TSTP Solution File: KLE158+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE158+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 : 600s
% DateTime : Sun Jul 17 01:51:40 EDT 2022
% Result : Theorem 33.77s 9.78s
% Output : Proof 60.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE158+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n007.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 : 600
% 0.12/0.33 % DateTime : Thu Jun 16 13:31:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.57 ____ _
% 0.55/0.57 ___ / __ \_____(_)___ ________ __________
% 0.55/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.57
% 0.55/0.57 A Theorem Prover for First-Order Logic
% 0.55/0.57 (ePrincess v.1.0)
% 0.55/0.57
% 0.55/0.57 (c) Philipp Rümmer, 2009-2015
% 0.55/0.57 (c) Peter Backeman, 2014-2015
% 0.55/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.57 Bug reports to peter@backeman.se
% 0.55/0.57
% 0.55/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.57
% 0.55/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.55/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.89 Prover 0: Preprocessing ...
% 2.08/1.14 Prover 0: Constructing countermodel ...
% 18.34/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.34/5.98 Prover 1: Preprocessing ...
% 18.64/6.05 Prover 1: Constructing countermodel ...
% 29.01/8.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 29.35/8.57 Prover 2: Preprocessing ...
% 29.73/8.66 Prover 2: Warning: ignoring some quantifiers
% 29.73/8.67 Prover 2: Constructing countermodel ...
% 33.77/9.78 Prover 2: proved (1238ms)
% 33.77/9.78 Prover 1: stopped
% 33.77/9.78 Prover 0: stopped
% 33.77/9.78
% 33.77/9.78 No countermodel exists, formula is valid
% 33.77/9.78 % SZS status Theorem for theBenchmark
% 33.77/9.78
% 33.77/9.78 Generating proof ... Warning: ignoring some quantifiers
% 59.95/25.59 found it (size 238)
% 59.95/25.59
% 59.95/25.59 % SZS output start Proof for theBenchmark
% 59.95/25.59 Assumed formulas after preprocessing and simplification:
% 59.95/25.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & strong_iteration(v2) = v7 & strong_iteration(v1) = v5 & leq(v6, v8) = v9 & leq(v3, v4) = 0 & multiplication(v7, v0) = v8 & multiplication(v2, v0) = v4 & multiplication(v0, v5) = v6 & multiplication(v0, v1) = v3 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (strong_iteration(v10) = v13) | ~ (leq(v12, v14) = v15) | ~ (multiplication(v13, v11) = v14) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & leq(v12, v17) = v18 & multiplication(v10, v12) = v16 & addition(v16, v11) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (leq(v14, v12) = v15) | ~ (star(v10) = v13) | ~ (multiplication(v13, v11) = v14) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & leq(v17, v12) = v18 & multiplication(v10, v12) = v16 & addition(v16, v11) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (leq(v14, v12) = v15) | ~ (star(v10) = v13) | ~ (multiplication(v11, v13) = v14) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & leq(v17, v12) = v18 & multiplication(v12, v10) = v16 & addition(v16, v11) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v11, v12) = v14) | ~ (multiplication(v10, v12) = v13) | ~ (addition(v13, v14) = v15) | ? [v16] : (multiplication(v16, v12) = v15 & addition(v10, v11) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v10, v12) = v14) | ~ (multiplication(v10, v11) = v13) | ~ (addition(v13, v14) = v15) | ? [v16] : (multiplication(v10, v16) = v15 & addition(v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v13, v12) = v14) | ~ (multiplication(v10, v11) = v13) | ? [v15] : (multiplication(v11, v12) = v15 & multiplication(v10, v15) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v13, v12) = v14) | ~ (addition(v10, v11) = v13) | ? [v15] : ? [v16] : (multiplication(v11, v12) = v16 & multiplication(v10, v12) = v15 & addition(v15, v16) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v12, v10) = v13) | ~ (addition(v13, v11) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & leq(v16, v12) = 0 & star(v10) = v15 & multiplication(v11, v15) = v16) | ( ~ (v15 = 0) & leq(v14, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v11, v12) = v13) | ~ (multiplication(v10, v13) = v14) | ? [v15] : (multiplication(v15, v12) = v14 & multiplication(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v10, v13) = v14) | ~ (addition(v11, v12) = v13) | ? [v15] : ? [v16] : (multiplication(v10, v12) = v16 & multiplication(v10, v11) = v15 & addition(v15, v16) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v10, v12) = v13) | ~ (addition(v13, v11) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & strong_iteration(v10) = v15 & leq(v12, v16) = 0 & multiplication(v15, v11) = v16) | ( ~ (v15 = 0) & leq(v12, v14) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v10, v12) = v13) | ~ (addition(v13, v11) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & leq(v16, v12) = 0 & star(v10) = v15 & multiplication(v15, v11) = v16) | ( ~ (v15 = 0) & leq(v14, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (addition(v13, v10) = v14) | ~ (addition(v12, v11) = v13) | ? [v15] : (addition(v12, v15) = v14 & addition(v11, v10) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (addition(v12, v13) = v14) | ~ (addition(v11, v10) = v13) | ? [v15] : (addition(v15, v10) = v14 & addition(v12, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (leq(v13, v12) = v11) | ~ (leq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (multiplication(v13, v12) = v11) | ~ (multiplication(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (addition(v13, v12) = v11) | ~ (addition(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (addition(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & leq(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (leq(v10, v11) = v12) | ? [v13] : ( ~ (v13 = v11) & addition(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (strong_iteration(v12) = v11) | ~ (strong_iteration(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (star(v12) = v11) | ~ (star(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (addition(v11, v10) = v12) | addition(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (addition(v10, v11) = v12) | addition(v11, v10) = v12) & ! [v10] : ! [v11] : (v11 = v10 | ~ (multiplication(v10, one) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (multiplication(one, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (addition(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (addition(v10, zero) = v11)) & ! [v10] : ! [v11] : (v11 = zero | ~ (multiplication(zero, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (strong_iteration(v10) = v11) | ? [v12] : ? [v13] : (star(v10) = v12 & multiplication(v11, zero) = v13 & addition(v12, v13) = v11)) & ! [v10] : ! [v11] : ( ~ (strong_iteration(v10) = v11) | ? [v12] : (multiplication(v10, v11) = v12 & addition(v12, one) = v11)) & ! [v10] : ! [v11] : ( ~ (leq(v10, v11) = 0) | addition(v10, v11) = v11) & ! [v10] : ! [v11] : ( ~ (star(v10) = v11) | ? [v12] : ? [v13] : (strong_iteration(v10) = v12 & multiplication(v12, zero) = v13 & addition(v11, v13) = v12)) & ! [v10] : ! [v11] : ( ~ (star(v10) = v11) | ? [v12] : (multiplication(v11, v10) = v12 & addition(one, v12) = v11)) & ! [v10] : ! [v11] : ( ~ (star(v10) = v11) | ? [v12] : (multiplication(v10, v11) = v12 & addition(one, v12) = v11)) & ! [v10] : ! [v11] : ( ~ (addition(v10, v11) = v11) | leq(v10, v11) = 0) & ? [v10] : ? [v11] : ? [v12] : leq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : multiplication(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : addition(v11, v10) = v12 & ? [v10] : ? [v11] : strong_iteration(v10) = v11 & ? [v10] : ? [v11] : star(v10) = v11)
% 60.30/25.64 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 60.30/25.64 | (1) ~ (all_0_0_0 = 0) & strong_iteration(all_0_7_7) = all_0_2_2 & strong_iteration(all_0_8_8) = all_0_4_4 & leq(all_0_3_3, all_0_1_1) = all_0_0_0 & leq(all_0_6_6, all_0_5_5) = 0 & multiplication(all_0_2_2, all_0_9_9) = all_0_1_1 & multiplication(all_0_7_7, all_0_9_9) = all_0_5_5 & multiplication(all_0_9_9, all_0_4_4) = all_0_3_3 & multiplication(all_0_9_9, all_0_8_8) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, v4) = v5) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v2, v0) = v6 & addition(v6, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v1, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & strong_iteration(v0) = v5 & leq(v2, v6) = 0 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v2, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & addition(v1, v3) = v2)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) & ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 & ? [v0] : ? [v1] : strong_iteration(v0) = v1 & ? [v0] : ? [v1] : star(v0) = v1
% 60.30/25.66 |
% 60.30/25.66 | Applying alpha-rule on (1) yields:
% 60.30/25.66 | (2) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 60.30/25.66 | (3) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2
% 60.30/25.66 | (4) leq(all_0_3_3, all_0_1_1) = all_0_0_0
% 60.30/25.66 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7))
% 60.30/25.66 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 60.30/25.66 | (7) ~ (all_0_0_0 = 0)
% 60.30/25.66 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4))
% 60.30/25.66 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 60.30/25.66 | (10) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2
% 60.30/25.66 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 60.30/25.66 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 60.30/25.66 | (13) strong_iteration(all_0_7_7) = all_0_2_2
% 60.30/25.66 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 60.30/25.66 | (15) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 60.30/25.66 | (16) strong_iteration(all_0_8_8) = all_0_4_4
% 60.30/25.66 | (17) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 60.30/25.66 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v1, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5)))
% 60.30/25.66 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6))
% 60.30/25.66 | (20) leq(all_0_6_6, all_0_5_5) = 0
% 60.30/25.66 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 60.30/25.66 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4))
% 60.30/25.66 | (23) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2
% 60.30/25.66 | (24) multiplication(all_0_9_9, all_0_4_4) = all_0_3_3
% 60.30/25.66 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0))
% 60.30/25.66 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 60.30/25.66 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v2, v0) = v6 & addition(v6, v1) = v7))
% 60.30/25.67 | (28) multiplication(all_0_7_7, all_0_9_9) = all_0_5_5
% 60.30/25.67 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, v4) = v5) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7))
% 60.30/25.67 | (30) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & addition(v1, v3) = v2))
% 60.30/25.67 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & strong_iteration(v0) = v5 & leq(v2, v6) = 0 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v2, v4) = v5)))
% 60.30/25.67 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5)))
% 60.30/25.67 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 60.30/25.67 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 60.30/25.67 | (35) multiplication(all_0_2_2, all_0_9_9) = all_0_1_1
% 60.30/25.67 | (36) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 60.30/25.67 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 60.30/25.67 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 60.30/25.67 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 60.30/25.67 | (40) multiplication(all_0_9_9, all_0_8_8) = all_0_6_6
% 60.30/25.67 | (41) ? [v0] : ? [v1] : star(v0) = v1
% 60.30/25.67 | (42) ? [v0] : ? [v1] : strong_iteration(v0) = v1
% 60.30/25.67 | (43) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 60.30/25.67 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 60.30/25.67 | (45) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 60.30/25.67 | (46) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 60.30/25.67 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 60.30/25.67 | (48) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 60.30/25.67 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 60.30/25.67 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 60.30/25.67 |
% 60.30/25.67 | Instantiating formula (17) with all_0_2_2, all_0_7_7 and discharging atoms strong_iteration(all_0_7_7) = all_0_2_2, yields:
% 60.30/25.67 | (51) ? [v0] : (multiplication(all_0_7_7, all_0_2_2) = v0 & addition(v0, one) = all_0_2_2)
% 60.30/25.67 |
% 60.30/25.67 | Instantiating formula (2) with all_0_4_4, all_0_8_8 and discharging atoms strong_iteration(all_0_8_8) = all_0_4_4, yields:
% 60.30/25.67 | (52) ? [v0] : ? [v1] : (star(all_0_8_8) = v0 & multiplication(all_0_4_4, zero) = v1 & addition(v0, v1) = all_0_4_4)
% 60.30/25.67 |
% 60.30/25.67 | Instantiating formula (17) with all_0_4_4, all_0_8_8 and discharging atoms strong_iteration(all_0_8_8) = all_0_4_4, yields:
% 60.30/25.67 | (53) ? [v0] : (multiplication(all_0_8_8, all_0_4_4) = v0 & addition(v0, one) = all_0_4_4)
% 60.30/25.67 |
% 60.30/25.67 | Instantiating formula (12) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms leq(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 60.30/25.67 | (54) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_3_3, all_0_1_1) = v0)
% 60.30/25.68 |
% 60.30/25.68 | Instantiating formula (46) with all_0_5_5, all_0_6_6 and discharging atoms leq(all_0_6_6, all_0_5_5) = 0, yields:
% 60.30/25.68 | (55) addition(all_0_6_6, all_0_5_5) = all_0_5_5
% 60.30/25.68 |
% 60.30/25.68 | Instantiating formula (29) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_9_9, all_0_7_7 and discharging atoms strong_iteration(all_0_7_7) = all_0_2_2, leq(all_0_3_3, all_0_1_1) = all_0_0_0, multiplication(all_0_2_2, all_0_9_9) = all_0_1_1, yields:
% 60.30/25.68 | (56) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & leq(all_0_3_3, v1) = v2 & multiplication(all_0_7_7, all_0_3_3) = v0 & addition(v0, all_0_9_9) = v1)
% 60.30/25.68 |
% 60.30/25.68 | Instantiating (53) with all_19_0_23 yields:
% 60.30/25.68 | (57) multiplication(all_0_8_8, all_0_4_4) = all_19_0_23 & addition(all_19_0_23, one) = all_0_4_4
% 60.30/25.68 |
% 60.30/25.68 | Applying alpha-rule on (57) yields:
% 60.30/25.68 | (58) multiplication(all_0_8_8, all_0_4_4) = all_19_0_23
% 60.30/25.68 | (59) addition(all_19_0_23, one) = all_0_4_4
% 60.30/25.68 |
% 60.30/25.68 | Instantiating (52) with all_21_0_24, all_21_1_25 yields:
% 60.30/25.68 | (60) star(all_0_8_8) = all_21_1_25 & multiplication(all_0_4_4, zero) = all_21_0_24 & addition(all_21_1_25, all_21_0_24) = all_0_4_4
% 60.30/25.68 |
% 60.30/25.68 | Applying alpha-rule on (60) yields:
% 60.30/25.68 | (61) star(all_0_8_8) = all_21_1_25
% 60.30/25.68 | (62) multiplication(all_0_4_4, zero) = all_21_0_24
% 60.30/25.68 | (63) addition(all_21_1_25, all_21_0_24) = all_0_4_4
% 60.30/25.68 |
% 60.30/25.68 | Instantiating (51) with all_23_0_26 yields:
% 60.30/25.68 | (64) multiplication(all_0_7_7, all_0_2_2) = all_23_0_26 & addition(all_23_0_26, one) = all_0_2_2
% 60.30/25.68 |
% 60.30/25.68 | Applying alpha-rule on (64) yields:
% 60.30/25.68 | (65) multiplication(all_0_7_7, all_0_2_2) = all_23_0_26
% 60.30/25.68 | (66) addition(all_23_0_26, one) = all_0_2_2
% 60.30/25.68 |
% 60.30/25.68 +-Applying beta-rule and splitting (56), into two cases.
% 60.30/25.68 |-Branch one:
% 60.30/25.68 | (67) all_0_0_0 = 0
% 60.30/25.68 |
% 60.30/25.68 | Equations (67) can reduce 7 to:
% 60.30/25.68 | (68) $false
% 60.30/25.68 |
% 60.30/25.68 |-The branch is then unsatisfiable
% 60.30/25.68 |-Branch two:
% 60.30/25.68 | (7) ~ (all_0_0_0 = 0)
% 60.30/25.68 | (70) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & leq(all_0_3_3, v1) = v2 & multiplication(all_0_7_7, all_0_3_3) = v0 & addition(v0, all_0_9_9) = v1)
% 60.30/25.68 |
% 60.30/25.68 | Instantiating (70) with all_31_0_29, all_31_1_30, all_31_2_31 yields:
% 60.30/25.68 | (71) ~ (all_31_0_29 = 0) & leq(all_0_3_3, all_31_1_30) = all_31_0_29 & multiplication(all_0_7_7, all_0_3_3) = all_31_2_31 & addition(all_31_2_31, all_0_9_9) = all_31_1_30
% 60.30/25.68 |
% 60.30/25.68 | Applying alpha-rule on (71) yields:
% 60.30/25.68 | (72) ~ (all_31_0_29 = 0)
% 60.30/25.68 | (73) leq(all_0_3_3, all_31_1_30) = all_31_0_29
% 60.30/25.68 | (74) multiplication(all_0_7_7, all_0_3_3) = all_31_2_31
% 60.30/25.68 | (75) addition(all_31_2_31, all_0_9_9) = all_31_1_30
% 60.30/25.68 |
% 60.30/25.68 +-Applying beta-rule and splitting (54), into two cases.
% 60.30/25.68 |-Branch one:
% 60.30/25.68 | (67) all_0_0_0 = 0
% 60.30/25.68 |
% 60.30/25.68 | Equations (67) can reduce 7 to:
% 60.30/25.68 | (68) $false
% 60.30/25.68 |
% 60.30/25.68 |-The branch is then unsatisfiable
% 60.30/25.68 |-Branch two:
% 60.30/25.68 | (7) ~ (all_0_0_0 = 0)
% 60.30/25.68 | (79) ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_3_3, all_0_1_1) = v0)
% 60.30/25.68 |
% 60.30/25.68 | Instantiating (79) with all_36_0_32 yields:
% 60.30/25.68 | (80) ~ (all_36_0_32 = all_0_1_1) & addition(all_0_3_3, all_0_1_1) = all_36_0_32
% 60.30/25.68 |
% 60.30/25.68 | Applying alpha-rule on (80) yields:
% 60.30/25.68 | (81) ~ (all_36_0_32 = all_0_1_1)
% 60.30/25.68 | (82) addition(all_0_3_3, all_0_1_1) = all_36_0_32
% 60.30/25.68 |
% 60.30/25.68 | Instantiating formula (12) with all_31_0_29, all_31_1_30, all_0_3_3 and discharging atoms leq(all_0_3_3, all_31_1_30) = all_31_0_29, yields:
% 60.48/25.68 | (83) all_31_0_29 = 0 | ? [v0] : ( ~ (v0 = all_31_1_30) & addition(all_0_3_3, all_31_1_30) = v0)
% 60.48/25.68 |
% 60.48/25.68 | Instantiating formula (36) with all_21_1_25, all_0_8_8 and discharging atoms star(all_0_8_8) = all_21_1_25, yields:
% 60.48/25.68 | (84) ? [v0] : (multiplication(all_21_1_25, all_0_8_8) = v0 & addition(one, v0) = all_21_1_25)
% 60.48/25.68 |
% 60.48/25.68 | Instantiating formula (15) with all_21_1_25, all_0_8_8 and discharging atoms star(all_0_8_8) = all_21_1_25, yields:
% 60.48/25.68 | (85) ? [v0] : (multiplication(all_0_8_8, all_21_1_25) = v0 & addition(one, v0) = all_21_1_25)
% 60.48/25.68 |
% 60.48/25.68 | Instantiating formula (39) with all_31_2_31, all_0_3_3, all_0_4_4, all_0_9_9, all_0_7_7 and discharging atoms multiplication(all_0_7_7, all_0_3_3) = all_31_2_31, multiplication(all_0_9_9, all_0_4_4) = all_0_3_3, yields:
% 60.48/25.68 | (86) ? [v0] : (multiplication(v0, all_0_4_4) = all_31_2_31 & multiplication(all_0_7_7, all_0_9_9) = v0)
% 60.48/25.68 |
% 60.48/25.68 | Instantiating formula (50) with all_31_1_30, all_31_2_31, all_0_9_9 and discharging atoms addition(all_31_2_31, all_0_9_9) = all_31_1_30, yields:
% 60.48/25.68 | (87) addition(all_0_9_9, all_31_2_31) = all_31_1_30
% 60.48/25.68 |
% 60.48/25.68 | Instantiating formula (8) with all_0_1_1, all_0_2_2, all_0_9_9, one, all_23_0_26 and discharging atoms multiplication(all_0_2_2, all_0_9_9) = all_0_1_1, addition(all_23_0_26, one) = all_0_2_2, yields:
% 60.48/25.68 | (88) ? [v0] : ? [v1] : (multiplication(all_23_0_26, all_0_9_9) = v0 & multiplication(one, all_0_9_9) = v1 & addition(v0, v1) = all_0_1_1)
% 60.48/25.69 |
% 60.48/25.69 | Instantiating formula (50) with all_0_2_2, all_23_0_26, one and discharging atoms addition(all_23_0_26, one) = all_0_2_2, yields:
% 60.48/25.69 | (89) addition(one, all_23_0_26) = all_0_2_2
% 60.48/25.69 |
% 60.48/25.69 | Instantiating formula (22) with all_0_3_3, all_0_4_4, all_21_0_24, all_21_1_25, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_4_4) = all_0_3_3, addition(all_21_1_25, all_21_0_24) = all_0_4_4, yields:
% 60.48/25.69 | (90) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_21_0_24) = v1 & multiplication(all_0_9_9, all_21_1_25) = v0 & addition(v0, v1) = all_0_3_3)
% 60.48/25.69 |
% 60.48/25.69 | Instantiating formula (22) with all_19_0_23, all_0_4_4, all_21_0_24, all_21_1_25, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_4_4) = all_19_0_23, addition(all_21_1_25, all_21_0_24) = all_0_4_4, yields:
% 60.48/25.69 | (91) ? [v0] : ? [v1] : (multiplication(all_0_8_8, all_21_0_24) = v1 & multiplication(all_0_8_8, all_21_1_25) = v0 & addition(v0, v1) = all_19_0_23)
% 60.48/25.69 |
% 60.48/25.69 | Instantiating formula (22) with all_0_3_3, all_0_4_4, one, all_19_0_23, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_4_4) = all_0_3_3, addition(all_19_0_23, one) = all_0_4_4, yields:
% 60.48/25.69 | (92) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_19_0_23) = v0 & multiplication(all_0_9_9, one) = v1 & addition(v0, v1) = all_0_3_3)
% 60.48/25.69 |
% 60.48/25.69 | Instantiating formula (22) with all_19_0_23, all_0_4_4, one, all_19_0_23, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_4_4) = all_19_0_23, addition(all_19_0_23, one) = all_0_4_4, yields:
% 60.48/25.69 | (93) ? [v0] : ? [v1] : (multiplication(all_0_8_8, all_19_0_23) = v0 & multiplication(all_0_8_8, one) = v1 & addition(v0, v1) = all_19_0_23)
% 60.48/25.69 |
% 60.48/25.69 | Instantiating formula (50) with all_0_4_4, all_19_0_23, one and discharging atoms addition(all_19_0_23, one) = all_0_4_4, yields:
% 60.48/25.69 | (94) addition(one, all_19_0_23) = all_0_4_4
% 60.48/25.69 |
% 60.48/25.69 | Instantiating formula (50) with all_36_0_32, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_36_0_32, yields:
% 60.48/25.69 | (95) addition(all_0_1_1, all_0_3_3) = all_36_0_32
% 60.48/25.69 |
% 60.48/25.69 | Instantiating formula (21) with all_0_5_5, all_0_5_5, all_0_6_6, all_0_6_6, all_0_5_5 and discharging atoms addition(all_0_6_6, all_0_5_5) = all_0_5_5, yields:
% 60.48/25.69 | (96) ? [v0] : (addition(v0, all_0_5_5) = all_0_5_5 & addition(all_0_6_6, all_0_6_6) = v0)
% 60.48/25.69 |
% 60.48/25.69 | Instantiating formula (50) with all_0_5_5, all_0_6_6, all_0_5_5 and discharging atoms addition(all_0_6_6, all_0_5_5) = all_0_5_5, yields:
% 60.48/25.69 | (97) addition(all_0_5_5, all_0_6_6) = all_0_5_5
% 60.48/25.69 |
% 60.48/25.69 | Instantiating (88) with all_46_0_39, all_46_1_40 yields:
% 60.48/25.69 | (98) multiplication(all_23_0_26, all_0_9_9) = all_46_1_40 & multiplication(one, all_0_9_9) = all_46_0_39 & addition(all_46_1_40, all_46_0_39) = all_0_1_1
% 60.48/25.69 |
% 60.48/25.69 | Applying alpha-rule on (98) yields:
% 60.48/25.69 | (99) multiplication(all_23_0_26, all_0_9_9) = all_46_1_40
% 60.48/25.69 | (100) multiplication(one, all_0_9_9) = all_46_0_39
% 60.48/25.69 | (101) addition(all_46_1_40, all_46_0_39) = all_0_1_1
% 60.48/25.69 |
% 60.48/25.69 | Instantiating (91) with all_54_0_47, all_54_1_48 yields:
% 60.48/25.69 | (102) multiplication(all_0_8_8, all_21_0_24) = all_54_0_47 & multiplication(all_0_8_8, all_21_1_25) = all_54_1_48 & addition(all_54_1_48, all_54_0_47) = all_19_0_23
% 60.48/25.69 |
% 60.48/25.69 | Applying alpha-rule on (102) yields:
% 60.48/25.69 | (103) multiplication(all_0_8_8, all_21_0_24) = all_54_0_47
% 60.48/25.69 | (104) multiplication(all_0_8_8, all_21_1_25) = all_54_1_48
% 60.48/25.69 | (105) addition(all_54_1_48, all_54_0_47) = all_19_0_23
% 60.48/25.69 |
% 60.48/25.69 | Instantiating (93) with all_58_0_51, all_58_1_52 yields:
% 60.48/25.69 | (106) multiplication(all_0_8_8, all_19_0_23) = all_58_1_52 & multiplication(all_0_8_8, one) = all_58_0_51 & addition(all_58_1_52, all_58_0_51) = all_19_0_23
% 60.48/25.69 |
% 60.48/25.69 | Applying alpha-rule on (106) yields:
% 60.48/25.69 | (107) multiplication(all_0_8_8, all_19_0_23) = all_58_1_52
% 60.48/25.69 | (108) multiplication(all_0_8_8, one) = all_58_0_51
% 60.48/25.69 | (109) addition(all_58_1_52, all_58_0_51) = all_19_0_23
% 60.48/25.69 |
% 60.48/25.69 | Instantiating (92) with all_63_0_58, all_63_1_59 yields:
% 60.48/25.69 | (110) multiplication(all_0_9_9, all_19_0_23) = all_63_1_59 & multiplication(all_0_9_9, one) = all_63_0_58 & addition(all_63_1_59, all_63_0_58) = all_0_3_3
% 60.48/25.69 |
% 60.48/25.69 | Applying alpha-rule on (110) yields:
% 60.48/25.69 | (111) multiplication(all_0_9_9, all_19_0_23) = all_63_1_59
% 60.48/25.69 | (112) multiplication(all_0_9_9, one) = all_63_0_58
% 60.48/25.69 | (113) addition(all_63_1_59, all_63_0_58) = all_0_3_3
% 60.48/25.69 |
% 60.48/25.69 | Instantiating (86) with all_70_0_71 yields:
% 60.48/25.69 | (114) multiplication(all_70_0_71, all_0_4_4) = all_31_2_31 & multiplication(all_0_7_7, all_0_9_9) = all_70_0_71
% 60.48/25.69 |
% 60.48/25.69 | Applying alpha-rule on (114) yields:
% 60.48/25.69 | (115) multiplication(all_70_0_71, all_0_4_4) = all_31_2_31
% 60.48/25.69 | (116) multiplication(all_0_7_7, all_0_9_9) = all_70_0_71
% 60.48/25.69 |
% 60.48/25.69 | Instantiating (85) with all_72_0_72 yields:
% 60.48/25.69 | (117) multiplication(all_0_8_8, all_21_1_25) = all_72_0_72 & addition(one, all_72_0_72) = all_21_1_25
% 60.48/25.69 |
% 60.48/25.69 | Applying alpha-rule on (117) yields:
% 60.48/25.69 | (118) multiplication(all_0_8_8, all_21_1_25) = all_72_0_72
% 60.48/25.69 | (119) addition(one, all_72_0_72) = all_21_1_25
% 60.48/25.69 |
% 60.48/25.69 | Instantiating (84) with all_74_0_73 yields:
% 60.48/25.69 | (120) multiplication(all_21_1_25, all_0_8_8) = all_74_0_73 & addition(one, all_74_0_73) = all_21_1_25
% 60.48/25.69 |
% 60.48/25.69 | Applying alpha-rule on (120) yields:
% 60.48/25.69 | (121) multiplication(all_21_1_25, all_0_8_8) = all_74_0_73
% 60.48/25.69 | (122) addition(one, all_74_0_73) = all_21_1_25
% 60.48/25.69 |
% 60.48/25.69 | Instantiating (96) with all_82_0_82 yields:
% 60.48/25.69 | (123) addition(all_82_0_82, all_0_5_5) = all_0_5_5 & addition(all_0_6_6, all_0_6_6) = all_82_0_82
% 60.48/25.69 |
% 60.48/25.69 | Applying alpha-rule on (123) yields:
% 60.48/25.69 | (124) addition(all_82_0_82, all_0_5_5) = all_0_5_5
% 60.48/25.69 | (125) addition(all_0_6_6, all_0_6_6) = all_82_0_82
% 60.48/25.69 |
% 60.48/25.69 | Instantiating (90) with all_87_0_92, all_87_1_93 yields:
% 60.48/25.69 | (126) multiplication(all_0_9_9, all_21_0_24) = all_87_0_92 & multiplication(all_0_9_9, all_21_1_25) = all_87_1_93 & addition(all_87_1_93, all_87_0_92) = all_0_3_3
% 60.48/25.69 |
% 60.48/25.69 | Applying alpha-rule on (126) yields:
% 60.48/25.70 | (127) multiplication(all_0_9_9, all_21_0_24) = all_87_0_92
% 60.48/25.70 | (128) multiplication(all_0_9_9, all_21_1_25) = all_87_1_93
% 60.48/25.70 | (129) addition(all_87_1_93, all_87_0_92) = all_0_3_3
% 60.48/25.70 |
% 60.48/25.70 +-Applying beta-rule and splitting (83), into two cases.
% 60.48/25.70 |-Branch one:
% 60.48/25.70 | (130) all_31_0_29 = 0
% 60.48/25.70 |
% 60.48/25.70 | Equations (130) can reduce 72 to:
% 60.48/25.70 | (68) $false
% 60.48/25.70 |
% 60.48/25.70 |-The branch is then unsatisfiable
% 60.48/25.70 |-Branch two:
% 60.48/25.70 | (72) ~ (all_31_0_29 = 0)
% 60.48/25.70 | (133) ? [v0] : ( ~ (v0 = all_31_1_30) & addition(all_0_3_3, all_31_1_30) = v0)
% 60.48/25.70 |
% 60.48/25.70 | Instantiating (133) with all_98_0_105 yields:
% 60.48/25.70 | (134) ~ (all_98_0_105 = all_31_1_30) & addition(all_0_3_3, all_31_1_30) = all_98_0_105
% 60.48/25.70 |
% 60.48/25.70 | Applying alpha-rule on (134) yields:
% 60.48/25.70 | (135) ~ (all_98_0_105 = all_31_1_30)
% 60.48/25.70 | (136) addition(all_0_3_3, all_31_1_30) = all_98_0_105
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (14) with all_0_7_7, all_0_9_9, all_70_0_71, all_0_5_5 and discharging atoms multiplication(all_0_7_7, all_0_9_9) = all_70_0_71, multiplication(all_0_7_7, all_0_9_9) = all_0_5_5, yields:
% 60.48/25.70 | (137) all_70_0_71 = all_0_5_5
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (14) with all_0_8_8, all_21_1_25, all_54_1_48, all_72_0_72 and discharging atoms multiplication(all_0_8_8, all_21_1_25) = all_72_0_72, multiplication(all_0_8_8, all_21_1_25) = all_54_1_48, yields:
% 60.48/25.70 | (138) all_72_0_72 = all_54_1_48
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (26) with all_58_0_51, all_0_8_8 and discharging atoms multiplication(all_0_8_8, one) = all_58_0_51, yields:
% 60.48/25.70 | (139) all_58_0_51 = all_0_8_8
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (26) with all_63_0_58, all_0_9_9 and discharging atoms multiplication(all_0_9_9, one) = all_63_0_58, yields:
% 60.48/25.70 | (140) all_63_0_58 = all_0_9_9
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (6) with all_46_0_39, all_0_9_9 and discharging atoms multiplication(one, all_0_9_9) = all_46_0_39, yields:
% 60.48/25.70 | (141) all_46_0_39 = all_0_9_9
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (43) with all_82_0_82, all_0_6_6 and discharging atoms addition(all_0_6_6, all_0_6_6) = all_82_0_82, yields:
% 60.48/25.70 | (142) all_82_0_82 = all_0_6_6
% 60.48/25.70 |
% 60.48/25.70 | From (137) and (115) follows:
% 60.48/25.70 | (143) multiplication(all_0_5_5, all_0_4_4) = all_31_2_31
% 60.48/25.70 |
% 60.48/25.70 | From (140) and (112) follows:
% 60.48/25.70 | (144) multiplication(all_0_9_9, one) = all_0_9_9
% 60.48/25.70 |
% 60.48/25.70 | From (141) and (100) follows:
% 60.48/25.70 | (145) multiplication(one, all_0_9_9) = all_0_9_9
% 60.48/25.70 |
% 60.48/25.70 | From (142) and (124) follows:
% 60.48/25.70 | (55) addition(all_0_6_6, all_0_5_5) = all_0_5_5
% 60.48/25.70 |
% 60.48/25.70 | From (140) and (113) follows:
% 60.48/25.70 | (147) addition(all_63_1_59, all_0_9_9) = all_0_3_3
% 60.48/25.70 |
% 60.48/25.70 | From (139) and (109) follows:
% 60.48/25.70 | (148) addition(all_58_1_52, all_0_8_8) = all_19_0_23
% 60.48/25.70 |
% 60.48/25.70 | From (141) and (101) follows:
% 60.48/25.70 | (149) addition(all_46_1_40, all_0_9_9) = all_0_1_1
% 60.48/25.70 |
% 60.48/25.70 | From (142) and (125) follows:
% 60.48/25.70 | (150) addition(all_0_6_6, all_0_6_6) = all_0_6_6
% 60.48/25.70 |
% 60.48/25.70 | From (138) and (119) follows:
% 60.48/25.70 | (151) addition(one, all_54_1_48) = all_21_1_25
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (8) with all_31_2_31, all_0_5_5, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_31_2_31, addition(all_0_6_6, all_0_5_5) = all_0_5_5, yields:
% 60.48/25.70 | (152) ? [v0] : ? [v1] : (multiplication(all_0_5_5, all_0_4_4) = v1 & multiplication(all_0_6_6, all_0_4_4) = v0 & addition(v0, v1) = all_31_2_31)
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (39) with all_63_1_59, all_19_0_23, all_0_4_4, all_0_8_8, all_0_9_9 and discharging atoms multiplication(all_0_8_8, all_0_4_4) = all_19_0_23, multiplication(all_0_9_9, all_19_0_23) = all_63_1_59, yields:
% 60.48/25.70 | (153) ? [v0] : (multiplication(v0, all_0_4_4) = all_63_1_59 & multiplication(all_0_9_9, all_0_8_8) = v0)
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (39) with all_46_1_40, all_0_9_9, one, all_0_9_9, all_23_0_26 and discharging atoms multiplication(all_23_0_26, all_0_9_9) = all_46_1_40, multiplication(all_0_9_9, one) = all_0_9_9, yields:
% 60.48/25.70 | (154) ? [v0] : (multiplication(v0, one) = all_46_1_40 & multiplication(all_23_0_26, all_0_9_9) = v0)
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (44) with all_0_6_6, all_0_9_9, all_0_8_8, all_0_9_9, one and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_0_6_6, multiplication(one, all_0_9_9) = all_0_9_9, yields:
% 60.48/25.70 | (155) ? [v0] : (multiplication(all_0_9_9, all_0_8_8) = v0 & multiplication(one, v0) = all_0_6_6)
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (44) with all_63_1_59, all_0_9_9, all_19_0_23, all_0_9_9, one and discharging atoms multiplication(all_0_9_9, all_19_0_23) = all_63_1_59, multiplication(one, all_0_9_9) = all_0_9_9, yields:
% 60.48/25.70 | (156) ? [v0] : (multiplication(all_0_9_9, all_19_0_23) = v0 & multiplication(one, v0) = all_63_1_59)
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (9) with all_36_0_32, all_0_3_3, all_63_1_59, all_0_9_9, all_0_1_1 and discharging atoms addition(all_63_1_59, all_0_9_9) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_36_0_32, yields:
% 60.48/25.70 | (157) ? [v0] : (addition(all_63_1_59, v0) = all_36_0_32 & addition(all_0_9_9, all_0_1_1) = v0)
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (22) with all_63_1_59, all_19_0_23, all_0_8_8, all_58_1_52, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_19_0_23) = all_63_1_59, addition(all_58_1_52, all_0_8_8) = all_19_0_23, yields:
% 60.48/25.70 | (158) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_58_1_52) = v0 & multiplication(all_0_9_9, all_0_8_8) = v1 & addition(v0, v1) = all_63_1_59)
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (9) with all_36_0_32, all_0_1_1, all_46_1_40, all_0_9_9, all_0_3_3 and discharging atoms addition(all_46_1_40, all_0_9_9) = all_0_1_1, addition(all_0_1_1, all_0_3_3) = all_36_0_32, yields:
% 60.48/25.70 | (159) ? [v0] : (addition(all_46_1_40, v0) = all_36_0_32 & addition(all_0_9_9, all_0_3_3) = v0)
% 60.48/25.70 |
% 60.48/25.70 | Instantiating formula (21) with all_98_0_105, all_31_1_30, all_0_3_3, all_31_2_31, all_0_9_9 and discharging atoms addition(all_31_2_31, all_0_9_9) = all_31_1_30, addition(all_0_3_3, all_31_1_30) = all_98_0_105, yields:
% 60.48/25.71 | (160) ? [v0] : (addition(v0, all_0_9_9) = all_98_0_105 & addition(all_0_3_3, all_31_2_31) = v0)
% 60.48/25.71 |
% 60.48/25.71 | Instantiating formula (9) with all_98_0_105, all_0_3_3, all_63_1_59, all_0_9_9, all_31_1_30 and discharging atoms addition(all_63_1_59, all_0_9_9) = all_0_3_3, addition(all_0_3_3, all_31_1_30) = all_98_0_105, yields:
% 60.48/25.71 | (161) ? [v0] : (addition(all_63_1_59, v0) = all_98_0_105 & addition(all_0_9_9, all_31_1_30) = v0)
% 60.48/25.71 |
% 60.48/25.71 | Instantiating formula (50) with all_98_0_105, all_0_3_3, all_31_1_30 and discharging atoms addition(all_0_3_3, all_31_1_30) = all_98_0_105, yields:
% 60.48/25.71 | (162) addition(all_31_1_30, all_0_3_3) = all_98_0_105
% 60.48/25.71 |
% 60.48/25.71 | Instantiating formula (8) with all_31_2_31, all_0_5_5, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_31_2_31, addition(all_0_5_5, all_0_6_6) = all_0_5_5, yields:
% 60.48/25.71 | (163) ? [v0] : ? [v1] : (multiplication(all_0_5_5, all_0_4_4) = v0 & multiplication(all_0_6_6, all_0_4_4) = v1 & addition(v0, v1) = all_31_2_31)
% 60.48/25.71 |
% 60.48/25.71 | Instantiating formula (47) with all_0_6_6, all_0_6_6, all_0_6_6, all_0_8_8, all_0_9_9, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_0_6_6, addition(all_0_6_6, all_0_6_6) = all_0_6_6, yields:
% 60.48/25.71 | (164) ? [v0] : (multiplication(v0, all_0_8_8) = all_0_6_6 & addition(all_0_9_9, all_0_9_9) = v0)
% 60.48/25.71 |
% 60.48/25.71 | Instantiating formula (21) with all_98_0_105, all_31_1_30, all_0_3_3, all_0_9_9, all_31_2_31 and discharging atoms addition(all_0_3_3, all_31_1_30) = all_98_0_105, addition(all_0_9_9, all_31_2_31) = all_31_1_30, yields:
% 60.48/25.71 | (165) ? [v0] : (addition(v0, all_31_2_31) = all_98_0_105 & addition(all_0_3_3, all_0_9_9) = v0)
% 60.48/25.71 |
% 60.48/25.71 | Instantiating formula (22) with all_87_1_93, all_21_1_25, all_74_0_73, one, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_21_1_25) = all_87_1_93, addition(one, all_74_0_73) = all_21_1_25, yields:
% 60.48/25.71 | (166) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_74_0_73) = v1 & multiplication(all_0_9_9, one) = v0 & addition(v0, v1) = all_87_1_93)
% 60.48/25.71 |
% 60.48/25.71 | Instantiating formula (22) with all_87_1_93, all_21_1_25, all_54_1_48, one, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_21_1_25) = all_87_1_93, addition(one, all_54_1_48) = all_21_1_25, yields:
% 60.48/25.71 | (167) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_54_1_48) = v1 & multiplication(all_0_9_9, one) = v0 & addition(v0, v1) = all_87_1_93)
% 60.48/25.71 |
% 60.48/25.71 | Instantiating formula (8) with all_0_1_1, all_0_2_2, all_0_9_9, all_23_0_26, one and discharging atoms multiplication(all_0_2_2, all_0_9_9) = all_0_1_1, addition(one, all_23_0_26) = all_0_2_2, yields:
% 60.48/25.71 | (168) ? [v0] : ? [v1] : (multiplication(all_23_0_26, all_0_9_9) = v1 & multiplication(one, all_0_9_9) = v0 & addition(v0, v1) = all_0_1_1)
% 60.48/25.71 |
% 60.48/25.71 | Instantiating formula (22) with all_0_3_3, all_0_4_4, all_19_0_23, one, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_4_4) = all_0_3_3, addition(one, all_19_0_23) = all_0_4_4, yields:
% 60.48/25.71 | (169) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_19_0_23) = v1 & multiplication(all_0_9_9, one) = v0 & addition(v0, v1) = all_0_3_3)
% 60.48/25.71 |
% 60.48/25.71 | Instantiating (157) with all_179_0_204 yields:
% 60.48/25.71 | (170) addition(all_63_1_59, all_179_0_204) = all_36_0_32 & addition(all_0_9_9, all_0_1_1) = all_179_0_204
% 60.48/25.71 |
% 60.48/25.71 | Applying alpha-rule on (170) yields:
% 60.48/25.71 | (171) addition(all_63_1_59, all_179_0_204) = all_36_0_32
% 60.48/25.71 | (172) addition(all_0_9_9, all_0_1_1) = all_179_0_204
% 60.48/25.71 |
% 60.48/25.71 | Instantiating (160) with all_187_0_213 yields:
% 60.48/25.71 | (173) addition(all_187_0_213, all_0_9_9) = all_98_0_105 & addition(all_0_3_3, all_31_2_31) = all_187_0_213
% 60.48/25.71 |
% 60.48/25.71 | Applying alpha-rule on (173) yields:
% 60.48/25.71 | (174) addition(all_187_0_213, all_0_9_9) = all_98_0_105
% 60.48/25.71 | (175) addition(all_0_3_3, all_31_2_31) = all_187_0_213
% 60.48/25.71 |
% 60.48/25.71 | Instantiating (159) with all_192_0_223 yields:
% 60.48/25.71 | (176) addition(all_46_1_40, all_192_0_223) = all_36_0_32 & addition(all_0_9_9, all_0_3_3) = all_192_0_223
% 60.48/25.71 |
% 60.48/25.71 | Applying alpha-rule on (176) yields:
% 60.48/25.71 | (177) addition(all_46_1_40, all_192_0_223) = all_36_0_32
% 60.48/25.71 | (178) addition(all_0_9_9, all_0_3_3) = all_192_0_223
% 60.48/25.71 |
% 60.48/25.71 | Instantiating (154) with all_239_0_283 yields:
% 60.48/25.71 | (179) multiplication(all_239_0_283, one) = all_46_1_40 & multiplication(all_23_0_26, all_0_9_9) = all_239_0_283
% 60.48/25.71 |
% 60.48/25.71 | Applying alpha-rule on (179) yields:
% 60.48/25.71 | (180) multiplication(all_239_0_283, one) = all_46_1_40
% 60.48/25.71 | (181) multiplication(all_23_0_26, all_0_9_9) = all_239_0_283
% 60.48/25.71 |
% 60.48/25.71 | Instantiating (152) with all_262_0_300, all_262_1_301 yields:
% 60.48/25.71 | (182) multiplication(all_0_5_5, all_0_4_4) = all_262_0_300 & multiplication(all_0_6_6, all_0_4_4) = all_262_1_301 & addition(all_262_1_301, all_262_0_300) = all_31_2_31
% 60.48/25.71 |
% 60.48/25.71 | Applying alpha-rule on (182) yields:
% 60.48/25.71 | (183) multiplication(all_0_5_5, all_0_4_4) = all_262_0_300
% 60.48/25.71 | (184) multiplication(all_0_6_6, all_0_4_4) = all_262_1_301
% 60.48/25.71 | (185) addition(all_262_1_301, all_262_0_300) = all_31_2_31
% 60.48/25.71 |
% 60.48/25.71 | Instantiating (153) with all_331_0_358 yields:
% 60.48/25.71 | (186) multiplication(all_331_0_358, all_0_4_4) = all_63_1_59 & multiplication(all_0_9_9, all_0_8_8) = all_331_0_358
% 60.48/25.71 |
% 60.48/25.71 | Applying alpha-rule on (186) yields:
% 60.48/25.71 | (187) multiplication(all_331_0_358, all_0_4_4) = all_63_1_59
% 60.48/25.71 | (188) multiplication(all_0_9_9, all_0_8_8) = all_331_0_358
% 60.48/25.71 |
% 60.48/25.71 | Instantiating (164) with all_346_0_373 yields:
% 60.48/25.71 | (189) multiplication(all_346_0_373, all_0_8_8) = all_0_6_6 & addition(all_0_9_9, all_0_9_9) = all_346_0_373
% 60.48/25.71 |
% 60.48/25.71 | Applying alpha-rule on (189) yields:
% 60.48/25.71 | (190) multiplication(all_346_0_373, all_0_8_8) = all_0_6_6
% 60.48/25.71 | (191) addition(all_0_9_9, all_0_9_9) = all_346_0_373
% 60.48/25.71 |
% 60.48/25.71 | Instantiating (168) with all_359_0_388, all_359_1_389 yields:
% 60.48/25.71 | (192) multiplication(all_23_0_26, all_0_9_9) = all_359_0_388 & multiplication(one, all_0_9_9) = all_359_1_389 & addition(all_359_1_389, all_359_0_388) = all_0_1_1
% 60.48/25.71 |
% 60.48/25.71 | Applying alpha-rule on (192) yields:
% 60.48/25.72 | (193) multiplication(all_23_0_26, all_0_9_9) = all_359_0_388
% 60.48/25.72 | (194) multiplication(one, all_0_9_9) = all_359_1_389
% 60.48/25.72 | (195) addition(all_359_1_389, all_359_0_388) = all_0_1_1
% 60.48/25.72 |
% 60.48/25.72 | Instantiating (169) with all_365_0_392, all_365_1_393 yields:
% 60.48/25.72 | (196) multiplication(all_0_9_9, all_19_0_23) = all_365_0_392 & multiplication(all_0_9_9, one) = all_365_1_393 & addition(all_365_1_393, all_365_0_392) = all_0_3_3
% 60.48/25.72 |
% 60.48/25.72 | Applying alpha-rule on (196) yields:
% 60.48/25.72 | (197) multiplication(all_0_9_9, all_19_0_23) = all_365_0_392
% 60.48/25.72 | (198) multiplication(all_0_9_9, one) = all_365_1_393
% 60.48/25.72 | (199) addition(all_365_1_393, all_365_0_392) = all_0_3_3
% 60.48/25.72 |
% 60.48/25.72 | Instantiating (163) with all_368_0_397, all_368_1_398 yields:
% 60.48/25.72 | (200) multiplication(all_0_5_5, all_0_4_4) = all_368_1_398 & multiplication(all_0_6_6, all_0_4_4) = all_368_0_397 & addition(all_368_1_398, all_368_0_397) = all_31_2_31
% 60.48/25.72 |
% 60.48/25.72 | Applying alpha-rule on (200) yields:
% 60.48/25.72 | (201) multiplication(all_0_5_5, all_0_4_4) = all_368_1_398
% 60.48/25.72 | (202) multiplication(all_0_6_6, all_0_4_4) = all_368_0_397
% 60.48/25.72 | (203) addition(all_368_1_398, all_368_0_397) = all_31_2_31
% 60.48/25.72 |
% 60.48/25.72 | Instantiating (167) with all_382_0_416, all_382_1_417 yields:
% 60.48/25.72 | (204) multiplication(all_0_9_9, all_54_1_48) = all_382_0_416 & multiplication(all_0_9_9, one) = all_382_1_417 & addition(all_382_1_417, all_382_0_416) = all_87_1_93
% 60.48/25.72 |
% 60.48/25.72 | Applying alpha-rule on (204) yields:
% 60.48/25.72 | (205) multiplication(all_0_9_9, all_54_1_48) = all_382_0_416
% 60.48/25.72 | (206) multiplication(all_0_9_9, one) = all_382_1_417
% 60.48/25.72 | (207) addition(all_382_1_417, all_382_0_416) = all_87_1_93
% 60.48/25.72 |
% 60.48/25.72 | Instantiating (161) with all_384_0_418 yields:
% 60.48/25.72 | (208) addition(all_63_1_59, all_384_0_418) = all_98_0_105 & addition(all_0_9_9, all_31_1_30) = all_384_0_418
% 60.48/25.72 |
% 60.48/25.72 | Applying alpha-rule on (208) yields:
% 60.48/25.72 | (209) addition(all_63_1_59, all_384_0_418) = all_98_0_105
% 60.48/25.72 | (210) addition(all_0_9_9, all_31_1_30) = all_384_0_418
% 60.48/25.72 |
% 60.48/25.72 | Instantiating (165) with all_393_0_432 yields:
% 60.48/25.72 | (211) addition(all_393_0_432, all_31_2_31) = all_98_0_105 & addition(all_0_3_3, all_0_9_9) = all_393_0_432
% 60.48/25.72 |
% 60.48/25.72 | Applying alpha-rule on (211) yields:
% 60.48/25.72 | (212) addition(all_393_0_432, all_31_2_31) = all_98_0_105
% 60.48/25.72 | (213) addition(all_0_3_3, all_0_9_9) = all_393_0_432
% 60.48/25.72 |
% 60.48/25.72 | Instantiating (166) with all_413_0_464, all_413_1_465 yields:
% 60.48/25.72 | (214) multiplication(all_0_9_9, all_74_0_73) = all_413_0_464 & multiplication(all_0_9_9, one) = all_413_1_465 & addition(all_413_1_465, all_413_0_464) = all_87_1_93
% 60.48/25.72 |
% 60.48/25.72 | Applying alpha-rule on (214) yields:
% 60.48/25.72 | (215) multiplication(all_0_9_9, all_74_0_73) = all_413_0_464
% 60.48/25.72 | (216) multiplication(all_0_9_9, one) = all_413_1_465
% 60.48/25.72 | (217) addition(all_413_1_465, all_413_0_464) = all_87_1_93
% 60.48/25.72 |
% 60.48/25.72 | Instantiating (158) with all_457_0_517, all_457_1_518 yields:
% 60.48/25.72 | (218) multiplication(all_0_9_9, all_58_1_52) = all_457_1_518 & multiplication(all_0_9_9, all_0_8_8) = all_457_0_517 & addition(all_457_1_518, all_457_0_517) = all_63_1_59
% 60.48/25.72 |
% 60.48/25.72 | Applying alpha-rule on (218) yields:
% 60.48/25.72 | (219) multiplication(all_0_9_9, all_58_1_52) = all_457_1_518
% 60.48/25.72 | (220) multiplication(all_0_9_9, all_0_8_8) = all_457_0_517
% 60.48/25.72 | (221) addition(all_457_1_518, all_457_0_517) = all_63_1_59
% 60.48/25.72 |
% 60.48/25.72 | Instantiating (156) with all_472_0_530 yields:
% 60.48/25.72 | (222) multiplication(all_0_9_9, all_19_0_23) = all_472_0_530 & multiplication(one, all_472_0_530) = all_63_1_59
% 60.48/25.72 |
% 60.48/25.72 | Applying alpha-rule on (222) yields:
% 60.48/25.72 | (223) multiplication(all_0_9_9, all_19_0_23) = all_472_0_530
% 60.48/25.72 | (224) multiplication(one, all_472_0_530) = all_63_1_59
% 60.48/25.72 |
% 60.48/25.72 | Instantiating (155) with all_513_0_553 yields:
% 60.48/25.72 | (225) multiplication(all_0_9_9, all_0_8_8) = all_513_0_553 & multiplication(one, all_513_0_553) = all_0_6_6
% 60.48/25.72 |
% 60.48/25.72 | Applying alpha-rule on (225) yields:
% 60.48/25.72 | (226) multiplication(all_0_9_9, all_0_8_8) = all_513_0_553
% 60.48/25.72 | (227) multiplication(one, all_513_0_553) = all_0_6_6
% 60.48/25.72 |
% 60.48/25.72 | Instantiating formula (14) with all_23_0_26, all_0_9_9, all_359_0_388, all_46_1_40 and discharging atoms multiplication(all_23_0_26, all_0_9_9) = all_359_0_388, multiplication(all_23_0_26, all_0_9_9) = all_46_1_40, yields:
% 60.48/25.72 | (228) all_359_0_388 = all_46_1_40
% 60.48/25.72 |
% 60.48/25.72 | Instantiating formula (14) with all_23_0_26, all_0_9_9, all_239_0_283, all_359_0_388 and discharging atoms multiplication(all_23_0_26, all_0_9_9) = all_359_0_388, multiplication(all_23_0_26, all_0_9_9) = all_239_0_283, yields:
% 60.48/25.72 | (229) all_359_0_388 = all_239_0_283
% 60.48/25.72 |
% 60.48/25.72 | Instantiating formula (14) with all_0_5_5, all_0_4_4, all_368_1_398, all_31_2_31 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_368_1_398, multiplication(all_0_5_5, all_0_4_4) = all_31_2_31, yields:
% 60.48/25.72 | (230) all_368_1_398 = all_31_2_31
% 60.48/25.72 |
% 60.48/25.72 | Instantiating formula (14) with all_0_5_5, all_0_4_4, all_262_0_300, all_368_1_398 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_368_1_398, multiplication(all_0_5_5, all_0_4_4) = all_262_0_300, yields:
% 60.48/25.72 | (231) all_368_1_398 = all_262_0_300
% 60.48/25.72 |
% 60.48/25.72 | Instantiating formula (14) with all_0_6_6, all_0_4_4, all_262_1_301, all_368_0_397 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_368_0_397, multiplication(all_0_6_6, all_0_4_4) = all_262_1_301, yields:
% 60.48/25.72 | (232) all_368_0_397 = all_262_1_301
% 60.48/25.72 |
% 60.48/25.72 | Instantiating formula (14) with all_0_9_9, all_19_0_23, all_365_0_392, all_472_0_530 and discharging atoms multiplication(all_0_9_9, all_19_0_23) = all_472_0_530, multiplication(all_0_9_9, all_19_0_23) = all_365_0_392, yields:
% 60.48/25.72 | (233) all_472_0_530 = all_365_0_392
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (14) with all_0_9_9, all_0_8_8, all_457_0_517, all_513_0_553 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_513_0_553, multiplication(all_0_9_9, all_0_8_8) = all_457_0_517, yields:
% 60.48/25.73 | (234) all_513_0_553 = all_457_0_517
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (14) with all_0_9_9, all_0_8_8, all_331_0_358, all_513_0_553 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_513_0_553, multiplication(all_0_9_9, all_0_8_8) = all_331_0_358, yields:
% 60.48/25.73 | (235) all_513_0_553 = all_331_0_358
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (14) with all_0_9_9, one, all_382_1_417, all_413_1_465 and discharging atoms multiplication(all_0_9_9, one) = all_413_1_465, multiplication(all_0_9_9, one) = all_382_1_417, yields:
% 60.48/25.73 | (236) all_413_1_465 = all_382_1_417
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (26) with all_382_1_417, all_0_9_9 and discharging atoms multiplication(all_0_9_9, one) = all_382_1_417, yields:
% 60.48/25.73 | (237) all_382_1_417 = all_0_9_9
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (14) with all_0_9_9, one, all_365_1_393, all_413_1_465 and discharging atoms multiplication(all_0_9_9, one) = all_413_1_465, multiplication(all_0_9_9, one) = all_365_1_393, yields:
% 60.48/25.73 | (238) all_413_1_465 = all_365_1_393
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (6) with all_0_6_6, all_513_0_553 and discharging atoms multiplication(one, all_513_0_553) = all_0_6_6, yields:
% 60.48/25.73 | (239) all_513_0_553 = all_0_6_6
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (6) with all_63_1_59, all_472_0_530 and discharging atoms multiplication(one, all_472_0_530) = all_63_1_59, yields:
% 60.48/25.73 | (240) all_472_0_530 = all_63_1_59
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (6) with all_359_1_389, all_0_9_9 and discharging atoms multiplication(one, all_0_9_9) = all_359_1_389, yields:
% 60.48/25.73 | (241) all_359_1_389 = all_0_9_9
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (43) with all_346_0_373, all_0_9_9 and discharging atoms addition(all_0_9_9, all_0_9_9) = all_346_0_373, yields:
% 60.48/25.73 | (242) all_346_0_373 = all_0_9_9
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (239,234) yields a new equation:
% 60.48/25.73 | (243) all_457_0_517 = all_0_6_6
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (235,234) yields a new equation:
% 60.48/25.73 | (244) all_457_0_517 = all_331_0_358
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (240,233) yields a new equation:
% 60.48/25.73 | (245) all_365_0_392 = all_63_1_59
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (244,243) yields a new equation:
% 60.48/25.73 | (246) all_331_0_358 = all_0_6_6
% 60.48/25.73 |
% 60.48/25.73 | Simplifying 246 yields:
% 60.48/25.73 | (247) all_331_0_358 = all_0_6_6
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (236,238) yields a new equation:
% 60.48/25.73 | (248) all_382_1_417 = all_365_1_393
% 60.48/25.73 |
% 60.48/25.73 | Simplifying 248 yields:
% 60.48/25.73 | (249) all_382_1_417 = all_365_1_393
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (249,237) yields a new equation:
% 60.48/25.73 | (250) all_365_1_393 = all_0_9_9
% 60.48/25.73 |
% 60.48/25.73 | Simplifying 250 yields:
% 60.48/25.73 | (251) all_365_1_393 = all_0_9_9
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (230,231) yields a new equation:
% 60.48/25.73 | (252) all_262_0_300 = all_31_2_31
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (228,229) yields a new equation:
% 60.48/25.73 | (253) all_239_0_283 = all_46_1_40
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (253,229) yields a new equation:
% 60.48/25.73 | (228) all_359_0_388 = all_46_1_40
% 60.48/25.73 |
% 60.48/25.73 | Combining equations (252,231) yields a new equation:
% 60.48/25.73 | (230) all_368_1_398 = all_31_2_31
% 60.48/25.73 |
% 60.48/25.73 | From (247) and (187) follows:
% 60.48/25.73 | (256) multiplication(all_0_6_6, all_0_4_4) = all_63_1_59
% 60.48/25.73 |
% 60.48/25.73 | From (232) and (202) follows:
% 60.48/25.73 | (184) multiplication(all_0_6_6, all_0_4_4) = all_262_1_301
% 60.48/25.73 |
% 60.48/25.73 | From (230)(232) and (203) follows:
% 60.48/25.73 | (258) addition(all_31_2_31, all_262_1_301) = all_31_2_31
% 60.48/25.73 |
% 60.48/25.73 | From (251)(245) and (199) follows:
% 60.48/25.73 | (259) addition(all_0_9_9, all_63_1_59) = all_0_3_3
% 60.48/25.73 |
% 60.48/25.73 | From (241)(228) and (195) follows:
% 60.48/25.73 | (260) addition(all_0_9_9, all_46_1_40) = all_0_1_1
% 60.48/25.73 |
% 60.48/25.73 | From (252) and (185) follows:
% 60.48/25.73 | (261) addition(all_262_1_301, all_31_2_31) = all_31_2_31
% 60.48/25.73 |
% 60.48/25.73 | From (242) and (191) follows:
% 60.48/25.73 | (262) addition(all_0_9_9, all_0_9_9) = all_0_9_9
% 60.48/25.73 |
% 60.48/25.73 | Instantiating formula (14) with all_0_6_6, all_0_4_4, all_63_1_59, all_262_1_301 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_262_1_301, multiplication(all_0_6_6, all_0_4_4) = all_63_1_59, yields:
% 60.48/25.73 | (263) all_262_1_301 = all_63_1_59
% 60.48/25.73 |
% 60.48/25.73 | From (263) and (261) follows:
% 60.48/25.73 | (264) addition(all_63_1_59, all_31_2_31) = all_31_2_31
% 60.48/25.73 |
% 60.48/25.73 | From (263) and (258) follows:
% 60.48/25.73 | (265) addition(all_31_2_31, all_63_1_59) = all_31_2_31
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (9) with all_98_0_105, all_31_1_30, all_0_9_9, all_31_2_31, all_0_3_3 and discharging atoms addition(all_31_1_30, all_0_3_3) = all_98_0_105, addition(all_0_9_9, all_31_2_31) = all_31_1_30, yields:
% 60.48/25.74 | (266) ? [v0] : (addition(all_31_2_31, all_0_3_3) = v0 & addition(all_0_9_9, v0) = all_98_0_105)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (21) with all_31_1_30, all_31_2_31, all_0_9_9, all_31_2_31, all_63_1_59 and discharging atoms addition(all_31_2_31, all_63_1_59) = all_31_2_31, addition(all_0_9_9, all_31_2_31) = all_31_1_30, yields:
% 60.48/25.74 | (267) ? [v0] : (addition(v0, all_63_1_59) = all_31_1_30 & addition(all_0_9_9, all_31_2_31) = v0)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (9) with all_187_0_213, all_0_3_3, all_63_1_59, all_0_9_9, all_31_2_31 and discharging atoms addition(all_63_1_59, all_0_9_9) = all_0_3_3, addition(all_0_3_3, all_31_2_31) = all_187_0_213, yields:
% 60.48/25.74 | (268) ? [v0] : (addition(all_63_1_59, v0) = all_187_0_213 & addition(all_0_9_9, all_31_2_31) = v0)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (50) with all_187_0_213, all_0_3_3, all_31_2_31 and discharging atoms addition(all_0_3_3, all_31_2_31) = all_187_0_213, yields:
% 60.48/25.74 | (269) addition(all_31_2_31, all_0_3_3) = all_187_0_213
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (9) with all_393_0_432, all_0_3_3, all_63_1_59, all_0_9_9, all_0_9_9 and discharging atoms addition(all_63_1_59, all_0_9_9) = all_0_3_3, addition(all_0_3_3, all_0_9_9) = all_393_0_432, yields:
% 60.48/25.74 | (270) ? [v0] : (addition(all_63_1_59, v0) = all_393_0_432 & addition(all_0_9_9, all_0_9_9) = v0)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (9) with all_187_0_213, all_0_3_3, all_0_9_9, all_63_1_59, all_31_2_31 and discharging atoms addition(all_0_3_3, all_31_2_31) = all_187_0_213, addition(all_0_9_9, all_63_1_59) = all_0_3_3, yields:
% 60.48/25.74 | (271) ? [v0] : (addition(all_63_1_59, all_31_2_31) = v0 & addition(all_0_9_9, v0) = all_187_0_213)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (21) with all_384_0_418, all_31_1_30, all_0_9_9, all_31_2_31, all_0_9_9 and discharging atoms addition(all_31_2_31, all_0_9_9) = all_31_1_30, addition(all_0_9_9, all_31_1_30) = all_384_0_418, yields:
% 60.48/25.74 | (272) ? [v0] : (addition(v0, all_0_9_9) = all_384_0_418 & addition(all_0_9_9, all_31_2_31) = v0)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (21) with all_384_0_418, all_31_1_30, all_0_9_9, all_0_9_9, all_31_2_31 and discharging atoms addition(all_0_9_9, all_31_1_30) = all_384_0_418, addition(all_0_9_9, all_31_2_31) = all_31_1_30, yields:
% 60.48/25.74 | (273) ? [v0] : (addition(v0, all_31_2_31) = all_384_0_418 & addition(all_0_9_9, all_0_9_9) = v0)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (21) with all_179_0_204, all_0_1_1, all_0_9_9, all_0_9_9, all_46_1_40 and discharging atoms addition(all_0_9_9, all_46_1_40) = all_0_1_1, addition(all_0_9_9, all_0_1_1) = all_179_0_204, yields:
% 60.48/25.74 | (274) ? [v0] : (addition(v0, all_46_1_40) = all_179_0_204 & addition(all_0_9_9, all_0_9_9) = v0)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (21) with all_192_0_223, all_0_3_3, all_0_9_9, all_0_9_9, all_63_1_59 and discharging atoms addition(all_0_9_9, all_63_1_59) = all_0_3_3, addition(all_0_9_9, all_0_3_3) = all_192_0_223, yields:
% 60.48/25.74 | (275) ? [v0] : (addition(v0, all_63_1_59) = all_192_0_223 & addition(all_0_9_9, all_0_9_9) = v0)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (9) with all_31_1_30, all_0_9_9, all_0_9_9, all_0_9_9, all_31_2_31 and discharging atoms addition(all_0_9_9, all_31_2_31) = all_31_1_30, addition(all_0_9_9, all_0_9_9) = all_0_9_9, yields:
% 60.48/25.74 | (276) ? [v0] : (addition(all_0_9_9, v0) = all_31_1_30 & addition(all_0_9_9, all_31_2_31) = v0)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating formula (9) with all_384_0_418, all_0_9_9, all_0_9_9, all_0_9_9, all_31_1_30 and discharging atoms addition(all_0_9_9, all_31_1_30) = all_384_0_418, addition(all_0_9_9, all_0_9_9) = all_0_9_9, yields:
% 60.48/25.74 | (277) ? [v0] : (addition(all_0_9_9, v0) = all_384_0_418 & addition(all_0_9_9, all_31_1_30) = v0)
% 60.48/25.74 |
% 60.48/25.74 | Instantiating (268) with all_895_0_1008 yields:
% 60.48/25.74 | (278) addition(all_63_1_59, all_895_0_1008) = all_187_0_213 & addition(all_0_9_9, all_31_2_31) = all_895_0_1008
% 60.48/25.74 |
% 60.48/25.74 | Applying alpha-rule on (278) yields:
% 60.48/25.74 | (279) addition(all_63_1_59, all_895_0_1008) = all_187_0_213
% 60.48/25.74 | (280) addition(all_0_9_9, all_31_2_31) = all_895_0_1008
% 60.48/25.74 |
% 60.48/25.74 | Instantiating (267) with all_1334_0_1603 yields:
% 60.48/25.74 | (281) addition(all_1334_0_1603, all_63_1_59) = all_31_1_30 & addition(all_0_9_9, all_31_2_31) = all_1334_0_1603
% 60.75/25.74 |
% 60.75/25.74 | Applying alpha-rule on (281) yields:
% 60.75/25.74 | (282) addition(all_1334_0_1603, all_63_1_59) = all_31_1_30
% 60.75/25.74 | (283) addition(all_0_9_9, all_31_2_31) = all_1334_0_1603
% 60.75/25.74 |
% 60.75/25.74 | Instantiating (266) with all_1412_0_1708 yields:
% 60.75/25.74 | (284) addition(all_31_2_31, all_0_3_3) = all_1412_0_1708 & addition(all_0_9_9, all_1412_0_1708) = all_98_0_105
% 60.75/25.74 |
% 60.75/25.74 | Applying alpha-rule on (284) yields:
% 60.75/25.74 | (285) addition(all_31_2_31, all_0_3_3) = all_1412_0_1708
% 60.75/25.74 | (286) addition(all_0_9_9, all_1412_0_1708) = all_98_0_105
% 60.75/25.74 |
% 60.75/25.74 | Instantiating (274) with all_1489_0_1786 yields:
% 60.75/25.74 | (287) addition(all_1489_0_1786, all_46_1_40) = all_179_0_204 & addition(all_0_9_9, all_0_9_9) = all_1489_0_1786
% 60.75/25.74 |
% 60.75/25.74 | Applying alpha-rule on (287) yields:
% 60.75/25.74 | (288) addition(all_1489_0_1786, all_46_1_40) = all_179_0_204
% 60.75/25.74 | (289) addition(all_0_9_9, all_0_9_9) = all_1489_0_1786
% 60.75/25.74 |
% 60.75/25.74 | Instantiating (275) with all_2206_0_2692 yields:
% 60.75/25.74 | (290) addition(all_2206_0_2692, all_63_1_59) = all_192_0_223 & addition(all_0_9_9, all_0_9_9) = all_2206_0_2692
% 60.75/25.74 |
% 60.75/25.74 | Applying alpha-rule on (290) yields:
% 60.75/25.74 | (291) addition(all_2206_0_2692, all_63_1_59) = all_192_0_223
% 60.75/25.74 | (292) addition(all_0_9_9, all_0_9_9) = all_2206_0_2692
% 60.75/25.74 |
% 60.75/25.74 | Instantiating (270) with all_2277_0_2752 yields:
% 60.75/25.74 | (293) addition(all_63_1_59, all_2277_0_2752) = all_393_0_432 & addition(all_0_9_9, all_0_9_9) = all_2277_0_2752
% 60.75/25.74 |
% 60.75/25.74 | Applying alpha-rule on (293) yields:
% 60.75/25.74 | (294) addition(all_63_1_59, all_2277_0_2752) = all_393_0_432
% 60.75/25.74 | (295) addition(all_0_9_9, all_0_9_9) = all_2277_0_2752
% 60.75/25.74 |
% 60.75/25.74 | Instantiating (276) with all_2315_0_2800 yields:
% 60.75/25.74 | (296) addition(all_0_9_9, all_2315_0_2800) = all_31_1_30 & addition(all_0_9_9, all_31_2_31) = all_2315_0_2800
% 60.75/25.74 |
% 60.75/25.74 | Applying alpha-rule on (296) yields:
% 60.75/25.74 | (297) addition(all_0_9_9, all_2315_0_2800) = all_31_1_30
% 60.75/25.74 | (298) addition(all_0_9_9, all_31_2_31) = all_2315_0_2800
% 60.75/25.74 |
% 60.75/25.74 | Instantiating (273) with all_2773_0_3469 yields:
% 60.75/25.74 | (299) addition(all_2773_0_3469, all_31_2_31) = all_384_0_418 & addition(all_0_9_9, all_0_9_9) = all_2773_0_3469
% 60.75/25.74 |
% 60.75/25.74 | Applying alpha-rule on (299) yields:
% 60.75/25.74 | (300) addition(all_2773_0_3469, all_31_2_31) = all_384_0_418
% 60.75/25.74 | (301) addition(all_0_9_9, all_0_9_9) = all_2773_0_3469
% 60.75/25.74 |
% 60.75/25.74 | Instantiating (272) with all_2777_0_3476 yields:
% 60.75/25.74 | (302) addition(all_2777_0_3476, all_0_9_9) = all_384_0_418 & addition(all_0_9_9, all_31_2_31) = all_2777_0_3476
% 60.75/25.75 |
% 60.75/25.75 | Applying alpha-rule on (302) yields:
% 60.75/25.75 | (303) addition(all_2777_0_3476, all_0_9_9) = all_384_0_418
% 60.75/25.75 | (304) addition(all_0_9_9, all_31_2_31) = all_2777_0_3476
% 60.75/25.75 |
% 60.75/25.75 | Instantiating (271) with all_2949_0_3718 yields:
% 60.75/25.75 | (305) addition(all_63_1_59, all_31_2_31) = all_2949_0_3718 & addition(all_0_9_9, all_2949_0_3718) = all_187_0_213
% 60.75/25.75 |
% 60.75/25.75 | Applying alpha-rule on (305) yields:
% 60.75/25.75 | (306) addition(all_63_1_59, all_31_2_31) = all_2949_0_3718
% 60.75/25.75 | (307) addition(all_0_9_9, all_2949_0_3718) = all_187_0_213
% 60.75/25.75 |
% 60.75/25.75 | Instantiating (277) with all_3802_0_4827 yields:
% 60.75/25.75 | (308) addition(all_0_9_9, all_3802_0_4827) = all_384_0_418 & addition(all_0_9_9, all_31_1_30) = all_3802_0_4827
% 60.75/25.75 |
% 60.75/25.75 | Applying alpha-rule on (308) yields:
% 60.75/25.75 | (309) addition(all_0_9_9, all_3802_0_4827) = all_384_0_418
% 60.75/25.75 | (310) addition(all_0_9_9, all_31_1_30) = all_3802_0_4827
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_63_1_59, all_31_2_31, all_2949_0_3718, all_31_2_31 and discharging atoms addition(all_63_1_59, all_31_2_31) = all_2949_0_3718, addition(all_63_1_59, all_31_2_31) = all_31_2_31, yields:
% 60.75/25.75 | (311) all_2949_0_3718 = all_31_2_31
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_31_2_31, all_0_3_3, all_187_0_213, all_1412_0_1708 and discharging atoms addition(all_31_2_31, all_0_3_3) = all_1412_0_1708, addition(all_31_2_31, all_0_3_3) = all_187_0_213, yields:
% 60.75/25.75 | (312) all_1412_0_1708 = all_187_0_213
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_31_1_30, all_3802_0_4827, all_384_0_418 and discharging atoms addition(all_0_9_9, all_31_1_30) = all_3802_0_4827, addition(all_0_9_9, all_31_1_30) = all_384_0_418, yields:
% 60.75/25.75 | (313) all_3802_0_4827 = all_384_0_418
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_31_2_31, all_2315_0_2800, all_31_1_30 and discharging atoms addition(all_0_9_9, all_31_2_31) = all_2315_0_2800, addition(all_0_9_9, all_31_2_31) = all_31_1_30, yields:
% 60.75/25.75 | (314) all_2315_0_2800 = all_31_1_30
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_31_2_31, all_2315_0_2800, all_2777_0_3476 and discharging atoms addition(all_0_9_9, all_31_2_31) = all_2777_0_3476, addition(all_0_9_9, all_31_2_31) = all_2315_0_2800, yields:
% 60.75/25.75 | (315) all_2777_0_3476 = all_2315_0_2800
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_31_2_31, all_1334_0_1603, all_2777_0_3476 and discharging atoms addition(all_0_9_9, all_31_2_31) = all_2777_0_3476, addition(all_0_9_9, all_31_2_31) = all_1334_0_1603, yields:
% 60.75/25.75 | (316) all_2777_0_3476 = all_1334_0_1603
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_31_2_31, all_895_0_1008, all_2315_0_2800 and discharging atoms addition(all_0_9_9, all_31_2_31) = all_2315_0_2800, addition(all_0_9_9, all_31_2_31) = all_895_0_1008, yields:
% 60.75/25.75 | (317) all_2315_0_2800 = all_895_0_1008
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_0_9_9, all_2277_0_2752, all_2773_0_3469 and discharging atoms addition(all_0_9_9, all_0_9_9) = all_2773_0_3469, addition(all_0_9_9, all_0_9_9) = all_2277_0_2752, yields:
% 60.75/25.75 | (318) all_2773_0_3469 = all_2277_0_2752
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (43) with all_2277_0_2752, all_0_9_9 and discharging atoms addition(all_0_9_9, all_0_9_9) = all_2277_0_2752, yields:
% 60.75/25.75 | (319) all_2277_0_2752 = all_0_9_9
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_0_9_9, all_2206_0_2692, all_2773_0_3469 and discharging atoms addition(all_0_9_9, all_0_9_9) = all_2773_0_3469, addition(all_0_9_9, all_0_9_9) = all_2206_0_2692, yields:
% 60.75/25.75 | (320) all_2773_0_3469 = all_2206_0_2692
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_0_9_9, all_1489_0_1786, all_2277_0_2752 and discharging atoms addition(all_0_9_9, all_0_9_9) = all_2277_0_2752, addition(all_0_9_9, all_0_9_9) = all_1489_0_1786, yields:
% 60.75/25.75 | (321) all_2277_0_2752 = all_1489_0_1786
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (315,316) yields a new equation:
% 60.75/25.75 | (322) all_2315_0_2800 = all_1334_0_1603
% 60.75/25.75 |
% 60.75/25.75 | Simplifying 322 yields:
% 60.75/25.75 | (323) all_2315_0_2800 = all_1334_0_1603
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (318,320) yields a new equation:
% 60.75/25.75 | (324) all_2277_0_2752 = all_2206_0_2692
% 60.75/25.75 |
% 60.75/25.75 | Simplifying 324 yields:
% 60.75/25.75 | (325) all_2277_0_2752 = all_2206_0_2692
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (317,323) yields a new equation:
% 60.75/25.75 | (326) all_1334_0_1603 = all_895_0_1008
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (314,323) yields a new equation:
% 60.75/25.75 | (327) all_1334_0_1603 = all_31_1_30
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (321,325) yields a new equation:
% 60.75/25.75 | (328) all_2206_0_2692 = all_1489_0_1786
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (319,325) yields a new equation:
% 60.75/25.75 | (329) all_2206_0_2692 = all_0_9_9
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (329,328) yields a new equation:
% 60.75/25.75 | (330) all_1489_0_1786 = all_0_9_9
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (327,326) yields a new equation:
% 60.75/25.75 | (331) all_895_0_1008 = all_31_1_30
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (330,328) yields a new equation:
% 60.75/25.75 | (329) all_2206_0_2692 = all_0_9_9
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (329,320) yields a new equation:
% 60.75/25.75 | (333) all_2773_0_3469 = all_0_9_9
% 60.75/25.75 |
% 60.75/25.75 | From (333) and (300) follows:
% 60.75/25.75 | (334) addition(all_0_9_9, all_31_2_31) = all_384_0_418
% 60.75/25.75 |
% 60.75/25.75 | From (311) and (307) follows:
% 60.75/25.75 | (335) addition(all_0_9_9, all_31_2_31) = all_187_0_213
% 60.75/25.75 |
% 60.75/25.75 | From (312) and (286) follows:
% 60.75/25.75 | (336) addition(all_0_9_9, all_187_0_213) = all_98_0_105
% 60.75/25.75 |
% 60.75/25.75 | From (313) and (310) follows:
% 60.75/25.75 | (210) addition(all_0_9_9, all_31_1_30) = all_384_0_418
% 60.75/25.75 |
% 60.75/25.75 | From (331) and (280) follows:
% 60.75/25.75 | (87) addition(all_0_9_9, all_31_2_31) = all_31_1_30
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_31_2_31, all_384_0_418, all_31_1_30 and discharging atoms addition(all_0_9_9, all_31_2_31) = all_384_0_418, addition(all_0_9_9, all_31_2_31) = all_31_1_30, yields:
% 60.75/25.75 | (339) all_384_0_418 = all_31_1_30
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_31_2_31, all_187_0_213, all_384_0_418 and discharging atoms addition(all_0_9_9, all_31_2_31) = all_384_0_418, addition(all_0_9_9, all_31_2_31) = all_187_0_213, yields:
% 60.75/25.75 | (340) all_384_0_418 = all_187_0_213
% 60.75/25.75 |
% 60.75/25.75 | Combining equations (340,339) yields a new equation:
% 60.75/25.75 | (341) all_187_0_213 = all_31_1_30
% 60.75/25.75 |
% 60.75/25.75 | Simplifying 341 yields:
% 60.75/25.75 | (342) all_187_0_213 = all_31_1_30
% 60.75/25.75 |
% 60.75/25.75 | From (342) and (336) follows:
% 60.75/25.75 | (343) addition(all_0_9_9, all_31_1_30) = all_98_0_105
% 60.75/25.75 |
% 60.75/25.75 | From (339) and (210) follows:
% 60.75/25.75 | (344) addition(all_0_9_9, all_31_1_30) = all_31_1_30
% 60.75/25.75 |
% 60.75/25.75 | Instantiating formula (33) with all_0_9_9, all_31_1_30, all_98_0_105, all_31_1_30 and discharging atoms addition(all_0_9_9, all_31_1_30) = all_98_0_105, addition(all_0_9_9, all_31_1_30) = all_31_1_30, yields:
% 60.75/25.75 | (345) all_98_0_105 = all_31_1_30
% 60.75/25.75 |
% 60.75/25.75 | Equations (345) can reduce 135 to:
% 60.75/25.75 | (68) $false
% 60.75/25.75 |
% 60.75/25.75 |-The branch is then unsatisfiable
% 60.75/25.75 % SZS output end Proof for theBenchmark
% 60.75/25.75
% 60.75/25.75 25169ms
%------------------------------------------------------------------------------