.66/3.58 | ALPHA: (25) implies: % 20.66/3.58 | (26) succ(n0) = all_53_2 % 20.66/3.58 | (27) succ(all_53_2) = all_53_1 % 20.66/3.58 | (28) succ(all_53_1) = all_53_0 % 20.66/3.58 | (29) succ(all_53_0) = n4 % 20.66/3.58 | % 20.66/3.58 | DELTA: instantiating (7) with fresh symbols all_55_0, all_55_1, all_55_2, % 20.66/3.58 | all_55_3 gives: % 20.66/3.58 | (30) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) = % 20.66/3.58 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 & % 20.66/3.58 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3) % 20.66/3.58 | % 20.66/3.58 | ALPHA: (30) implies: % 20.66/3.58 | (31) succ(n0) = all_55_3 % 20.66/3.58 | (32) succ(all_55_3) = all_55_2 % 20.66/3.58 | (33) succ(all_55_2) = all_55_1 % 20.66/3.58 | (34) succ(all_55_1) = all_55_0 % 20.66/3.58 | (35) succ(all_55_0) = n5 % 20.66/3.58 | % 20.66/3.58 | DELTA: instantiating (13) with fresh symbol all_74_0 gives: % 20.66/3.59 | (36) leq(tptp_float_0_001, pv76) = 0 & leq(n1, loopcounter) = 0 & % 20.66/3.59 | gt(loopcounter, n0) = all_74_0 & gt(n1, loopcounter) = 0 & ! [v0: $i] % 20.66/3.59 | : ! [v1: $i] : (v1 = init | ~ (a_select3(center_init, v0, n0) = v1) % 20.66/3.59 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & % 20.66/3.59 | leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ( % 20.66/3.59 | ~ (leq(v0, n135299) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 20.66/3.59 | leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ % 20.66/3.59 | (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 20.66/3.59 | [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | % 20.66/3.59 | ~ (v3 = 0))))) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & % 20.66/3.59 | a_select2(muold_init, v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & % 20.66/3.59 | $i(v1) & $i(v0)) & ( ~ (all_74_0 = 0) | ! [v0: $i] : ! [v1: $i] : % 20.66/3.59 | (v1 = init | ~ (a_select2(sigma_init, v0) = v1) | ~ $i(v0) | ? % 20.66/3.59 | [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & % 20.66/3.59 | ( ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ (all_74_0 = 0) | ! [v0: % 20.66/3.59 | $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rho_init, v0) = v1) % 20.66/3.59 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & % 20.66/3.59 | leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ % 20.66/3.59 | (all_74_0 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 20.66/3.59 | (a_select2(mu_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 20.66/3.59 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 20.66/3.59 | (v2 = 0))))) % 20.66/3.59 | % 20.66/3.59 | ALPHA: (36) implies: % 20.66/3.59 | (37) gt(n1, loopcounter) = 0 % 20.66/3.59 | (38) gt(loopcounter, n0) = all_74_0 % 20.66/3.59 | (39) leq(n1, loopcounter) = 0 % 20.66/3.59 | (40) ~ (all_74_0 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ % 20.66/3.59 | (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 20.66/3.59 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ % 20.66/3.59 | (v2 = 0)))) % 20.66/3.59 | % 20.66/3.59 | GROUND_INST: instantiating (14) with all_51_1, all_53_2, n0, simplifying with % 20.66/3.59 | (22), (26) gives: % 20.66/3.59 | (41) all_53_2 = all_51_1 % 20.66/3.59 | % 20.66/3.59 | GROUND_INST: instantiating (14) with all_49_0, all_53_2, n0, simplifying with % 20.66/3.59 | (19), (26) gives: % 20.66/3.59 | (42) all_53_2 = all_49_0 % 20.66/3.59 | % 20.66/3.59 | GROUND_INST: instantiating (14) with all_53_2, all_55_3, n0, simplifying with % 20.66/3.59 | (26), (31) gives: % 20.66/3.59 | (43) all_55_3 = all_53_2 % 20.66/3.59 | % 20.66/3.59 | GROUND_INST: instantiating (14) with n1, all_55_3, n0, simplifying with (8), % 20.66/3.59 | (31) gives: % 20.66/3.59 | (44) all_55_3 = n1 % 20.66/3.59 | % 20.66/3.59 | COMBINE_EQS: (43), (44) imply: % 20.66/3.59 | (45) all_53_2 = n1 % 20.66/3.59 | % 20.66/3.59 | SIMP: (45) implies: % 20.66/3.59 | (46) all_53_2 = n1 % 20.66/3.59 | % 20.66/3.59 | COMBINE_EQS: (41), (46) imply: % 20.66/3.59 | (47) all_51_1 = n1 % 20.66/3.59 | % 20.66/3.59 | COMBINE_EQS: (41), (42) imply: % 20.66/3.59 | (48) all_51_1 = all_49_0 % 20.66/3.59 | % 20.66/3.59 | COMBINE_EQS: (47), (48) imply: % 20.66/3.59 | (49) all_49_0 = n1 % 20.66/3.59 | % 20.66/3.59 | REDUCE: (32), (44) imply: % 20.66/3.59 | (50) succ(n1) = all_55_2 % 20.66/3.59 | % 20.66/3.59 | REDUCE: (27), (46) imply: % 20.66/3.59 | (51) succ(n1) = all_53_1 % 20.66/3.59 | % 20.66/3.59 | REDUCE: (23), (47) imply: % 20.66/3.59 | (52) succ(n1) = all_51_0 % 20.66/3.59 | % 20.66/3.59 | REDUCE: (20), (49) imply: % 20.66/3.59 | (53) succ(n1) = n2 % 20.66/3.59 | % 20.66/3.59 | REDUCE: (18), (49) imply: % 20.66/3.59 | (54) $i(n1) % 20.66/3.59 | % 20.66/3.59 | GROUND_INST: instantiating (14) with all_51_0, all_53_1, n1, simplifying with % 20.66/3.59 | (51), (52) gives: % 20.66/3.60 | (55) all_53_1 = all_51_0 % 20.66/3.60 | % 20.66/3.60 | GROUND_INST: instantiating (14) with all_53_1, all_55_2, n1, simplifying with % 20.66/3.60 | (50), (51) gives: % 20.66/3.60 | (56) all_55_2 = all_53_1 % 20.66/3.60 | % 20.66/3.60 | GROUND_INST: instantiating (14) with n2, all_55_2, n1, simplifying with (50), % 20.66/3.60 | (53) gives: % 20.66/3.60 | (57) all_55_2 = n2 % 20.66/3.60 | % 20.66/3.60 | COMBINE_EQS: (56), (57) imply: % 20.66/3.60 | (58) all_53_1 = n2 % 20.66/3.60 | % 20.66/3.60 | SIMP: (58) implies: % 20.66/3.60 | (59) all_53_1 = n2 % 20.66/3.60 | % 20.66/3.60 | COMBINE_EQS: (55), (59) imply: % 20.66/3.60 | (60) all_51_0 = n2 % 20.66/3.60 | % 20.66/3.60 | REDUCE: (33), (57) imply: % 20.66/3.60 | (61) succ(n2) = all_55_1 % 20.66/3.60 | % 20.66/3.60 | REDUCE: (28), (59) imply: % 20.66/3.60 | (62) succ(n2) = all_53_0 % 20.66/3.60 | % 20.66/3.60 | REDUCE: (24), (60) imply: % 20.66/3.60 | (63) succ(n2) = n3 % 20.66/3.60 | % 20.66/3.60 | GROUND_INST: instantiating (14) with all_53_0, all_55_1, n2, simplifying with % 20.66/3.60 | (61), (62) gives: % 20.66/3.60 | (64) all_55_1 = all_53_0 % 20.66/3.60 | % 20.66/3.60 | GROUND_INST: instantiating (14) with n3, all_55_1, n2, simplifying with (61), % 20.66/3.60 | (63) gives: % 20.66/3.60 | (65) all_55_1 = n3 % 20.66/3.60 | % 20.66/3.60 | COMBINE_EQS: (64), (65) imply: % 20.66/3.60 | (66) all_53_0 = n3 % 20.66/3.60 | % 20.66/3.60 | SIMP: (66) implies: % 20.66/3.60 | (67) all_53_0 = n3 % 20.66/3.60 | % 20.66/3.60 | REDUCE: (34), (65) imply: % 20.66/3.60 | (68) succ(n3) = all_55_0 % 20.66/3.60 | % 20.66/3.60 | REDUCE: (29), (67) imply: % 20.66/3.60 | (69) succ(n3) = n4 % 20.66/3.60 | % 20.66/3.60 | GROUND_INST: instantiating (14) with n4, all_55_0, n3, simplifying with (68), % 20.66/3.60 | (69) gives: % 20.66/3.60 | (70) all_55_0 = n4 % 20.66/3.60 | % 20.66/3.60 | REDUCE: (35), (70) imply: % 20.66/3.60 | (71) succ(n4) = n5 % 20.66/3.60 | % 20.66/3.60 | GROUND_INST: instantiating (leq_succ_gt) with n0, loopcounter, n1, simplifying % 20.66/3.60 | with (8), (11), (12), (39) gives: % 20.66/3.60 | (72) gt(loopcounter, n0) = 0 % 20.66/3.60 | % 20.66/3.60 | GROUND_INST: instantiating (1) with loopcounter, n0, n1, simplifying with (8), % 20.66/3.60 | (11), (12), (37) gives: % 20.66/3.60 | (73) leq(loopcounter, n0) = 0 % 20.66/3.60 | % 20.66/3.60 | GROUND_INST: instantiating (1) with n0, n1, n2, simplifying with (3), (11), % 20.66/3.60 | (53), (54) gives: % 20.66/3.60 | (74) leq(n0, n1) = 0 % 20.66/3.60 | % 20.66/3.60 | GROUND_INST: instantiating (15) with all_74_0, 0, n0, loopcounter, simplifying % 20.66/3.60 | with (38), (72) gives: % 20.66/3.60 | (75) all_74_0 = 0 % 20.66/3.60 | % 20.66/3.60 | BETA: splitting (40) gives: % 20.66/3.60 | % 20.66/3.60 | Case 1: % 20.66/3.60 | | % 20.66/3.60 | | (76) ~ (all_74_0 = 0) % 20.66/3.60 | | % 20.66/3.60 | | REDUCE: (75), (76) imply: % 20.66/3.60 | | (77) $false % 20.66/3.60 | | % 20.66/3.60 | | CLOSE: (77) is inconsistent. % 20.66/3.60 | | % 20.66/3.60 | Case 2: % 20.66/3.60 | | % 20.66/3.60 | | % 20.66/3.60 | | GROUND_INST: instantiating (leq_gt1) with n0, loopcounter, simplifying with % 20.66/3.60 | | (11), (12), (72) gives: % 20.66/3.60 | | (78) leq(n0, loopcounter) = 0 % 20.66/3.60 | | % 20.66/3.60 | | GROUND_INST: instantiating (4) with n1, simplifying with (54), (74) gives: % 20.66/3.61 | | (79) n1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(n1, n0) = v0) % 20.66/3.61 | | % 20.66/3.61 | | GROUND_INST: instantiating (4) with loopcounter, simplifying with (12), (78) % 20.66/3.61 | | gives: % 20.66/3.61 | | (80) loopcounter = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(loopcounter, % 20.66/3.61 | | n0) = v0) % 20.66/3.61 | | % 20.66/3.61 | | BETA: splitting (80) gives: % 20.66/3.61 | | % 20.66/3.61 | | Case 1: % 20.66/3.61 | | | % 20.66/3.61 | | | (81) loopcounter = n0 % 20.66/3.61 | | | % 20.66/3.61 | | | REDUCE: (39), (81) imply: % 20.66/3.61 | | | (82) leq(n1, n0) = 0 % 20.66/3.61 | | | % 20.66/3.61 | | | BETA: splitting (79) gives: % 20.66/3.61 | | | % 20.66/3.61 | | | Case 1: % 20.66/3.61 | | | | % 20.66/3.61 | | | | (83) n1 = n0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | REDUCE: (53), (83) imply: % 20.66/3.61 | | | | (84) succ(n0) = n2 % 20.66/3.61 | | | | % 20.66/3.61 | | | | REDUCE: (8), (83) imply: % 20.66/3.61 | | | | (85) succ(n0) = n0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | GROUND_INST: instantiating (14) with n0, n2, n0, simplifying with (84), % 20.66/3.61 | | | | (85) gives: % 20.66/3.61 | | | | (86) n2 = n0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | REDUCE: (63), (86) imply: % 20.66/3.61 | | | | (87) succ(n0) = n3 % 20.66/3.61 | | | | % 20.66/3.61 | | | | GROUND_INST: instantiating (14) with n0, n3, n0, simplifying with (85), % 20.66/3.61 | | | | (87) gives: % 20.66/3.61 | | | | (88) n3 = n0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | REDUCE: (69), (88) imply: % 20.66/3.61 | | | | (89) succ(n0) = n4 % 20.66/3.61 | | | | % 20.66/3.61 | | | | GROUND_INST: instantiating (14) with n0, n4, n0, simplifying with (85), % 20.66/3.61 | | | | (89) gives: % 20.66/3.61 | | | | (90) n4 = n0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | REDUCE: (71), (90) imply: % 20.66/3.61 | | | | (91) succ(n0) = n5 % 20.66/3.61 | | | | % 20.66/3.61 | | | | REDUCE: (2), (90) imply: % 20.66/3.61 | | | | (92) gt(n5, n0) = 0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | GROUND_INST: instantiating (14) with n0, n5, n0, simplifying with (85), % 20.66/3.61 | | | | (91) gives: % 20.66/3.61 | | | | (93) n5 = n0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | REDUCE: (92), (93) imply: % 20.66/3.61 | | | | (94) gt(n0, n0) = 0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with % 20.66/3.61 | | | | (11), (94) gives: % 20.66/3.61 | | | | (95) $false % 20.66/3.61 | | | | % 20.66/3.61 | | | | CLOSE: (95) is inconsistent. % 20.66/3.61 | | | | % 20.66/3.61 | | | Case 2: % 20.66/3.61 | | | | % 20.66/3.61 | | | | (96) ? [v0: int] : ( ~ (v0 = 0) & leq(n1, n0) = v0) % 20.66/3.61 | | | | % 20.66/3.61 | | | | DELTA: instantiating (96) with fresh symbol all_153_0 gives: % 20.66/3.61 | | | | (97) ~ (all_153_0 = 0) & leq(n1, n0) = all_153_0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | ALPHA: (97) implies: % 20.66/3.61 | | | | (98) ~ (all_153_0 = 0) % 20.66/3.61 | | | | (99) leq(n1, n0) = all_153_0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | GROUND_INST: instantiating (16) with 0, all_153_0, n0, n1, simplifying % 20.66/3.61 | | | | with (82), (99) gives: % 20.66/3.61 | | | | (100) all_153_0 = 0 % 20.66/3.61 | | | | % 20.66/3.61 | | | | REDUCE: (98), (100) imply: % 20.66/3.61 | | | | (101) $false % 20.66/3.61 | | | | % 20.66/3.61 | | | | CLOSE: (101) is inconsistent. % 20.66/3.61 | | | | % 20.66/3.61 | | | End of split % 20.66/3.61 | | | % 20.66/3.61 | | Case 2: % 20.66/3.61 | | | % 20.66/3.61 | | | (102) ? [v0: int] : ( ~ (v0 = 0) & leq(loopcounter, n0) = v0) % 20.66/3.61 | | | % 20.66/3.61 | | | DELTA: instantiating (102) with fresh symbol all_149_0 gives: % 20.66/3.61 | | | (103) ~ (all_149_0 = 0) & leq(loopcounter, n0) = all_149_0 % 20.66/3.61 | | | % 20.66/3.61 | | | ALPHA: (103) implies: % 20.66/3.61 | | | (104) ~ (all_149_0 = 0) % 20.66/3.61 | | | (105) leq(loopcounter, n0) = all_149_0 % 20.66/3.61 | | | % 20.66/3.61 | | | GROUND_INST: instantiating (16) with 0, all_149_0, n0, loopcounter, % 20.66/3.61 | | | simplifying with (73), (105) gives: % 20.66/3.61 | | | (106) all_149_0 = 0 % 20.66/3.61 | | | % 20.66/3.61 | | | REDUCE: (104), (106) imply: % 20.66/3.61 | | | (107) $false % 20.66/3.61 | | | % 20.66/3.61 | | | CLOSE: (107) is inconsistent. % 20.66/3.61 | | | % 20.66/3.61 | | End of split % 20.66/3.61 | | % 20.66/3.61 | End of split % 20.66/3.61 | % 20.66/3.61 End of proof % 20.66/3.61 % SZS output end Proof for theBenchmark % 20.66/3.61 % 20.66/3.61 3011ms %------------------------------------------------------------------------------