TSTP Solution File: HAL002+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : HAL002+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 : Sat Jul 16 12:45:06 EDT 2022
% Result : Theorem 7.07s 2.28s
% Output : Proof 21.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : HAL002+1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 21:23:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.58/0.59 ____ _
% 0.58/0.59 ___ / __ \_____(_)___ ________ __________
% 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.59
% 0.58/0.59 A Theorem Prover for First-Order Logic
% 0.58/0.60 (ePrincess v.1.0)
% 0.58/0.60
% 0.58/0.60 (c) Philipp Rümmer, 2009-2015
% 0.58/0.60 (c) Peter Backeman, 2014-2015
% 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.60 Bug reports to peter@backeman.se
% 0.58/0.60
% 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.60
% 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/0.96 Prover 0: Preprocessing ...
% 2.69/1.25 Prover 0: Constructing countermodel ...
% 3.24/1.45 Prover 0: gave up
% 3.24/1.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.67/1.49 Prover 1: Preprocessing ...
% 4.23/1.64 Prover 1: Constructing countermodel ...
% 5.05/1.79 Prover 1: gave up
% 5.05/1.79 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.17/1.82 Prover 2: Preprocessing ...
% 6.05/2.01 Prover 2: Warning: ignoring some quantifiers
% 6.05/2.02 Prover 2: Constructing countermodel ...
% 7.07/2.28 Prover 2: proved (494ms)
% 7.07/2.28
% 7.07/2.28 No countermodel exists, formula is valid
% 7.07/2.28 % SZS status Theorem for theBenchmark
% 7.07/2.28
% 7.07/2.28 Generating proof ... Warning: ignoring some quantifiers
% 20.79/5.55 found it (size 210)
% 20.79/5.55
% 20.79/5.55 % SZS output start Proof for theBenchmark
% 20.79/5.55 Assumed formulas after preprocessing and simplification:
% 20.79/5.55 | (0) ? [v0] : ? [v1] : (injection_2(x) = v1 & injection(x) = v0 & morphism(x, any1, any2) = 0 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (commute(v2, v3, v4, v5) = 0) | ~ (morphism(v5, v8, v9) = 0) | ~ (morphism(v2, v6, v7) = 0) | ~ (apply(v4, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v13 & apply(v5, v11) = v13 & apply(v3, v12) = v13 & apply(v2, v10) = v12) | ( ~ (v12 = 0) & morphism(v4, v6, v8) = v12) | ( ~ (v12 = 0) & morphism(v3, v7, v9) = v12) | ( ~ (v12 = 0) & element(v10, v6) = v12))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (commute(v2, v3, v4, v5) = 0) | ~ (morphism(v5, v8, v9) = 0) | ~ (morphism(v2, v6, v7) = 0) | ~ (apply(v2, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v12 & apply(v5, v13) = v12 & apply(v4, v10) = v13 & apply(v3, v11) = v12) | ( ~ (v12 = 0) & morphism(v4, v6, v8) = v12) | ( ~ (v12 = 0) & morphism(v3, v7, v9) = v12) | ( ~ (v12 = 0) & element(v10, v6) = v12))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (commute(v2, v3, v4, v5) = 0) | ~ (morphism(v4, v6, v8) = 0) | ~ (morphism(v3, v7, v9) = 0) | ~ (apply(v4, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v13 & apply(v5, v11) = v13 & apply(v3, v12) = v13 & apply(v2, v10) = v12) | ( ~ (v12 = 0) & morphism(v5, v8, v9) = v12) | ( ~ (v12 = 0) & morphism(v2, v6, v7) = v12) | ( ~ (v12 = 0) & element(v10, v6) = v12))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (commute(v2, v3, v4, v5) = 0) | ~ (morphism(v4, v6, v8) = 0) | ~ (morphism(v3, v7, v9) = 0) | ~ (apply(v2, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v12 & apply(v5, v13) = v12 & apply(v4, v10) = v13 & apply(v3, v11) = v12) | ( ~ (v12 = 0) & morphism(v5, v8, v9) = v12) | ( ~ (v12 = 0) & morphism(v2, v6, v7) = v12) | ( ~ (v12 = 0) & element(v10, v6) = v12))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (morphism(v5, v8, v9) = 0) | ~ (morphism(v4, v6, v8) = 0) | ~ (morphism(v3, v7, v9) = 0) | ~ (morphism(v2, v6, v7) = 0) | ~ (apply(v4, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v13 & apply(v5, v11) = v13 & apply(v3, v12) = v13 & apply(v2, v10) = v12) | ( ~ (v12 = 0) & commute(v2, v3, v4, v5) = v12) | ( ~ (v12 = 0) & element(v10, v6) = v12))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (morphism(v5, v8, v9) = 0) | ~ (morphism(v4, v6, v8) = 0) | ~ (morphism(v3, v7, v9) = 0) | ~ (morphism(v2, v6, v7) = 0) | ~ (apply(v2, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v12 & apply(v5, v13) = v12 & apply(v4, v10) = v13 & apply(v3, v11) = v12) | ( ~ (v12 = 0) & commute(v2, v3, v4, v5) = v12) | ( ~ (v12 = 0) & element(v10, v6) = v12))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (commute(v2, v3, v4, v5) = v10) | ~ (morphism(v5, v8, v9) = 0) | ~ (morphism(v2, v6, v7) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v12 = 0 & ~ (v16 = v14) & apply(v5, v15) = v16 & apply(v4, v11) = v15 & apply(v3, v13) = v14 & apply(v2, v11) = v13 & element(v11, v6) = 0) | ( ~ (v11 = 0) & morphism(v4, v6, v8) = v11) | ( ~ (v11 = 0) & morphism(v3, v7, v9) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (commute(v2, v3, v4, v5) = v10) | ~ (morphism(v4, v6, v8) = 0) | ~ (morphism(v3, v7, v9) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v12 = 0 & ~ (v16 = v14) & apply(v5, v15) = v16 & apply(v4, v11) = v15 & apply(v3, v13) = v14 & apply(v2, v11) = v13 & element(v11, v6) = 0) | ( ~ (v11 = 0) & morphism(v5, v8, v9) = v11) | ( ~ (v11 = 0) & morphism(v2, v6, v7) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (apply(v3, v8) = v9) | ~ (apply(v2, v10) = v8) | ? [v11] : (( ~ (v11 = 0) & morphism(v3, v5, v6) = v11) | ( ~ (v11 = 0) & element(v10, v4) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (apply(v3, v8) = v9) | ~ (element(v10, v4) = 0) | ? [v11] : (( ~ (v11 = v8) & apply(v2, v10) = v11) | ( ~ (v11 = 0) & morphism(v3, v5, v6) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (apply(v2, v10) = v8) | ~ (element(v8, v5) = v9) | ? [v11] : (( ~ (v11 = 0) & morphism(v3, v5, v6) = v11) | ( ~ (v11 = 0) & element(v10, v4) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (element(v10, v4) = 0) | ~ (element(v8, v5) = v9) | ? [v11] : (( ~ (v11 = v8) & apply(v2, v10) = v11) | ( ~ (v11 = 0) & morphism(v3, v5, v6) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (commute(v2, v3, v4, v5) = 0) | ~ (morphism(v5, v8, v9) = 0) | ~ (morphism(v2, v6, v7) = 0) | ~ (element(v10, v6) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = v12 & apply(v5, v13) = v12 & apply(v4, v10) = v13 & apply(v3, v11) = v12 & apply(v2, v10) = v11) | ( ~ (v11 = 0) & morphism(v4, v6, v8) = v11) | ( ~ (v11 = 0) & morphism(v3, v7, v9) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (commute(v2, v3, v4, v5) = 0) | ~ (morphism(v4, v6, v8) = 0) | ~ (morphism(v3, v7, v9) = 0) | ~ (element(v10, v6) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = v12 & apply(v5, v13) = v12 & apply(v4, v10) = v13 & apply(v3, v11) = v12 & apply(v2, v10) = v11) | ( ~ (v11 = 0) & morphism(v5, v8, v9) = v11) | ( ~ (v11 = 0) & morphism(v2, v6, v7) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (apply(v3, v8) = v9) | ~ (apply(v2, v10) = v8) | ? [v11] : ((v11 = 0 & element(v8, v5) = 0) | ( ~ (v11 = 0) & morphism(v3, v5, v6) = v11) | ( ~ (v11 = 0) & element(v10, v4) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (apply(v3, v8) = v9) | ~ (element(v10, v4) = 0) | ? [v11] : ((v11 = 0 & element(v8, v5) = 0) | ( ~ (v11 = v8) & apply(v2, v10) = v11) | ( ~ (v11 = 0) & morphism(v3, v5, v6) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (apply(v2, v10) = v8) | ~ (element(v8, v5) = v9) | ? [v11] : ((v11 = v7 & apply(v3, v8) = v7) | ( ~ (v11 = 0) & morphism(v3, v5, v6) = v11) | ( ~ (v11 = 0) & element(v10, v4) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (element(v10, v4) = 0) | ~ (element(v8, v5) = v9) | ? [v11] : ((v11 = v7 & apply(v3, v8) = v7) | ( ~ (v11 = v8) & apply(v2, v10) = v11) | ( ~ (v11 = 0) & morphism(v3, v5, v6) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (morphism(v5, v8, v9) = 0) | ~ (morphism(v4, v6, v8) = 0) | ~ (morphism(v3, v7, v9) = 0) | ~ (morphism(v2, v6, v7) = 0) | ~ (element(v10, v6) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = v12 & apply(v5, v13) = v12 & apply(v4, v10) = v13 & apply(v3, v11) = v12 & apply(v2, v10) = v11) | ( ~ (v11 = 0) & commute(v2, v3, v4, v5) = v11))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (subtract(v4, v7, v8) = v9) | ~ (morphism(v2, v3, v4) = 0) | ~ (apply(v2, v6) = v8) | ~ (apply(v2, v5) = v7) | ? [v10] : ? [v11] : ((v11 = v9 & subtract(v3, v5, v6) = v10 & apply(v2, v10) = v9) | ( ~ (v10 = 0) & element(v6, v3) = v10) | ( ~ (v10 = 0) & element(v5, v3) = v10))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (morphism(v5, v8, v9) = 0) | ~ (morphism(v4, v6, v8) = 0) | ~ (morphism(v3, v7, v9) = 0) | ~ (morphism(v2, v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v11 = 0 & ~ (v15 = v13) & apply(v5, v14) = v15 & apply(v4, v10) = v14 & apply(v3, v12) = v13 & apply(v2, v10) = v12 & element(v10, v6) = 0) | (v10 = 0 & commute(v2, v3, v4, v5) = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (exact(v2, v3) = v8) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (( ~ (v9 = 0) & morphism(v3, v5, v6) = v9) | (((v14 = v9 & v13 = 0 & apply(v2, v12) = v9 & element(v12, v4) = 0) | (v11 = v7 & v10 = 0 & apply(v3, v9) = v7 & element(v9, v5) = 0)) & (( ~ (v11 = v7) & apply(v3, v9) = v11) | ( ~ (v10 = 0) & element(v9, v5) = v10) | ( ! [v15] : ( ~ (apply(v2, v15) = v9) | ? [v16] : ( ~ (v16 = 0) & element(v15, v4) = v16)) & ! [v15] : ( ~ (element(v15, v4) = 0) | ? [v16] : ( ~ (v16 = v9) & apply(v2, v15) = v16))))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (apply(v3, v8) = v7) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & apply(v2, v9) = v8 & element(v9, v4) = 0) | ( ~ (v9 = 0) & morphism(v3, v5, v6) = v9) | ( ~ (v9 = 0) & element(v8, v5) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v2, v3) = 0) | ~ (morphism(v2, v4, v5) = 0) | ~ (zero(v6) = v7) | ~ (element(v8, v5) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & apply(v2, v9) = v8 & element(v9, v4) = 0) | ( ~ (v9 = v7) & apply(v3, v8) = v9) | ( ~ (v9 = 0) & morphism(v3, v5, v6) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (morphism(v2, v3, v4) = 0) | ~ (apply(v2, v6) = v7) | ~ (apply(v2, v5) = v7) | ? [v8] : (( ~ (v8 = 0) & injection(v2) = v8) | ( ~ (v8 = 0) & element(v6, v3) = v8) | ( ~ (v8 = 0) & element(v5, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (morphism(v2, v3, v4) = 0) | ~ (apply(v2, v6) = v7) | ~ (element(v5, v3) = 0) | ? [v8] : (( ~ (v8 = v7) & apply(v2, v5) = v8) | ( ~ (v8 = 0) & injection(v2) = v8) | ( ~ (v8 = 0) & element(v6, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (morphism(v2, v3, v4) = 0) | ~ (apply(v2, v5) = v7) | ~ (element(v6, v3) = 0) | ? [v8] : (( ~ (v8 = v7) & apply(v2, v6) = v8) | ( ~ (v8 = 0) & injection(v2) = v8) | ( ~ (v8 = 0) & element(v5, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v3 = v2 | ~ (commute(v7, v6, v5, v4) = v3) | ~ (commute(v7, v6, v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (subtract(v3, v5, v6) = v7) | ~ (morphism(v2, v3, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & subtract(v4, v9, v10) = v8 & apply(v2, v7) = v8 & apply(v2, v6) = v10 & apply(v2, v5) = v9) | ( ~ (v8 = 0) & element(v6, v3) = v8) | ( ~ (v8 = 0) & element(v5, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (morphism(v2, v3, v4) = 0) | ~ (element(v6, v3) = 0) | ~ (element(v5, v3) = 0) | ? [v7] : ? [v8] : (( ~ (v8 = v7) & apply(v2, v6) = v8 & apply(v2, v5) = v7) | ( ~ (v7 = 0) & injection(v2) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v2 | ~ (subtract(v6, v5, v4) = v3) | ~ (subtract(v6, v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v2 | ~ (morphism(v6, v5, v4) = v3) | ~ (morphism(v6, v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (morphism(v3, v5, v6) = 0) | ~ (morphism(v2, v4, v5) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v7 = 0 & exact(v2, v3) = 0) | (zero(v6) = v7 & ((v13 = v8 & v12 = 0 & apply(v2, v11) = v8 & element(v11, v4) = 0) | (v10 = v7 & v9 = 0 & apply(v3, v8) = v7 & element(v8, v5) = 0)) & (( ~ (v10 = v7) & apply(v3, v8) = v10) | ( ~ (v9 = 0) & element(v8, v5) = v9) | ( ! [v14] : ( ~ (apply(v2, v14) = v8) | ? [v15] : ( ~ (v15 = 0) & element(v14, v4) = v15)) & ! [v14] : ( ~ (element(v14, v4) = 0) | ? [v15] : ( ~ (v15 = v8) & apply(v2, v14) = v15))))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (morphism(v3, v5, v6) = 0) | ~ (morphism(v2, v4, v5) = 0) | ? [v7] : (( ~ (v7 = 0) & exact(v2, v3) = v7) | (zero(v6) = v7 & ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | ~ (apply(v3, v8) = v9) | ~ (apply(v2, v10) = v8) | ? [v11] : ( ~ (v11 = 0) & element(v10, v4) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | ~ (apply(v3, v8) = v9) | ~ (element(v10, v4) = 0) | ? [v11] : ( ~ (v11 = v8) & apply(v2, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (apply(v2, v10) = v8) | ~ (element(v8, v5) = v9) | ? [v11] : ( ~ (v11 = 0) & element(v10, v4) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (element(v10, v4) = 0) | ~ (element(v8, v5) = v9) | ? [v11] : ( ~ (v11 = v8) & apply(v2, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (apply(v3, v8) = v9) | ~ (apply(v2, v10) = v8) | ? [v11] : ((v11 = 0 & element(v8, v5) = 0) | ( ~ (v11 = 0) & element(v10, v4) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (apply(v3, v8) = v9) | ~ (element(v10, v4) = 0) | ? [v11] : ((v11 = 0 & element(v8, v5) = 0) | ( ~ (v11 = v8) & apply(v2, v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (apply(v2, v10) = v8) | ~ (element(v8, v5) = v9) | ? [v11] : ((v11 = v7 & apply(v3, v8) = v7) | ( ~ (v11 = 0) & element(v10, v4) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (element(v10, v4) = 0) | ~ (element(v8, v5) = v9) | ? [v11] : ((v11 = v7 & apply(v3, v8) = v7) | ( ~ (v11 = v8) & apply(v2, v10) = v11))) & ! [v8] : ( ~ (apply(v3, v8) = v7) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & apply(v2, v9) = v8 & element(v9, v4) = 0) | ( ~ (v9 = 0) & element(v8, v5) = v9))) & ! [v8] : ( ~ (element(v8, v5) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & apply(v2, v9) = v8 & element(v9, v4) = 0) | ( ~ (v9 = v7) & apply(v3, v8) = v9)))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (morphism(v2, v3, v4) = 0) | ~ (apply(v2, v5) = v6) | ? [v7] : ((v7 = 0 & element(v6, v4) = 0) | ( ~ (v7 = 0) & element(v5, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (exact(v5, v4) = v3) | ~ (exact(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (apply(v5, v4) = v3) | ~ (apply(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (element(v5, v4) = v3) | ~ (element(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subtract(v2, v3, v4) = v5) | ? [v6] : ((v6 = v4 & subtract(v2, v3, v5) = v4) | ( ~ (v6 = 0) & element(v4, v2) = v6) | ( ~ (v6 = 0) & element(v3, v2) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subtract(v2, v3, v4) = v5) | ? [v6] : ((v6 = 0 & element(v5, v2) = 0) | ( ~ (v6 = 0) & element(v4, v2) = v6) | ( ~ (v6 = 0) & element(v3, v2) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (morphism(v2, v3, v4) = 0) | ~ (element(v5, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & v7 = 0 & apply(v2, v6) = v5 & element(v6, v3) = 0) | ( ~ (v6 = 0) & surjection(v2) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (morphism(v2, v3, v4) = 0) | ~ (element(v5, v3) = 0) | ? [v6] : (apply(v2, v5) = v6 & element(v6, v4) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (injection_2(v4) = v3) | ~ (injection_2(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (surjection(v4) = v3) | ~ (surjection(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (injection(v4) = v3) | ~ (injection(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (zero(v4) = v3) | ~ (zero(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subtract(v2, v3, v3) = v4) | ? [v5] : ((v5 = v4 & zero(v2) = v4) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v2, v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = v9 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v2, v6) = v9 & apply(v2, v5) = v9 & element(v6, v3) = 0 & element(v5, v3) = 0) | (v5 = 0 & injection(v2) = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v2, v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = v5 & v8 = 0 & ~ (v7 = v6) & zero(v4) = v5 & zero(v3) = v6 & apply(v2, v7) = v5 & element(v7, v3) = 0) | (v5 = 0 & injection_2(v2) = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v2, v3, v4) = 0) | ? [v5] : ? [v6] : (zero(v4) = v6 & zero(v3) = v5 & apply(v2, v5) = v6)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v2, v3, v4) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & element(v5, v4) = 0 & ! [v7] : ( ~ (apply(v2, v7) = v5) | ? [v8] : ( ~ (v8 = 0) & element(v7, v3) = v8)) & ! [v7] : ( ~ (element(v7, v3) = 0) | ? [v8] : ( ~ (v8 = v5) & apply(v2, v7) = v8))) | (v5 = 0 & surjection(v2) = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v2, v3, v4) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & injection_2(v2) = v5) | (zero(v4) = v5 & zero(v3) = v6 & ! [v7] : (v7 = v6 | ~ (apply(v2, v7) = v5) | ? [v8] : ( ~ (v8 = 0) & element(v7, v3) = v8)) & ! [v7] : (v7 = v6 | ~ (element(v7, v3) = 0) | ? [v8] : ( ~ (v8 = v5) & apply(v2, v7) = v8))))) & ! [v2] : ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (subtract(v2, v3, v3) = v4 & zero(v2) = v4)) & ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : commute(v5, v4, v3, v2) = v6 & ? [v2] : ? [v3] : ? [v4] : ? [v5] : subtract(v4, v3, v2) = v5 & ? [v2] : ? [v3] : ? [v4] : ? [v5] : morphism(v4, v3, v2) = v5 & ? [v2] : ? [v3] : ? [v4] : exact(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : apply(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : element(v3, v2) = v4 & ? [v2] : ? [v3] : injection_2(v2) = v3 & ? [v2] : ? [v3] : surjection(v2) = v3 & ? [v2] : ? [v3] : injection(v2) = v3 & ? [v2] : ? [v3] : zero(v2) = v3 & ((v1 = 0 & ~ (v0 = 0)) | (v0 = 0 & ~ (v1 = 0))))
% 21.33/5.65 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 21.33/5.65 | (1) injection_2(x) = all_0_0_0 & injection(x) = all_0_1_1 & morphism(x, any1, any2) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (apply(v2, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v11 & apply(v3, v9) = v11 & apply(v1, v10) = v11 & apply(v0, v8) = v10) | ( ~ (v10 = 0) & morphism(v2, v4, v6) = v10) | ( ~ (v10 = 0) & morphism(v1, v5, v7) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (apply(v0, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10) | ( ~ (v10 = 0) & morphism(v2, v4, v6) = v10) | ( ~ (v10 = 0) & morphism(v1, v5, v7) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (apply(v2, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v11 & apply(v3, v9) = v11 & apply(v1, v10) = v11 & apply(v0, v8) = v10) | ( ~ (v10 = 0) & morphism(v3, v6, v7) = v10) | ( ~ (v10 = 0) & morphism(v0, v4, v5) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (apply(v0, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10) | ( ~ (v10 = 0) & morphism(v3, v6, v7) = v10) | ( ~ (v10 = 0) & morphism(v0, v4, v5) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (apply(v2, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v11 & apply(v3, v9) = v11 & apply(v1, v10) = v11 & apply(v0, v8) = v10) | ( ~ (v10 = 0) & commute(v0, v1, v2, v3) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (apply(v0, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10) | ( ~ (v10 = 0) & commute(v0, v1, v2, v3) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (commute(v0, v1, v2, v3) = v8) | ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v10 = 0 & ~ (v14 = v12) & apply(v3, v13) = v14 & apply(v2, v9) = v13 & apply(v1, v11) = v12 & apply(v0, v9) = v11 & element(v9, v4) = 0) | ( ~ (v9 = 0) & morphism(v2, v4, v6) = v9) | ( ~ (v9 = 0) & morphism(v1, v5, v7) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (commute(v0, v1, v2, v3) = v8) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v10 = 0 & ~ (v14 = v12) & apply(v3, v13) = v14 & apply(v2, v9) = v13 & apply(v1, v11) = v12 & apply(v0, v9) = v11 & element(v9, v4) = 0) | ( ~ (v9 = 0) & morphism(v3, v6, v7) = v9) | ( ~ (v9 = 0) & morphism(v0, v4, v5) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v7) | ~ (apply(v0, v8) = v6) | ? [v9] : (( ~ (v9 = 0) & morphism(v1, v3, v4) = v9) | ( ~ (v9 = 0) & element(v8, v2) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v7) | ~ (element(v8, v2) = 0) | ? [v9] : (( ~ (v9 = v6) & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v0, v8) = v6) | ~ (element(v6, v3) = v7) | ? [v9] : (( ~ (v9 = 0) & morphism(v1, v3, v4) = v9) | ( ~ (v9 = 0) & element(v8, v2) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (element(v8, v2) = 0) | ~ (element(v6, v3) = v7) | ? [v9] : (( ~ (v9 = v6) & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (element(v8, v4) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10 & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v2, v4, v6) = v9) | ( ~ (v9 = 0) & morphism(v1, v5, v7) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (element(v8, v4) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10 & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v3, v6, v7) = v9) | ( ~ (v9 = 0) & morphism(v0, v4, v5) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v7) | ~ (apply(v0, v8) = v6) | ? [v9] : ((v9 = 0 & element(v6, v3) = 0) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9) | ( ~ (v9 = 0) & element(v8, v2) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v7) | ~ (element(v8, v2) = 0) | ? [v9] : ((v9 = 0 & element(v6, v3) = 0) | ( ~ (v9 = v6) & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v0, v8) = v6) | ~ (element(v6, v3) = v7) | ? [v9] : ((v9 = v5 & apply(v1, v6) = v5) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9) | ( ~ (v9 = 0) & element(v8, v2) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (element(v8, v2) = 0) | ~ (element(v6, v3) = v7) | ? [v9] : ((v9 = v5 & apply(v1, v6) = v5) | ( ~ (v9 = v6) & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (element(v8, v4) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10 & apply(v0, v8) = v9) | ( ~ (v9 = 0) & commute(v0, v1, v2, v3) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (subtract(v2, v5, v6) = v7) | ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v4) = v6) | ~ (apply(v0, v3) = v5) | ? [v8] : ? [v9] : ((v9 = v7 & subtract(v1, v3, v4) = v8 & apply(v0, v8) = v7) | ( ~ (v8 = 0) & element(v4, v1) = v8) | ( ~ (v8 = 0) & element(v3, v1) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v9 = 0 & ~ (v13 = v11) & apply(v3, v12) = v13 & apply(v2, v8) = v12 & apply(v1, v10) = v11 & apply(v0, v8) = v10 & element(v8, v4) = 0) | (v8 = 0 & commute(v0, v1, v2, v3) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (exact(v0, v1) = v6) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (( ~ (v7 = 0) & morphism(v1, v3, v4) = v7) | (((v12 = v7 & v11 = 0 & apply(v0, v10) = v7 & element(v10, v2) = 0) | (v9 = v5 & v8 = 0 & apply(v1, v7) = v5 & element(v7, v3) = 0)) & (( ~ (v9 = v5) & apply(v1, v7) = v9) | ( ~ (v8 = 0) & element(v7, v3) = v8) | ( ! [v13] : ( ~ (apply(v0, v13) = v7) | ? [v14] : ( ~ (v14 = 0) & element(v13, v2) = v14)) & ! [v13] : ( ~ (element(v13, v2) = 0) | ? [v14] : ( ~ (v14 = v7) & apply(v0, v13) = v14))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v5) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & v8 = 0 & apply(v0, v7) = v6 & element(v7, v2) = 0) | ( ~ (v7 = 0) & morphism(v1, v3, v4) = v7) | ( ~ (v7 = 0) & element(v6, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (element(v6, v3) = 0) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & v8 = 0 & apply(v0, v7) = v6 & element(v7, v2) = 0) | ( ~ (v7 = v5) & apply(v1, v6) = v7) | ( ~ (v7 = 0) & morphism(v1, v3, v4) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v4) = v5) | ~ (apply(v0, v3) = v5) | ? [v6] : (( ~ (v6 = 0) & injection(v0) = v6) | ( ~ (v6 = 0) & element(v4, v1) = v6) | ( ~ (v6 = 0) & element(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : (( ~ (v6 = v5) & apply(v0, v3) = v6) | ( ~ (v6 = 0) & injection(v0) = v6) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v3) = v5) | ~ (element(v4, v1) = 0) | ? [v6] : (( ~ (v6 = v5) & apply(v0, v4) = v6) | ( ~ (v6 = 0) & injection(v0) = v6) | ( ~ (v6 = 0) & element(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (commute(v5, v4, v3, v2) = v1) | ~ (commute(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subtract(v1, v3, v4) = v5) | ~ (morphism(v0, v1, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & subtract(v2, v7, v8) = v6 & apply(v0, v5) = v6 & apply(v0, v4) = v8 & apply(v0, v3) = v7) | ( ~ (v6 = 0) & element(v4, v1) = v6) | ( ~ (v6 = 0) & element(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (morphism(v0, v1, v2) = 0) | ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & apply(v0, v4) = v6 & apply(v0, v3) = v5) | ( ~ (v5 = 0) & injection(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subtract(v4, v3, v2) = v1) | ~ (subtract(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (morphism(v4, v3, v2) = v1) | ~ (morphism(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v1, v3, v4) = 0) | ~ (morphism(v0, v2, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v5 = 0 & exact(v0, v1) = 0) | (zero(v4) = v5 & ((v11 = v6 & v10 = 0 & apply(v0, v9) = v6 & element(v9, v2) = 0) | (v8 = v5 & v7 = 0 & apply(v1, v6) = v5 & element(v6, v3) = 0)) & (( ~ (v8 = v5) & apply(v1, v6) = v8) | ( ~ (v7 = 0) & element(v6, v3) = v7) | ( ! [v12] : ( ~ (apply(v0, v12) = v6) | ? [v13] : ( ~ (v13 = 0) & element(v12, v2) = v13)) & ! [v12] : ( ~ (element(v12, v2) = 0) | ? [v13] : ( ~ (v13 = v6) & apply(v0, v12) = v13))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v1, v3, v4) = 0) | ~ (morphism(v0, v2, v3) = 0) | ? [v5] : (( ~ (v5 = 0) & exact(v0, v1) = v5) | (zero(v4) = v5 & ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | ~ (apply(v1, v6) = v7) | ~ (apply(v0, v8) = v6) | ? [v9] : ( ~ (v9 = 0) & element(v8, v2) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | ~ (apply(v1, v6) = v7) | ~ (element(v8, v2) = 0) | ? [v9] : ( ~ (v9 = v6) & apply(v0, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (apply(v0, v8) = v6) | ~ (element(v6, v3) = v7) | ? [v9] : ( ~ (v9 = 0) & element(v8, v2) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (element(v8, v2) = 0) | ~ (element(v6, v3) = v7) | ? [v9] : ( ~ (v9 = v6) & apply(v0, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v1, v6) = v7) | ~ (apply(v0, v8) = v6) | ? [v9] : ((v9 = 0 & element(v6, v3) = 0) | ( ~ (v9 = 0) & element(v8, v2) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v1, v6) = v7) | ~ (element(v8, v2) = 0) | ? [v9] : ((v9 = 0 & element(v6, v3) = 0) | ( ~ (v9 = v6) & apply(v0, v8) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v0, v8) = v6) | ~ (element(v6, v3) = v7) | ? [v9] : ((v9 = v5 & apply(v1, v6) = v5) | ( ~ (v9 = 0) & element(v8, v2) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (element(v8, v2) = 0) | ~ (element(v6, v3) = v7) | ? [v9] : ((v9 = v5 & apply(v1, v6) = v5) | ( ~ (v9 = v6) & apply(v0, v8) = v9))) & ! [v6] : ( ~ (apply(v1, v6) = v5) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & v8 = 0 & apply(v0, v7) = v6 & element(v7, v2) = 0) | ( ~ (v7 = 0) & element(v6, v3) = v7))) & ! [v6] : ( ~ (element(v6, v3) = 0) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & v8 = 0 & apply(v0, v7) = v6 & element(v7, v2) = 0) | ( ~ (v7 = v5) & apply(v1, v6) = v7)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v3) = v4) | ? [v5] : ((v5 = 0 & element(v4, v2) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (exact(v3, v2) = v1) | ~ (exact(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subtract(v0, v1, v2) = v3) | ? [v4] : ((v4 = v2 & subtract(v0, v1, v3) = v2) | ( ~ (v4 = 0) & element(v2, v0) = v4) | ( ~ (v4 = 0) & element(v1, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subtract(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & element(v3, v0) = 0) | ( ~ (v4 = 0) & element(v2, v0) = v4) | ( ~ (v4 = 0) & element(v1, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (morphism(v0, v1, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v3 & v5 = 0 & apply(v0, v4) = v3 & element(v4, v1) = 0) | ( ~ (v4 = 0) & surjection(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (morphism(v0, v1, v2) = 0) | ~ (element(v3, v1) = 0) | ? [v4] : (apply(v0, v3) = v4 & element(v4, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (injection_2(v2) = v1) | ~ (injection_2(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (surjection(v2) = v1) | ~ (surjection(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (injection(v2) = v1) | ~ (injection(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (zero(v2) = v1) | ~ (zero(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subtract(v0, v1, v1) = v2) | ? [v3] : ((v3 = v2 & zero(v0) = v2) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & apply(v0, v4) = v7 & apply(v0, v3) = v7 & element(v4, v1) = 0 & element(v3, v1) = 0) | (v3 = 0 & injection(v0) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v3 & v6 = 0 & ~ (v5 = v4) & zero(v2) = v3 & zero(v1) = v4 & apply(v0, v5) = v3 & element(v5, v1) = 0) | (v3 = 0 & injection_2(v0) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (zero(v2) = v4 & zero(v1) = v3 & apply(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & element(v3, v2) = 0 & ! [v5] : ( ~ (apply(v0, v5) = v3) | ? [v6] : ( ~ (v6 = 0) & element(v5, v1) = v6)) & ! [v5] : ( ~ (element(v5, v1) = 0) | ? [v6] : ( ~ (v6 = v3) & apply(v0, v5) = v6))) | (v3 = 0 & surjection(v0) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & injection_2(v0) = v3) | (zero(v2) = v3 & zero(v1) = v4 & ! [v5] : (v5 = v4 | ~ (apply(v0, v5) = v3) | ? [v6] : ( ~ (v6 = 0) & element(v5, v1) = v6)) & ! [v5] : (v5 = v4 | ~ (element(v5, v1) = 0) | ? [v6] : ( ~ (v6 = v3) & apply(v0, v5) = v6))))) & ! [v0] : ! [v1] : ( ~ (element(v1, v0) = 0) | ? [v2] : (subtract(v0, v1, v1) = v2 & zero(v0) = v2)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : commute(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : subtract(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : morphism(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : exact(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : injection_2(v0) = v1 & ? [v0] : ? [v1] : surjection(v0) = v1 & ? [v0] : ? [v1] : injection(v0) = v1 & ? [v0] : ? [v1] : zero(v0) = v1 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))
% 21.33/5.69 |
% 21.33/5.69 | Applying alpha-rule on (1) yields:
% 21.33/5.69 | (2) ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2
% 21.33/5.69 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & element(v3, v2) = 0 & ! [v5] : ( ~ (apply(v0, v5) = v3) | ? [v6] : ( ~ (v6 = 0) & element(v5, v1) = v6)) & ! [v5] : ( ~ (element(v5, v1) = 0) | ? [v6] : ( ~ (v6 = v3) & apply(v0, v5) = v6))) | (v3 = 0 & surjection(v0) = 0)))
% 21.33/5.69 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (apply(v0, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10) | ( ~ (v10 = 0) & commute(v0, v1, v2, v3) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10)))
% 21.33/5.69 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v7) | ~ (apply(v0, v8) = v6) | ? [v9] : (( ~ (v9 = 0) & morphism(v1, v3, v4) = v9) | ( ~ (v9 = 0) & element(v8, v2) = v9)))
% 21.33/5.69 | (6) ! [v0] : ! [v1] : ( ~ (element(v1, v0) = 0) | ? [v2] : (subtract(v0, v1, v1) = v2 & zero(v0) = v2))
% 21.33/5.69 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (apply(v2, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v11 & apply(v3, v9) = v11 & apply(v1, v10) = v11 & apply(v0, v8) = v10) | ( ~ (v10 = 0) & morphism(v2, v4, v6) = v10) | ( ~ (v10 = 0) & morphism(v1, v5, v7) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10)))
% 21.33/5.69 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : (( ~ (v6 = v5) & apply(v0, v3) = v6) | ( ~ (v6 = 0) & injection(v0) = v6) | ( ~ (v6 = 0) & element(v4, v1) = v6)))
% 21.33/5.69 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (subtract(v0, v1, v1) = v2) | ? [v3] : ((v3 = v2 & zero(v0) = v2) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 21.33/5.69 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v4) = v5) | ~ (apply(v0, v3) = v5) | ? [v6] : (( ~ (v6 = 0) & injection(v0) = v6) | ( ~ (v6 = 0) & element(v4, v1) = v6) | ( ~ (v6 = 0) & element(v3, v1) = v6)))
% 21.33/5.70 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (element(v8, v4) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10 & apply(v0, v8) = v9) | ( ~ (v9 = 0) & commute(v0, v1, v2, v3) = v9)))
% 21.33/5.70 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subtract(v0, v1, v2) = v3) | ? [v4] : ((v4 = v2 & subtract(v0, v1, v3) = v2) | ( ~ (v4 = 0) & element(v2, v0) = v4) | ( ~ (v4 = 0) & element(v1, v0) = v4)))
% 21.33/5.70 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (morphism(v0, v1, v2) = 0) | ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & apply(v0, v4) = v6 & apply(v0, v3) = v5) | ( ~ (v5 = 0) & injection(v0) = v5)))
% 21.33/5.70 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (element(v8, v4) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10 & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v2, v4, v6) = v9) | ( ~ (v9 = 0) & morphism(v1, v5, v7) = v9)))
% 21.33/5.70 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 21.33/5.70 | (16) ? [v0] : ? [v1] : zero(v0) = v1
% 21.33/5.70 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (morphism(v4, v3, v2) = v1) | ~ (morphism(v4, v3, v2) = v0))
% 21.33/5.70 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v1, v3, v4) = 0) | ~ (morphism(v0, v2, v3) = 0) | ? [v5] : (( ~ (v5 = 0) & exact(v0, v1) = v5) | (zero(v4) = v5 & ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | ~ (apply(v1, v6) = v7) | ~ (apply(v0, v8) = v6) | ? [v9] : ( ~ (v9 = 0) & element(v8, v2) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | ~ (apply(v1, v6) = v7) | ~ (element(v8, v2) = 0) | ? [v9] : ( ~ (v9 = v6) & apply(v0, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (apply(v0, v8) = v6) | ~ (element(v6, v3) = v7) | ? [v9] : ( ~ (v9 = 0) & element(v8, v2) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (element(v8, v2) = 0) | ~ (element(v6, v3) = v7) | ? [v9] : ( ~ (v9 = v6) & apply(v0, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v1, v6) = v7) | ~ (apply(v0, v8) = v6) | ? [v9] : ((v9 = 0 & element(v6, v3) = 0) | ( ~ (v9 = 0) & element(v8, v2) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v1, v6) = v7) | ~ (element(v8, v2) = 0) | ? [v9] : ((v9 = 0 & element(v6, v3) = 0) | ( ~ (v9 = v6) & apply(v0, v8) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v0, v8) = v6) | ~ (element(v6, v3) = v7) | ? [v9] : ((v9 = v5 & apply(v1, v6) = v5) | ( ~ (v9 = 0) & element(v8, v2) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (element(v8, v2) = 0) | ~ (element(v6, v3) = v7) | ? [v9] : ((v9 = v5 & apply(v1, v6) = v5) | ( ~ (v9 = v6) & apply(v0, v8) = v9))) & ! [v6] : ( ~ (apply(v1, v6) = v5) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & v8 = 0 & apply(v0, v7) = v6 & element(v7, v2) = 0) | ( ~ (v7 = 0) & element(v6, v3) = v7))) & ! [v6] : ( ~ (element(v6, v3) = 0) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & v8 = 0 & apply(v0, v7) = v6 & element(v7, v2) = 0) | ( ~ (v7 = v5) & apply(v1, v6) = v7))))))
% 21.33/5.70 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subtract(v0, v1, v2) = v3) | ? [v4] : ((v4 = 0 & element(v3, v0) = 0) | ( ~ (v4 = 0) & element(v2, v0) = v4) | ( ~ (v4 = 0) & element(v1, v0) = v4)))
% 21.33/5.70 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (commute(v0, v1, v2, v3) = v8) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v10 = 0 & ~ (v14 = v12) & apply(v3, v13) = v14 & apply(v2, v9) = v13 & apply(v1, v11) = v12 & apply(v0, v9) = v11 & element(v9, v4) = 0) | ( ~ (v9 = 0) & morphism(v3, v6, v7) = v9) | ( ~ (v9 = 0) & morphism(v0, v4, v5) = v9)))
% 21.33/5.70 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (apply(v2, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v11 & apply(v3, v9) = v11 & apply(v1, v10) = v11 & apply(v0, v8) = v10) | ( ~ (v10 = 0) & morphism(v3, v6, v7) = v10) | ( ~ (v10 = 0) & morphism(v0, v4, v5) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10)))
% 21.33/5.71 | (22) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))
% 21.33/5.71 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (zero(v2) = v1) | ~ (zero(v2) = v0))
% 21.33/5.71 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (exact(v3, v2) = v1) | ~ (exact(v3, v2) = v0))
% 21.33/5.71 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (commute(v5, v4, v3, v2) = v1) | ~ (commute(v5, v4, v3, v2) = v0))
% 21.33/5.71 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v7) | ~ (element(v8, v2) = 0) | ? [v9] : ((v9 = 0 & element(v6, v3) = 0) | ( ~ (v9 = v6) & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9)))
% 21.33/5.71 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (element(v6, v3) = 0) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & v8 = 0 & apply(v0, v7) = v6 & element(v7, v2) = 0) | ( ~ (v7 = v5) & apply(v1, v6) = v7) | ( ~ (v7 = 0) & morphism(v1, v3, v4) = v7)))
% 21.33/5.71 | (28) morphism(x, any1, any2) = 0
% 21.33/5.71 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v9 = 0 & ~ (v13 = v11) & apply(v3, v12) = v13 & apply(v2, v8) = v12 & apply(v1, v10) = v11 & apply(v0, v8) = v10 & element(v8, v4) = 0) | (v8 = 0 & commute(v0, v1, v2, v3) = 0)))
% 21.33/5.71 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v7) | ~ (element(v8, v2) = 0) | ? [v9] : (( ~ (v9 = v6) & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9)))
% 21.33/5.71 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v3) = v4) | ? [v5] : ((v5 = 0 & element(v4, v2) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5)))
% 21.33/5.71 | (32) ? [v0] : ? [v1] : ? [v2] : exact(v1, v0) = v2
% 21.33/5.71 | (33) injection_2(x) = all_0_0_0
% 21.33/5.71 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (morphism(v0, v1, v2) = 0) | ~ (element(v3, v1) = 0) | ? [v4] : (apply(v0, v3) = v4 & element(v4, v2) = 0))
% 21.33/5.71 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (element(v8, v4) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10 & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v3, v6, v7) = v9) | ( ~ (v9 = 0) & morphism(v0, v4, v5) = v9)))
% 21.33/5.71 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v0, v8) = v6) | ~ (element(v6, v3) = v7) | ? [v9] : ((v9 = v5 & apply(v1, v6) = v5) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9) | ( ~ (v9 = 0) & element(v8, v2) = v9)))
% 21.33/5.71 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (apply(v0, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10) | ( ~ (v10 = 0) & morphism(v2, v4, v6) = v10) | ( ~ (v10 = 0) & morphism(v1, v5, v7) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10)))
% 21.77/5.71 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subtract(v4, v3, v2) = v1) | ~ (subtract(v4, v3, v2) = v0))
% 21.77/5.71 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (element(v8, v2) = 0) | ~ (element(v6, v3) = v7) | ? [v9] : ((v9 = v5 & apply(v1, v6) = v5) | ( ~ (v9 = v6) & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9)))
% 21.77/5.71 | (40) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 21.77/5.71 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ~ (apply(v2, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v11 & apply(v3, v9) = v11 & apply(v1, v10) = v11 & apply(v0, v8) = v10) | ( ~ (v10 = 0) & commute(v0, v1, v2, v3) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10)))
% 21.77/5.72 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (exact(v0, v1) = v6) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (( ~ (v7 = 0) & morphism(v1, v3, v4) = v7) | (((v12 = v7 & v11 = 0 & apply(v0, v10) = v7 & element(v10, v2) = 0) | (v9 = v5 & v8 = 0 & apply(v1, v7) = v5 & element(v7, v3) = 0)) & (( ~ (v9 = v5) & apply(v1, v7) = v9) | ( ~ (v8 = 0) & element(v7, v3) = v8) | ( ! [v13] : ( ~ (apply(v0, v13) = v7) | ? [v14] : ( ~ (v14 = 0) & element(v13, v2) = v14)) & ! [v13] : ( ~ (element(v13, v2) = 0) | ? [v14] : ( ~ (v14 = v7) & apply(v0, v13) = v14)))))))
% 21.77/5.72 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (injection_2(v2) = v1) | ~ (injection_2(v2) = v0))
% 21.77/5.72 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 21.77/5.72 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (subtract(v2, v5, v6) = v7) | ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v4) = v6) | ~ (apply(v0, v3) = v5) | ? [v8] : ? [v9] : ((v9 = v7 & subtract(v1, v3, v4) = v8 & apply(v0, v8) = v7) | ( ~ (v8 = 0) & element(v4, v1) = v8) | ( ~ (v8 = 0) & element(v3, v1) = v8)))
% 21.77/5.72 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (surjection(v2) = v1) | ~ (surjection(v2) = v0))
% 21.77/5.72 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (zero(v2) = v4 & zero(v1) = v3 & apply(v0, v3) = v4))
% 21.77/5.72 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (morphism(v0, v1, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v3 & v5 = 0 & apply(v0, v4) = v3 & element(v4, v1) = 0) | ( ~ (v4 = 0) & surjection(v0) = v4)))
% 21.77/5.72 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (commute(v0, v1, v2, v3) = 0) | ~ (morphism(v2, v4, v6) = 0) | ~ (morphism(v1, v5, v7) = 0) | ~ (apply(v0, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v10 & apply(v3, v11) = v10 & apply(v2, v8) = v11 & apply(v1, v9) = v10) | ( ~ (v10 = 0) & morphism(v3, v6, v7) = v10) | ( ~ (v10 = 0) & morphism(v0, v4, v5) = v10) | ( ~ (v10 = 0) & element(v8, v4) = v10)))
% 21.77/5.72 | (50) ? [v0] : ? [v1] : injection_2(v0) = v1
% 21.77/5.72 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & injection_2(v0) = v3) | (zero(v2) = v3 & zero(v1) = v4 & ! [v5] : (v5 = v4 | ~ (apply(v0, v5) = v3) | ? [v6] : ( ~ (v6 = 0) & element(v5, v1) = v6)) & ! [v5] : (v5 = v4 | ~ (element(v5, v1) = 0) | ? [v6] : ( ~ (v6 = v3) & apply(v0, v5) = v6)))))
% 21.77/5.72 | (52) ? [v0] : ? [v1] : ? [v2] : ? [v3] : morphism(v2, v1, v0) = v3
% 21.77/5.72 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subtract(v1, v3, v4) = v5) | ~ (morphism(v0, v1, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & subtract(v2, v7, v8) = v6 & apply(v0, v5) = v6 & apply(v0, v4) = v8 & apply(v0, v3) = v7) | ( ~ (v6 = 0) & element(v4, v1) = v6) | ( ~ (v6 = 0) & element(v3, v1) = v6)))
% 21.77/5.72 | (54) ? [v0] : ? [v1] : ? [v2] : ? [v3] : subtract(v2, v1, v0) = v3
% 21.77/5.72 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & apply(v0, v4) = v7 & apply(v0, v3) = v7 & element(v4, v1) = 0 & element(v3, v1) = 0) | (v3 = 0 & injection(v0) = 0)))
% 21.77/5.72 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (morphism(v0, v1, v2) = 0) | ~ (apply(v0, v3) = v5) | ~ (element(v4, v1) = 0) | ? [v6] : (( ~ (v6 = v5) & apply(v0, v4) = v6) | ( ~ (v6 = 0) & injection(v0) = v6) | ( ~ (v6 = 0) & element(v3, v1) = v6)))
% 21.77/5.72 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v0, v8) = v6) | ~ (element(v6, v3) = v7) | ? [v9] : (( ~ (v9 = 0) & morphism(v1, v3, v4) = v9) | ( ~ (v9 = 0) & element(v8, v2) = v9)))
% 21.77/5.72 | (58) injection(x) = all_0_1_1
% 21.77/5.72 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v5) | ? [v7] : ? [v8] : ? [v9] : ((v9 = v6 & v8 = 0 & apply(v0, v7) = v6 & element(v7, v2) = 0) | ( ~ (v7 = 0) & morphism(v1, v3, v4) = v7) | ( ~ (v7 = 0) & element(v6, v3) = v7)))
% 21.77/5.72 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (element(v8, v2) = 0) | ~ (element(v6, v3) = v7) | ? [v9] : (( ~ (v9 = v6) & apply(v0, v8) = v9) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9)))
% 21.77/5.72 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (injection(v2) = v1) | ~ (injection(v2) = v0))
% 21.77/5.72 | (62) ? [v0] : ? [v1] : injection(v0) = v1
% 21.77/5.72 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (morphism(v1, v3, v4) = 0) | ~ (morphism(v0, v2, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v5 = 0 & exact(v0, v1) = 0) | (zero(v4) = v5 & ((v11 = v6 & v10 = 0 & apply(v0, v9) = v6 & element(v9, v2) = 0) | (v8 = v5 & v7 = 0 & apply(v1, v6) = v5 & element(v6, v3) = 0)) & (( ~ (v8 = v5) & apply(v1, v6) = v8) | ( ~ (v7 = 0) & element(v6, v3) = v7) | ( ! [v12] : ( ~ (apply(v0, v12) = v6) | ? [v13] : ( ~ (v13 = 0) & element(v12, v2) = v13)) & ! [v12] : ( ~ (element(v12, v2) = 0) | ? [v13] : ( ~ (v13 = v6) & apply(v0, v12) = v13)))))))
% 21.77/5.73 | (64) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : commute(v3, v2, v1, v0) = v4
% 21.77/5.73 | (65) ? [v0] : ? [v1] : surjection(v0) = v1
% 21.77/5.73 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (exact(v0, v1) = 0) | ~ (morphism(v0, v2, v3) = 0) | ~ (zero(v4) = v5) | ~ (apply(v1, v6) = v7) | ~ (apply(v0, v8) = v6) | ? [v9] : ((v9 = 0 & element(v6, v3) = 0) | ( ~ (v9 = 0) & morphism(v1, v3, v4) = v9) | ( ~ (v9 = 0) & element(v8, v2) = v9)))
% 21.77/5.73 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (morphism(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v3 & v6 = 0 & ~ (v5 = v4) & zero(v2) = v3 & zero(v1) = v4 & apply(v0, v5) = v3 & element(v5, v1) = 0) | (v3 = 0 & injection_2(v0) = 0)))
% 21.77/5.73 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (commute(v0, v1, v2, v3) = v8) | ~ (morphism(v3, v6, v7) = 0) | ~ (morphism(v0, v4, v5) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v10 = 0 & ~ (v14 = v12) & apply(v3, v13) = v14 & apply(v2, v9) = v13 & apply(v1, v11) = v12 & apply(v0, v9) = v11 & element(v9, v4) = 0) | ( ~ (v9 = 0) & morphism(v2, v4, v6) = v9) | ( ~ (v9 = 0) & morphism(v1, v5, v7) = v9)))
% 21.77/5.73 |
% 21.77/5.73 | Instantiating formula (55) with any2, any1, x and discharging atoms morphism(x, any1, any2) = 0, yields:
% 21.77/5.73 | (69) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = v4 & v3 = 0 & v2 = 0 & ~ (v1 = v0) & apply(x, v1) = v4 & apply(x, v0) = v4 & element(v1, any1) = 0 & element(v0, any1) = 0) | (v0 = 0 & injection(x) = 0))
% 21.77/5.73 |
% 21.77/5.73 | Instantiating formula (67) with any2, any1, x and discharging atoms morphism(x, any1, any2) = 0, yields:
% 21.77/5.73 | (70) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ~ (v2 = v1) & zero(any2) = v0 & zero(any1) = v1 & apply(x, v2) = v0 & element(v2, any1) = 0) | (v0 = 0 & injection_2(x) = 0))
% 21.77/5.73 |
% 21.77/5.73 | Instantiating formula (47) with any2, any1, x and discharging atoms morphism(x, any1, any2) = 0, yields:
% 21.77/5.73 | (71) ? [v0] : ? [v1] : (zero(any2) = v1 & zero(any1) = v0 & apply(x, v0) = v1)
% 21.77/5.73 |
% 21.77/5.73 | Instantiating formula (51) with any2, any1, x and discharging atoms morphism(x, any1, any2) = 0, yields:
% 21.77/5.73 | (72) ? [v0] : ? [v1] : (( ~ (v0 = 0) & injection_2(x) = v0) | (zero(any2) = v0 & zero(any1) = v1 & ! [v2] : (v2 = v1 | ~ (apply(x, v2) = v0) | ? [v3] : ( ~ (v3 = 0) & element(v2, any1) = v3)) & ! [v2] : (v2 = v1 | ~ (element(v2, any1) = 0) | ? [v3] : ( ~ (v3 = v0) & apply(x, v2) = v3))))
% 21.77/5.73 |
% 21.77/5.73 | Instantiating (72) with all_28_0_32, all_28_1_33 yields:
% 21.77/5.73 | (73) ( ~ (all_28_1_33 = 0) & injection_2(x) = all_28_1_33) | (zero(any2) = all_28_1_33 & zero(any1) = all_28_0_32 & ! [v0] : (v0 = all_28_0_32 | ~ (apply(x, v0) = all_28_1_33) | ? [v1] : ( ~ (v1 = 0) & element(v0, any1) = v1)) & ! [v0] : (v0 = all_28_0_32 | ~ (element(v0, any1) = 0) | ? [v1] : ( ~ (v1 = all_28_1_33) & apply(x, v0) = v1)))
% 21.77/5.73 |
% 21.77/5.73 | Instantiating (71) with all_29_0_34, all_29_1_35 yields:
% 21.77/5.73 | (74) zero(any2) = all_29_0_34 & zero(any1) = all_29_1_35 & apply(x, all_29_1_35) = all_29_0_34
% 21.77/5.73 |
% 21.77/5.73 | Applying alpha-rule on (74) yields:
% 21.77/5.73 | (75) zero(any2) = all_29_0_34
% 21.77/5.73 | (76) zero(any1) = all_29_1_35
% 21.77/5.73 | (77) apply(x, all_29_1_35) = all_29_0_34
% 21.77/5.73 |
% 21.77/5.73 | Instantiating (69) with all_31_0_36, all_31_1_37, all_31_2_38, all_31_3_39, all_31_4_40, all_31_5_41 yields:
% 21.77/5.73 | (78) (all_31_0_36 = all_31_1_37 & all_31_2_38 = 0 & all_31_3_39 = 0 & ~ (all_31_4_40 = all_31_5_41) & apply(x, all_31_4_40) = all_31_1_37 & apply(x, all_31_5_41) = all_31_1_37 & element(all_31_4_40, any1) = 0 & element(all_31_5_41, any1) = 0) | (all_31_5_41 = 0 & injection(x) = 0)
% 21.77/5.73 |
% 21.77/5.73 | Instantiating (70) with all_32_0_42, all_32_1_43, all_32_2_44, all_32_3_45, all_32_4_46 yields:
% 21.77/5.73 | (79) (all_32_0_42 = all_32_4_46 & all_32_1_43 = 0 & ~ (all_32_2_44 = all_32_3_45) & zero(any2) = all_32_4_46 & zero(any1) = all_32_3_45 & apply(x, all_32_2_44) = all_32_4_46 & element(all_32_2_44, any1) = 0) | (all_32_4_46 = 0 & injection_2(x) = 0)
% 21.77/5.73 |
% 21.77/5.73 +-Applying beta-rule and splitting (22), into two cases.
% 21.77/5.73 |-Branch one:
% 21.77/5.73 | (80) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 21.77/5.73 |
% 21.77/5.73 | Applying alpha-rule on (80) yields:
% 21.77/5.73 | (81) all_0_0_0 = 0
% 21.77/5.73 | (82) ~ (all_0_1_1 = 0)
% 21.77/5.73 |
% 21.77/5.73 | From (81) and (33) follows:
% 21.77/5.73 | (83) injection_2(x) = 0
% 21.77/5.73 |
% 21.77/5.73 +-Applying beta-rule and splitting (73), into two cases.
% 21.77/5.73 |-Branch one:
% 21.77/5.73 | (84) ~ (all_28_1_33 = 0) & injection_2(x) = all_28_1_33
% 21.77/5.73 |
% 21.77/5.73 | Applying alpha-rule on (84) yields:
% 21.77/5.73 | (85) ~ (all_28_1_33 = 0)
% 21.77/5.73 | (86) injection_2(x) = all_28_1_33
% 21.77/5.73 |
% 21.77/5.73 | Instantiating formula (43) with x, 0, all_28_1_33 and discharging atoms injection_2(x) = all_28_1_33, injection_2(x) = 0, yields:
% 21.77/5.73 | (87) all_28_1_33 = 0
% 21.77/5.73 |
% 21.77/5.73 | Equations (87) can reduce 85 to:
% 21.77/5.73 | (88) $false
% 21.77/5.73 |
% 21.77/5.73 |-The branch is then unsatisfiable
% 21.77/5.73 |-Branch two:
% 21.77/5.73 | (89) zero(any2) = all_28_1_33 & zero(any1) = all_28_0_32 & ! [v0] : (v0 = all_28_0_32 | ~ (apply(x, v0) = all_28_1_33) | ? [v1] : ( ~ (v1 = 0) & element(v0, any1) = v1)) & ! [v0] : (v0 = all_28_0_32 | ~ (element(v0, any1) = 0) | ? [v1] : ( ~ (v1 = all_28_1_33) & apply(x, v0) = v1))
% 21.77/5.73 |
% 21.77/5.73 | Applying alpha-rule on (89) yields:
% 21.77/5.73 | (90) zero(any2) = all_28_1_33
% 21.77/5.73 | (91) zero(any1) = all_28_0_32
% 21.77/5.73 | (92) ! [v0] : (v0 = all_28_0_32 | ~ (apply(x, v0) = all_28_1_33) | ? [v1] : ( ~ (v1 = 0) & element(v0, any1) = v1))
% 21.77/5.73 | (93) ! [v0] : (v0 = all_28_0_32 | ~ (element(v0, any1) = 0) | ? [v1] : ( ~ (v1 = all_28_1_33) & apply(x, v0) = v1))
% 21.77/5.74 |
% 21.77/5.74 +-Applying beta-rule and splitting (78), into two cases.
% 21.77/5.74 |-Branch one:
% 21.77/5.74 | (94) all_31_0_36 = all_31_1_37 & all_31_2_38 = 0 & all_31_3_39 = 0 & ~ (all_31_4_40 = all_31_5_41) & apply(x, all_31_4_40) = all_31_1_37 & apply(x, all_31_5_41) = all_31_1_37 & element(all_31_4_40, any1) = 0 & element(all_31_5_41, any1) = 0
% 21.77/5.74 |
% 21.77/5.74 | Applying alpha-rule on (94) yields:
% 21.77/5.74 | (95) all_31_3_39 = 0
% 21.77/5.74 | (96) element(all_31_4_40, any1) = 0
% 21.77/5.74 | (97) all_31_0_36 = all_31_1_37
% 21.77/5.74 | (98) apply(x, all_31_4_40) = all_31_1_37
% 21.77/5.74 | (99) all_31_2_38 = 0
% 21.77/5.74 | (100) element(all_31_5_41, any1) = 0
% 21.77/5.74 | (101) ~ (all_31_4_40 = all_31_5_41)
% 21.77/5.74 | (102) apply(x, all_31_5_41) = all_31_1_37
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (23) with any2, all_28_1_33, all_29_0_34 and discharging atoms zero(any2) = all_29_0_34, zero(any2) = all_28_1_33, yields:
% 21.77/5.74 | (103) all_29_0_34 = all_28_1_33
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (23) with any1, all_28_0_32, all_29_1_35 and discharging atoms zero(any1) = all_29_1_35, zero(any1) = all_28_0_32, yields:
% 21.77/5.74 | (104) all_29_1_35 = all_28_0_32
% 21.77/5.74 |
% 21.77/5.74 | From (103) and (75) follows:
% 21.77/5.74 | (90) zero(any2) = all_28_1_33
% 21.77/5.74 |
% 21.77/5.74 | From (104) and (76) follows:
% 21.77/5.74 | (91) zero(any1) = all_28_0_32
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (34) with all_31_4_40, any2, any1, x and discharging atoms morphism(x, any1, any2) = 0, element(all_31_4_40, any1) = 0, yields:
% 21.77/5.74 | (107) ? [v0] : (apply(x, all_31_4_40) = v0 & element(v0, any2) = 0)
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (6) with all_31_4_40, any1 and discharging atoms element(all_31_4_40, any1) = 0, yields:
% 21.77/5.74 | (108) ? [v0] : (subtract(any1, all_31_4_40, all_31_4_40) = v0 & zero(any1) = v0)
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (34) with all_31_5_41, any2, any1, x and discharging atoms morphism(x, any1, any2) = 0, element(all_31_5_41, any1) = 0, yields:
% 21.77/5.74 | (109) ? [v0] : (apply(x, all_31_5_41) = v0 & element(v0, any2) = 0)
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (6) with all_31_5_41, any1 and discharging atoms element(all_31_5_41, any1) = 0, yields:
% 21.77/5.74 | (110) ? [v0] : (subtract(any1, all_31_5_41, all_31_5_41) = v0 & zero(any1) = v0)
% 21.77/5.74 |
% 21.77/5.74 | Instantiating (110) with all_60_0_50 yields:
% 21.77/5.74 | (111) subtract(any1, all_31_5_41, all_31_5_41) = all_60_0_50 & zero(any1) = all_60_0_50
% 21.77/5.74 |
% 21.77/5.74 | Applying alpha-rule on (111) yields:
% 21.77/5.74 | (112) subtract(any1, all_31_5_41, all_31_5_41) = all_60_0_50
% 21.77/5.74 | (113) zero(any1) = all_60_0_50
% 21.77/5.74 |
% 21.77/5.74 | Instantiating (107) with all_62_0_51 yields:
% 21.77/5.74 | (114) apply(x, all_31_4_40) = all_62_0_51 & element(all_62_0_51, any2) = 0
% 21.77/5.74 |
% 21.77/5.74 | Applying alpha-rule on (114) yields:
% 21.77/5.74 | (115) apply(x, all_31_4_40) = all_62_0_51
% 21.77/5.74 | (116) element(all_62_0_51, any2) = 0
% 21.77/5.74 |
% 21.77/5.74 | Instantiating (109) with all_65_0_53 yields:
% 21.77/5.74 | (117) apply(x, all_31_5_41) = all_65_0_53 & element(all_65_0_53, any2) = 0
% 21.77/5.74 |
% 21.77/5.74 | Applying alpha-rule on (117) yields:
% 21.77/5.74 | (118) apply(x, all_31_5_41) = all_65_0_53
% 21.77/5.74 | (119) element(all_65_0_53, any2) = 0
% 21.77/5.74 |
% 21.77/5.74 | Instantiating (108) with all_67_0_54 yields:
% 21.77/5.74 | (120) subtract(any1, all_31_4_40, all_31_4_40) = all_67_0_54 & zero(any1) = all_67_0_54
% 21.77/5.74 |
% 21.77/5.74 | Applying alpha-rule on (120) yields:
% 21.77/5.74 | (121) subtract(any1, all_31_4_40, all_31_4_40) = all_67_0_54
% 21.77/5.74 | (122) zero(any1) = all_67_0_54
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (23) with any1, all_67_0_54, all_28_0_32 and discharging atoms zero(any1) = all_67_0_54, zero(any1) = all_28_0_32, yields:
% 21.77/5.74 | (123) all_67_0_54 = all_28_0_32
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (23) with any1, all_60_0_50, all_67_0_54 and discharging atoms zero(any1) = all_67_0_54, zero(any1) = all_60_0_50, yields:
% 21.77/5.74 | (124) all_67_0_54 = all_60_0_50
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (44) with x, all_31_4_40, all_62_0_51, all_31_1_37 and discharging atoms apply(x, all_31_4_40) = all_62_0_51, apply(x, all_31_4_40) = all_31_1_37, yields:
% 21.77/5.74 | (125) all_62_0_51 = all_31_1_37
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (44) with x, all_31_5_41, all_65_0_53, all_31_1_37 and discharging atoms apply(x, all_31_5_41) = all_65_0_53, apply(x, all_31_5_41) = all_31_1_37, yields:
% 21.77/5.74 | (126) all_65_0_53 = all_31_1_37
% 21.77/5.74 |
% 21.77/5.74 | Combining equations (124,123) yields a new equation:
% 21.77/5.74 | (127) all_60_0_50 = all_28_0_32
% 21.77/5.74 |
% 21.77/5.74 | Simplifying 127 yields:
% 21.77/5.74 | (128) all_60_0_50 = all_28_0_32
% 21.77/5.74 |
% 21.77/5.74 | From (123) and (121) follows:
% 21.77/5.74 | (129) subtract(any1, all_31_4_40, all_31_4_40) = all_28_0_32
% 21.77/5.74 |
% 21.77/5.74 | From (128) and (112) follows:
% 21.77/5.74 | (130) subtract(any1, all_31_5_41, all_31_5_41) = all_28_0_32
% 21.77/5.74 |
% 21.77/5.74 | From (125) and (115) follows:
% 21.77/5.74 | (98) apply(x, all_31_4_40) = all_31_1_37
% 21.77/5.74 |
% 21.77/5.74 | From (126) and (118) follows:
% 21.77/5.74 | (102) apply(x, all_31_5_41) = all_31_1_37
% 21.77/5.74 |
% 21.77/5.74 | From (125) and (116) follows:
% 21.77/5.74 | (133) element(all_31_1_37, any2) = 0
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (53) with all_28_0_32, all_31_4_40, all_31_4_40, any2, any1, x and discharging atoms subtract(any1, all_31_4_40, all_31_4_40) = all_28_0_32, morphism(x, any1, any2) = 0, yields:
% 21.77/5.74 | (134) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & subtract(any2, v1, v2) = v0 & apply(x, all_31_4_40) = v2 & apply(x, all_31_4_40) = v1 & apply(x, all_28_0_32) = v0) | ( ~ (v0 = 0) & element(all_31_4_40, any1) = v0))
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (12) with all_28_0_32, all_31_4_40, all_31_4_40, any1 and discharging atoms subtract(any1, all_31_4_40, all_31_4_40) = all_28_0_32, yields:
% 21.77/5.74 | (135) ? [v0] : ((v0 = all_31_4_40 & subtract(any1, all_31_4_40, all_28_0_32) = all_31_4_40) | ( ~ (v0 = 0) & element(all_31_4_40, any1) = v0))
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (53) with all_28_0_32, all_31_5_41, all_31_5_41, any2, any1, x and discharging atoms subtract(any1, all_31_5_41, all_31_5_41) = all_28_0_32, morphism(x, any1, any2) = 0, yields:
% 21.77/5.74 | (136) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & subtract(any2, v1, v2) = v0 & apply(x, all_31_5_41) = v2 & apply(x, all_31_5_41) = v1 & apply(x, all_28_0_32) = v0) | ( ~ (v0 = 0) & element(all_31_5_41, any1) = v0))
% 21.77/5.74 |
% 21.77/5.74 | Instantiating formula (6) with all_31_1_37, any2 and discharging atoms element(all_31_1_37, any2) = 0, yields:
% 21.77/5.74 | (137) ? [v0] : (subtract(any2, all_31_1_37, all_31_1_37) = v0 & zero(any2) = v0)
% 21.77/5.74 |
% 21.77/5.74 | Instantiating (137) with all_87_0_56 yields:
% 21.77/5.74 | (138) subtract(any2, all_31_1_37, all_31_1_37) = all_87_0_56 & zero(any2) = all_87_0_56
% 21.77/5.74 |
% 21.77/5.74 | Applying alpha-rule on (138) yields:
% 21.77/5.74 | (139) subtract(any2, all_31_1_37, all_31_1_37) = all_87_0_56
% 21.77/5.74 | (140) zero(any2) = all_87_0_56
% 21.77/5.74 |
% 21.77/5.74 | Instantiating (136) with all_92_0_62, all_92_1_63, all_92_2_64, all_92_3_65 yields:
% 21.77/5.74 | (141) (all_92_0_62 = all_92_3_65 & subtract(any2, all_92_2_64, all_92_1_63) = all_92_3_65 & apply(x, all_31_5_41) = all_92_1_63 & apply(x, all_31_5_41) = all_92_2_64 & apply(x, all_28_0_32) = all_92_3_65) | ( ~ (all_92_3_65 = 0) & element(all_31_5_41, any1) = all_92_3_65)
% 21.77/5.74 |
% 21.77/5.74 | Instantiating (135) with all_94_0_67 yields:
% 21.77/5.74 | (142) (all_94_0_67 = all_31_4_40 & subtract(any1, all_31_4_40, all_28_0_32) = all_31_4_40) | ( ~ (all_94_0_67 = 0) & element(all_31_4_40, any1) = all_94_0_67)
% 21.77/5.74 |
% 21.77/5.74 | Instantiating (134) with all_95_0_68, all_95_1_69, all_95_2_70, all_95_3_71 yields:
% 21.77/5.74 | (143) (all_95_0_68 = all_95_3_71 & subtract(any2, all_95_2_70, all_95_1_69) = all_95_3_71 & apply(x, all_31_4_40) = all_95_1_69 & apply(x, all_31_4_40) = all_95_2_70 & apply(x, all_28_0_32) = all_95_3_71) | ( ~ (all_95_3_71 = 0) & element(all_31_4_40, any1) = all_95_3_71)
% 21.77/5.74 |
% 21.77/5.74 +-Applying beta-rule and splitting (143), into two cases.
% 21.77/5.74 |-Branch one:
% 21.77/5.74 | (144) all_95_0_68 = all_95_3_71 & subtract(any2, all_95_2_70, all_95_1_69) = all_95_3_71 & apply(x, all_31_4_40) = all_95_1_69 & apply(x, all_31_4_40) = all_95_2_70 & apply(x, all_28_0_32) = all_95_3_71
% 21.77/5.74 |
% 21.77/5.74 | Applying alpha-rule on (144) yields:
% 21.77/5.74 | (145) subtract(any2, all_95_2_70, all_95_1_69) = all_95_3_71
% 21.77/5.74 | (146) apply(x, all_31_4_40) = all_95_2_70
% 21.77/5.74 | (147) all_95_0_68 = all_95_3_71
% 21.77/5.74 | (148) apply(x, all_28_0_32) = all_95_3_71
% 21.77/5.74 | (149) apply(x, all_31_4_40) = all_95_1_69
% 21.77/5.75 |
% 21.77/5.75 +-Applying beta-rule and splitting (141), into two cases.
% 21.77/5.75 |-Branch one:
% 21.77/5.75 | (150) all_92_0_62 = all_92_3_65 & subtract(any2, all_92_2_64, all_92_1_63) = all_92_3_65 & apply(x, all_31_5_41) = all_92_1_63 & apply(x, all_31_5_41) = all_92_2_64 & apply(x, all_28_0_32) = all_92_3_65
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (150) yields:
% 21.77/5.75 | (151) subtract(any2, all_92_2_64, all_92_1_63) = all_92_3_65
% 21.77/5.75 | (152) apply(x, all_28_0_32) = all_92_3_65
% 21.77/5.75 | (153) apply(x, all_31_5_41) = all_92_2_64
% 21.77/5.75 | (154) apply(x, all_31_5_41) = all_92_1_63
% 21.77/5.75 | (155) all_92_0_62 = all_92_3_65
% 21.77/5.75 |
% 21.77/5.75 +-Applying beta-rule and splitting (142), into two cases.
% 21.77/5.75 |-Branch one:
% 21.77/5.75 | (156) all_94_0_67 = all_31_4_40 & subtract(any1, all_31_4_40, all_28_0_32) = all_31_4_40
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (156) yields:
% 21.77/5.75 | (157) all_94_0_67 = all_31_4_40
% 21.77/5.75 | (158) subtract(any1, all_31_4_40, all_28_0_32) = all_31_4_40
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (23) with any2, all_87_0_56, all_28_1_33 and discharging atoms zero(any2) = all_87_0_56, zero(any2) = all_28_1_33, yields:
% 21.77/5.75 | (159) all_87_0_56 = all_28_1_33
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (44) with x, all_31_4_40, all_95_1_69, all_31_1_37 and discharging atoms apply(x, all_31_4_40) = all_95_1_69, apply(x, all_31_4_40) = all_31_1_37, yields:
% 21.77/5.75 | (160) all_95_1_69 = all_31_1_37
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (44) with x, all_31_4_40, all_95_2_70, all_95_1_69 and discharging atoms apply(x, all_31_4_40) = all_95_1_69, apply(x, all_31_4_40) = all_95_2_70, yields:
% 21.77/5.75 | (161) all_95_1_69 = all_95_2_70
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (44) with x, all_31_5_41, all_92_1_63, all_31_1_37 and discharging atoms apply(x, all_31_5_41) = all_92_1_63, apply(x, all_31_5_41) = all_31_1_37, yields:
% 21.77/5.75 | (162) all_92_1_63 = all_31_1_37
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (44) with x, all_31_5_41, all_92_2_64, all_92_1_63 and discharging atoms apply(x, all_31_5_41) = all_92_1_63, apply(x, all_31_5_41) = all_92_2_64, yields:
% 21.77/5.75 | (163) all_92_1_63 = all_92_2_64
% 21.77/5.75 |
% 21.77/5.75 | Combining equations (160,161) yields a new equation:
% 21.77/5.75 | (164) all_95_2_70 = all_31_1_37
% 21.77/5.75 |
% 21.77/5.75 | Combining equations (163,162) yields a new equation:
% 21.77/5.75 | (165) all_92_2_64 = all_31_1_37
% 21.77/5.75 |
% 21.77/5.75 | Simplifying 165 yields:
% 21.77/5.75 | (166) all_92_2_64 = all_31_1_37
% 21.77/5.75 |
% 21.77/5.75 | From (159) and (139) follows:
% 21.77/5.75 | (167) subtract(any2, all_31_1_37, all_31_1_37) = all_28_1_33
% 21.77/5.75 |
% 21.77/5.75 | From (164) and (146) follows:
% 21.77/5.75 | (98) apply(x, all_31_4_40) = all_31_1_37
% 21.77/5.75 |
% 21.77/5.75 | From (166) and (153) follows:
% 21.77/5.75 | (102) apply(x, all_31_5_41) = all_31_1_37
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (45) with all_28_1_33, all_31_1_37, all_31_1_37, all_31_5_41, all_31_4_40, any2, any1, x and discharging atoms subtract(any2, all_31_1_37, all_31_1_37) = all_28_1_33, morphism(x, any1, any2) = 0, apply(x, all_31_4_40) = all_31_1_37, apply(x, all_31_5_41) = all_31_1_37, yields:
% 21.77/5.75 | (170) ? [v0] : ? [v1] : ((v1 = all_28_1_33 & subtract(any1, all_31_4_40, all_31_5_41) = v0 & apply(x, v0) = all_28_1_33) | ( ~ (v0 = 0) & element(all_31_4_40, any1) = v0) | ( ~ (v0 = 0) & element(all_31_5_41, any1) = v0))
% 21.77/5.75 |
% 21.77/5.75 | Instantiating (170) with all_141_0_86, all_141_1_87 yields:
% 21.77/5.75 | (171) (all_141_0_86 = all_28_1_33 & subtract(any1, all_31_4_40, all_31_5_41) = all_141_1_87 & apply(x, all_141_1_87) = all_28_1_33) | ( ~ (all_141_1_87 = 0) & element(all_31_4_40, any1) = all_141_1_87) | ( ~ (all_141_1_87 = 0) & element(all_31_5_41, any1) = all_141_1_87)
% 21.77/5.75 |
% 21.77/5.75 +-Applying beta-rule and splitting (171), into two cases.
% 21.77/5.75 |-Branch one:
% 21.77/5.75 | (172) (all_141_0_86 = all_28_1_33 & subtract(any1, all_31_4_40, all_31_5_41) = all_141_1_87 & apply(x, all_141_1_87) = all_28_1_33) | ( ~ (all_141_1_87 = 0) & element(all_31_4_40, any1) = all_141_1_87)
% 21.77/5.75 |
% 21.77/5.75 +-Applying beta-rule and splitting (172), into two cases.
% 21.77/5.75 |-Branch one:
% 21.77/5.75 | (173) all_141_0_86 = all_28_1_33 & subtract(any1, all_31_4_40, all_31_5_41) = all_141_1_87 & apply(x, all_141_1_87) = all_28_1_33
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (173) yields:
% 21.77/5.75 | (174) all_141_0_86 = all_28_1_33
% 21.77/5.75 | (175) subtract(any1, all_31_4_40, all_31_5_41) = all_141_1_87
% 21.77/5.75 | (176) apply(x, all_141_1_87) = all_28_1_33
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (12) with all_141_1_87, all_31_5_41, all_31_4_40, any1 and discharging atoms subtract(any1, all_31_4_40, all_31_5_41) = all_141_1_87, yields:
% 21.77/5.75 | (177) ? [v0] : ((v0 = all_31_5_41 & subtract(any1, all_31_4_40, all_141_1_87) = all_31_5_41) | ( ~ (v0 = 0) & element(all_31_4_40, any1) = v0) | ( ~ (v0 = 0) & element(all_31_5_41, any1) = v0))
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (19) with all_141_1_87, all_31_5_41, all_31_4_40, any1 and discharging atoms subtract(any1, all_31_4_40, all_31_5_41) = all_141_1_87, yields:
% 21.77/5.75 | (178) ? [v0] : ((v0 = 0 & element(all_141_1_87, any1) = 0) | ( ~ (v0 = 0) & element(all_31_4_40, any1) = v0) | ( ~ (v0 = 0) & element(all_31_5_41, any1) = v0))
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (92) with all_141_1_87 and discharging atoms apply(x, all_141_1_87) = all_28_1_33, yields:
% 21.77/5.75 | (179) all_141_1_87 = all_28_0_32 | ? [v0] : ( ~ (v0 = 0) & element(all_141_1_87, any1) = v0)
% 21.77/5.75 |
% 21.77/5.75 | Instantiating (178) with all_207_0_340 yields:
% 21.77/5.75 | (180) (all_207_0_340 = 0 & element(all_141_1_87, any1) = 0) | ( ~ (all_207_0_340 = 0) & element(all_31_4_40, any1) = all_207_0_340) | ( ~ (all_207_0_340 = 0) & element(all_31_5_41, any1) = all_207_0_340)
% 21.77/5.75 |
% 21.77/5.75 | Instantiating (177) with all_208_0_341 yields:
% 21.77/5.75 | (181) (all_208_0_341 = all_31_5_41 & subtract(any1, all_31_4_40, all_141_1_87) = all_31_5_41) | ( ~ (all_208_0_341 = 0) & element(all_31_4_40, any1) = all_208_0_341) | ( ~ (all_208_0_341 = 0) & element(all_31_5_41, any1) = all_208_0_341)
% 21.77/5.75 |
% 21.77/5.75 +-Applying beta-rule and splitting (181), into two cases.
% 21.77/5.75 |-Branch one:
% 21.77/5.75 | (182) (all_208_0_341 = all_31_5_41 & subtract(any1, all_31_4_40, all_141_1_87) = all_31_5_41) | ( ~ (all_208_0_341 = 0) & element(all_31_4_40, any1) = all_208_0_341)
% 21.77/5.75 |
% 21.77/5.75 +-Applying beta-rule and splitting (182), into two cases.
% 21.77/5.75 |-Branch one:
% 21.77/5.75 | (183) all_208_0_341 = all_31_5_41 & subtract(any1, all_31_4_40, all_141_1_87) = all_31_5_41
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (183) yields:
% 21.77/5.75 | (184) all_208_0_341 = all_31_5_41
% 21.77/5.75 | (185) subtract(any1, all_31_4_40, all_141_1_87) = all_31_5_41
% 21.77/5.75 |
% 21.77/5.75 +-Applying beta-rule and splitting (180), into two cases.
% 21.77/5.75 |-Branch one:
% 21.77/5.75 | (186) (all_207_0_340 = 0 & element(all_141_1_87, any1) = 0) | ( ~ (all_207_0_340 = 0) & element(all_31_4_40, any1) = all_207_0_340)
% 21.77/5.75 |
% 21.77/5.75 +-Applying beta-rule and splitting (186), into two cases.
% 21.77/5.75 |-Branch one:
% 21.77/5.75 | (187) all_207_0_340 = 0 & element(all_141_1_87, any1) = 0
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (187) yields:
% 21.77/5.75 | (188) all_207_0_340 = 0
% 21.77/5.75 | (189) element(all_141_1_87, any1) = 0
% 21.77/5.75 |
% 21.77/5.75 +-Applying beta-rule and splitting (179), into two cases.
% 21.77/5.75 |-Branch one:
% 21.77/5.75 | (190) all_141_1_87 = all_28_0_32
% 21.77/5.75 |
% 21.77/5.75 | From (190) and (185) follows:
% 21.77/5.75 | (191) subtract(any1, all_31_4_40, all_28_0_32) = all_31_5_41
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (38) with any1, all_31_4_40, all_28_0_32, all_31_5_41, all_31_4_40 and discharging atoms subtract(any1, all_31_4_40, all_28_0_32) = all_31_4_40, subtract(any1, all_31_4_40, all_28_0_32) = all_31_5_41, yields:
% 21.77/5.75 | (192) all_31_4_40 = all_31_5_41
% 21.77/5.75 |
% 21.77/5.75 | Equations (192) can reduce 101 to:
% 21.77/5.75 | (88) $false
% 21.77/5.75 |
% 21.77/5.75 |-The branch is then unsatisfiable
% 21.77/5.75 |-Branch two:
% 21.77/5.75 | (194) ~ (all_141_1_87 = all_28_0_32)
% 21.77/5.75 | (195) ? [v0] : ( ~ (v0 = 0) & element(all_141_1_87, any1) = v0)
% 21.77/5.75 |
% 21.77/5.75 | Instantiating (195) with all_240_0_355 yields:
% 21.77/5.75 | (196) ~ (all_240_0_355 = 0) & element(all_141_1_87, any1) = all_240_0_355
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (196) yields:
% 21.77/5.75 | (197) ~ (all_240_0_355 = 0)
% 21.77/5.75 | (198) element(all_141_1_87, any1) = all_240_0_355
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (15) with all_141_1_87, any1, 0, all_240_0_355 and discharging atoms element(all_141_1_87, any1) = all_240_0_355, element(all_141_1_87, any1) = 0, yields:
% 21.77/5.75 | (199) all_240_0_355 = 0
% 21.77/5.75 |
% 21.77/5.75 | Equations (199) can reduce 197 to:
% 21.77/5.75 | (88) $false
% 21.77/5.75 |
% 21.77/5.75 |-The branch is then unsatisfiable
% 21.77/5.75 |-Branch two:
% 21.77/5.75 | (201) ~ (all_207_0_340 = 0) & element(all_31_4_40, any1) = all_207_0_340
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (201) yields:
% 21.77/5.75 | (202) ~ (all_207_0_340 = 0)
% 21.77/5.75 | (203) element(all_31_4_40, any1) = all_207_0_340
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (15) with all_31_4_40, any1, all_207_0_340, 0 and discharging atoms element(all_31_4_40, any1) = all_207_0_340, element(all_31_4_40, any1) = 0, yields:
% 21.77/5.75 | (188) all_207_0_340 = 0
% 21.77/5.75 |
% 21.77/5.75 | Equations (188) can reduce 202 to:
% 21.77/5.75 | (88) $false
% 21.77/5.75 |
% 21.77/5.75 |-The branch is then unsatisfiable
% 21.77/5.75 |-Branch two:
% 21.77/5.75 | (206) ~ (all_207_0_340 = 0) & element(all_31_5_41, any1) = all_207_0_340
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (206) yields:
% 21.77/5.75 | (202) ~ (all_207_0_340 = 0)
% 21.77/5.75 | (208) element(all_31_5_41, any1) = all_207_0_340
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (15) with all_31_5_41, any1, all_207_0_340, 0 and discharging atoms element(all_31_5_41, any1) = all_207_0_340, element(all_31_5_41, any1) = 0, yields:
% 21.77/5.75 | (188) all_207_0_340 = 0
% 21.77/5.75 |
% 21.77/5.75 | Equations (188) can reduce 202 to:
% 21.77/5.75 | (88) $false
% 21.77/5.75 |
% 21.77/5.75 |-The branch is then unsatisfiable
% 21.77/5.75 |-Branch two:
% 21.77/5.75 | (211) ~ (all_208_0_341 = 0) & element(all_31_4_40, any1) = all_208_0_341
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (211) yields:
% 21.77/5.75 | (212) ~ (all_208_0_341 = 0)
% 21.77/5.75 | (213) element(all_31_4_40, any1) = all_208_0_341
% 21.77/5.75 |
% 21.77/5.75 | Instantiating formula (15) with all_31_4_40, any1, all_208_0_341, 0 and discharging atoms element(all_31_4_40, any1) = all_208_0_341, element(all_31_4_40, any1) = 0, yields:
% 21.77/5.75 | (214) all_208_0_341 = 0
% 21.77/5.75 |
% 21.77/5.75 | Equations (214) can reduce 212 to:
% 21.77/5.75 | (88) $false
% 21.77/5.75 |
% 21.77/5.75 |-The branch is then unsatisfiable
% 21.77/5.75 |-Branch two:
% 21.77/5.75 | (216) ~ (all_208_0_341 = 0) & element(all_31_5_41, any1) = all_208_0_341
% 21.77/5.75 |
% 21.77/5.75 | Applying alpha-rule on (216) yields:
% 21.77/5.75 | (212) ~ (all_208_0_341 = 0)
% 21.77/5.75 | (218) element(all_31_5_41, any1) = all_208_0_341
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (15) with all_31_5_41, any1, all_208_0_341, 0 and discharging atoms element(all_31_5_41, any1) = all_208_0_341, element(all_31_5_41, any1) = 0, yields:
% 21.77/5.76 | (214) all_208_0_341 = 0
% 21.77/5.76 |
% 21.77/5.76 | Equations (214) can reduce 212 to:
% 21.77/5.76 | (88) $false
% 21.77/5.76 |
% 21.77/5.76 |-The branch is then unsatisfiable
% 21.77/5.76 |-Branch two:
% 21.77/5.76 | (221) ~ (all_141_1_87 = 0) & element(all_31_4_40, any1) = all_141_1_87
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (221) yields:
% 21.77/5.76 | (222) ~ (all_141_1_87 = 0)
% 21.77/5.76 | (223) element(all_31_4_40, any1) = all_141_1_87
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (15) with all_31_4_40, any1, all_141_1_87, 0 and discharging atoms element(all_31_4_40, any1) = all_141_1_87, element(all_31_4_40, any1) = 0, yields:
% 21.77/5.76 | (224) all_141_1_87 = 0
% 21.77/5.76 |
% 21.77/5.76 | Equations (224) can reduce 222 to:
% 21.77/5.76 | (88) $false
% 21.77/5.76 |
% 21.77/5.76 |-The branch is then unsatisfiable
% 21.77/5.76 |-Branch two:
% 21.77/5.76 | (226) ~ (all_141_1_87 = 0) & element(all_31_5_41, any1) = all_141_1_87
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (226) yields:
% 21.77/5.76 | (222) ~ (all_141_1_87 = 0)
% 21.77/5.76 | (228) element(all_31_5_41, any1) = all_141_1_87
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (15) with all_31_5_41, any1, all_141_1_87, 0 and discharging atoms element(all_31_5_41, any1) = all_141_1_87, element(all_31_5_41, any1) = 0, yields:
% 21.77/5.76 | (224) all_141_1_87 = 0
% 21.77/5.76 |
% 21.77/5.76 | Equations (224) can reduce 222 to:
% 21.77/5.76 | (88) $false
% 21.77/5.76 |
% 21.77/5.76 |-The branch is then unsatisfiable
% 21.77/5.76 |-Branch two:
% 21.77/5.76 | (231) ~ (all_94_0_67 = 0) & element(all_31_4_40, any1) = all_94_0_67
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (231) yields:
% 21.77/5.76 | (232) ~ (all_94_0_67 = 0)
% 21.77/5.76 | (233) element(all_31_4_40, any1) = all_94_0_67
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (15) with all_31_4_40, any1, all_94_0_67, 0 and discharging atoms element(all_31_4_40, any1) = all_94_0_67, element(all_31_4_40, any1) = 0, yields:
% 21.77/5.76 | (234) all_94_0_67 = 0
% 21.77/5.76 |
% 21.77/5.76 | Equations (234) can reduce 232 to:
% 21.77/5.76 | (88) $false
% 21.77/5.76 |
% 21.77/5.76 |-The branch is then unsatisfiable
% 21.77/5.76 |-Branch two:
% 21.77/5.76 | (236) ~ (all_92_3_65 = 0) & element(all_31_5_41, any1) = all_92_3_65
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (236) yields:
% 21.77/5.76 | (237) ~ (all_92_3_65 = 0)
% 21.77/5.76 | (238) element(all_31_5_41, any1) = all_92_3_65
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (15) with all_31_5_41, any1, all_92_3_65, 0 and discharging atoms element(all_31_5_41, any1) = all_92_3_65, element(all_31_5_41, any1) = 0, yields:
% 21.77/5.76 | (239) all_92_3_65 = 0
% 21.77/5.76 |
% 21.77/5.76 | Equations (239) can reduce 237 to:
% 21.77/5.76 | (88) $false
% 21.77/5.76 |
% 21.77/5.76 |-The branch is then unsatisfiable
% 21.77/5.76 |-Branch two:
% 21.77/5.76 | (241) ~ (all_95_3_71 = 0) & element(all_31_4_40, any1) = all_95_3_71
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (241) yields:
% 21.77/5.76 | (242) ~ (all_95_3_71 = 0)
% 21.77/5.76 | (243) element(all_31_4_40, any1) = all_95_3_71
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (15) with all_31_4_40, any1, all_95_3_71, 0 and discharging atoms element(all_31_4_40, any1) = all_95_3_71, element(all_31_4_40, any1) = 0, yields:
% 21.77/5.76 | (244) all_95_3_71 = 0
% 21.77/5.76 |
% 21.77/5.76 | Equations (244) can reduce 242 to:
% 21.77/5.76 | (88) $false
% 21.77/5.76 |
% 21.77/5.76 |-The branch is then unsatisfiable
% 21.77/5.76 |-Branch two:
% 21.77/5.76 | (246) all_31_5_41 = 0 & injection(x) = 0
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (246) yields:
% 21.77/5.76 | (247) all_31_5_41 = 0
% 21.77/5.76 | (248) injection(x) = 0
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (61) with x, 0, all_0_1_1 and discharging atoms injection(x) = all_0_1_1, injection(x) = 0, yields:
% 21.77/5.76 | (249) all_0_1_1 = 0
% 21.77/5.76 |
% 21.77/5.76 | Equations (249) can reduce 82 to:
% 21.77/5.76 | (88) $false
% 21.77/5.76 |
% 21.77/5.76 |-The branch is then unsatisfiable
% 21.77/5.76 |-Branch two:
% 21.77/5.76 | (251) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (251) yields:
% 21.77/5.76 | (249) all_0_1_1 = 0
% 21.77/5.76 | (253) ~ (all_0_0_0 = 0)
% 21.77/5.76 |
% 21.77/5.76 | From (249) and (58) follows:
% 21.77/5.76 | (248) injection(x) = 0
% 21.77/5.76 |
% 21.77/5.76 +-Applying beta-rule and splitting (79), into two cases.
% 21.77/5.76 |-Branch one:
% 21.77/5.76 | (255) all_32_0_42 = all_32_4_46 & all_32_1_43 = 0 & ~ (all_32_2_44 = all_32_3_45) & zero(any2) = all_32_4_46 & zero(any1) = all_32_3_45 & apply(x, all_32_2_44) = all_32_4_46 & element(all_32_2_44, any1) = 0
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (255) yields:
% 21.77/5.76 | (256) zero(any1) = all_32_3_45
% 21.77/5.76 | (257) ~ (all_32_2_44 = all_32_3_45)
% 21.77/5.76 | (258) all_32_0_42 = all_32_4_46
% 21.77/5.76 | (259) element(all_32_2_44, any1) = 0
% 21.77/5.76 | (260) zero(any2) = all_32_4_46
% 21.77/5.76 | (261) apply(x, all_32_2_44) = all_32_4_46
% 21.77/5.76 | (262) all_32_1_43 = 0
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (23) with any2, all_32_4_46, all_29_0_34 and discharging atoms zero(any2) = all_32_4_46, zero(any2) = all_29_0_34, yields:
% 21.77/5.76 | (263) all_32_4_46 = all_29_0_34
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (23) with any1, all_32_3_45, all_29_1_35 and discharging atoms zero(any1) = all_32_3_45, zero(any1) = all_29_1_35, yields:
% 21.77/5.76 | (264) all_32_3_45 = all_29_1_35
% 21.77/5.76 |
% 21.77/5.76 | Equations (264) can reduce 257 to:
% 21.77/5.76 | (265) ~ (all_32_2_44 = all_29_1_35)
% 21.77/5.76 |
% 21.77/5.76 | From (264) and (256) follows:
% 21.77/5.76 | (76) zero(any1) = all_29_1_35
% 21.77/5.76 |
% 21.77/5.76 | From (263) and (261) follows:
% 21.77/5.76 | (267) apply(x, all_32_2_44) = all_29_0_34
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (10) with all_29_0_34, all_32_2_44, all_29_1_35, any2, any1, x and discharging atoms morphism(x, any1, any2) = 0, apply(x, all_32_2_44) = all_29_0_34, apply(x, all_29_1_35) = all_29_0_34, yields:
% 21.77/5.76 | (268) all_32_2_44 = all_29_1_35 | ? [v0] : (( ~ (v0 = 0) & injection(x) = v0) | ( ~ (v0 = 0) & element(all_32_2_44, any1) = v0) | ( ~ (v0 = 0) & element(all_29_1_35, any1) = v0))
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (8) with all_29_0_34, all_29_1_35, all_32_2_44, any2, any1, x and discharging atoms morphism(x, any1, any2) = 0, apply(x, all_29_1_35) = all_29_0_34, element(all_32_2_44, any1) = 0, yields:
% 21.77/5.76 | (269) all_32_2_44 = all_29_1_35 | ? [v0] : (( ~ (v0 = all_29_0_34) & apply(x, all_32_2_44) = v0) | ( ~ (v0 = 0) & injection(x) = v0) | ( ~ (v0 = 0) & element(all_29_1_35, any1) = v0))
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (34) with all_32_2_44, any2, any1, x and discharging atoms morphism(x, any1, any2) = 0, element(all_32_2_44, any1) = 0, yields:
% 21.77/5.76 | (270) ? [v0] : (apply(x, all_32_2_44) = v0 & element(v0, any2) = 0)
% 21.77/5.76 |
% 21.77/5.76 | Instantiating formula (6) with all_32_2_44, any1 and discharging atoms element(all_32_2_44, any1) = 0, yields:
% 21.77/5.76 | (271) ? [v0] : (subtract(any1, all_32_2_44, all_32_2_44) = v0 & zero(any1) = v0)
% 21.77/5.76 |
% 21.77/5.76 | Instantiating (271) with all_55_0_358 yields:
% 21.77/5.76 | (272) subtract(any1, all_32_2_44, all_32_2_44) = all_55_0_358 & zero(any1) = all_55_0_358
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (272) yields:
% 21.77/5.76 | (273) subtract(any1, all_32_2_44, all_32_2_44) = all_55_0_358
% 21.77/5.76 | (274) zero(any1) = all_55_0_358
% 21.77/5.76 |
% 21.77/5.76 | Instantiating (270) with all_57_0_359 yields:
% 21.77/5.76 | (275) apply(x, all_32_2_44) = all_57_0_359 & element(all_57_0_359, any2) = 0
% 21.77/5.76 |
% 21.77/5.76 | Applying alpha-rule on (275) yields:
% 21.77/5.76 | (276) apply(x, all_32_2_44) = all_57_0_359
% 21.77/5.76 | (277) element(all_57_0_359, any2) = 0
% 21.77/5.76 |
% 21.77/5.76 +-Applying beta-rule and splitting (268), into two cases.
% 21.77/5.76 |-Branch one:
% 21.77/5.76 | (278) all_32_2_44 = all_29_1_35
% 21.77/5.76 |
% 21.77/5.76 | Equations (278) can reduce 265 to:
% 21.77/5.76 | (88) $false
% 21.77/5.76 |
% 21.77/5.76 |-The branch is then unsatisfiable
% 21.77/5.76 |-Branch two:
% 21.77/5.76 | (265) ~ (all_32_2_44 = all_29_1_35)
% 21.77/5.76 | (281) ? [v0] : (( ~ (v0 = 0) & injection(x) = v0) | ( ~ (v0 = 0) & element(all_32_2_44, any1) = v0) | ( ~ (v0 = 0) & element(all_29_1_35, any1) = v0))
% 21.77/5.76 |
% 21.77/5.76 | Instantiating (281) with all_68_0_361 yields:
% 21.77/5.76 | (282) ( ~ (all_68_0_361 = 0) & injection(x) = all_68_0_361) | ( ~ (all_68_0_361 = 0) & element(all_32_2_44, any1) = all_68_0_361) | ( ~ (all_68_0_361 = 0) & element(all_29_1_35, any1) = all_68_0_361)
% 21.77/5.76 |
% 21.77/5.76 +-Applying beta-rule and splitting (269), into two cases.
% 21.77/5.76 |-Branch one:
% 21.77/5.76 | (278) all_32_2_44 = all_29_1_35
% 21.77/5.76 |
% 21.77/5.76 | Equations (278) can reduce 265 to:
% 21.77/5.76 | (88) $false
% 21.77/5.76 |
% 21.77/5.76 |-The branch is then unsatisfiable
% 21.77/5.76 |-Branch two:
% 21.77/5.76 | (265) ~ (all_32_2_44 = all_29_1_35)
% 21.77/5.76 | (286) ? [v0] : (( ~ (v0 = all_29_0_34) & apply(x, all_32_2_44) = v0) | ( ~ (v0 = 0) & injection(x) = v0) | ( ~ (v0 = 0) & element(all_29_1_35, any1) = v0))
% 21.77/5.76 |
% 21.77/5.76 | Instantiating (286) with all_72_0_362 yields:
% 21.77/5.76 | (287) ( ~ (all_72_0_362 = all_29_0_34) & apply(x, all_32_2_44) = all_72_0_362) | ( ~ (all_72_0_362 = 0) & injection(x) = all_72_0_362) | ( ~ (all_72_0_362 = 0) & element(all_29_1_35, any1) = all_72_0_362)
% 21.77/5.76 |
% 21.77/5.76 +-Applying beta-rule and splitting (282), into two cases.
% 21.77/5.76 |-Branch one:
% 21.77/5.76 | (288) ( ~ (all_68_0_361 = 0) & injection(x) = all_68_0_361) | ( ~ (all_68_0_361 = 0) & element(all_32_2_44, any1) = all_68_0_361)
% 21.77/5.76 |
% 21.77/5.76 +-Applying beta-rule and splitting (288), into two cases.
% 21.77/5.76 |-Branch one:
% 21.77/5.76 | (289) ~ (all_68_0_361 = 0) & injection(x) = all_68_0_361
% 21.77/5.77 |
% 21.77/5.77 | Applying alpha-rule on (289) yields:
% 21.77/5.77 | (290) ~ (all_68_0_361 = 0)
% 21.77/5.77 | (291) injection(x) = all_68_0_361
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (61) with x, all_68_0_361, 0 and discharging atoms injection(x) = all_68_0_361, injection(x) = 0, yields:
% 21.77/5.77 | (292) all_68_0_361 = 0
% 21.77/5.77 |
% 21.77/5.77 | Equations (292) can reduce 290 to:
% 21.77/5.77 | (88) $false
% 21.77/5.77 |
% 21.77/5.77 |-The branch is then unsatisfiable
% 21.77/5.77 |-Branch two:
% 21.77/5.77 | (294) ~ (all_68_0_361 = 0) & element(all_32_2_44, any1) = all_68_0_361
% 21.77/5.77 |
% 21.77/5.77 | Applying alpha-rule on (294) yields:
% 21.77/5.77 | (290) ~ (all_68_0_361 = 0)
% 21.77/5.77 | (296) element(all_32_2_44, any1) = all_68_0_361
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (15) with all_32_2_44, any1, all_68_0_361, 0 and discharging atoms element(all_32_2_44, any1) = all_68_0_361, element(all_32_2_44, any1) = 0, yields:
% 21.77/5.77 | (292) all_68_0_361 = 0
% 21.77/5.77 |
% 21.77/5.77 | Equations (292) can reduce 290 to:
% 21.77/5.77 | (88) $false
% 21.77/5.77 |
% 21.77/5.77 |-The branch is then unsatisfiable
% 21.77/5.77 |-Branch two:
% 21.77/5.77 | (299) ~ (all_68_0_361 = 0) & element(all_29_1_35, any1) = all_68_0_361
% 21.77/5.77 |
% 21.77/5.77 | Applying alpha-rule on (299) yields:
% 21.77/5.77 | (290) ~ (all_68_0_361 = 0)
% 21.77/5.77 | (301) element(all_29_1_35, any1) = all_68_0_361
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (23) with any1, all_55_0_358, all_29_1_35 and discharging atoms zero(any1) = all_55_0_358, zero(any1) = all_29_1_35, yields:
% 21.77/5.77 | (302) all_55_0_358 = all_29_1_35
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (44) with x, all_32_2_44, all_57_0_359, all_29_0_34 and discharging atoms apply(x, all_32_2_44) = all_57_0_359, apply(x, all_32_2_44) = all_29_0_34, yields:
% 21.77/5.77 | (303) all_57_0_359 = all_29_0_34
% 21.77/5.77 |
% 21.77/5.77 | From (302) and (273) follows:
% 21.77/5.77 | (304) subtract(any1, all_32_2_44, all_32_2_44) = all_29_1_35
% 21.77/5.77 |
% 21.77/5.77 | From (303) and (276) follows:
% 21.77/5.77 | (267) apply(x, all_32_2_44) = all_29_0_34
% 21.77/5.77 |
% 21.77/5.77 +-Applying beta-rule and splitting (287), into two cases.
% 21.77/5.77 |-Branch one:
% 21.77/5.77 | (306) ( ~ (all_72_0_362 = all_29_0_34) & apply(x, all_32_2_44) = all_72_0_362) | ( ~ (all_72_0_362 = 0) & injection(x) = all_72_0_362)
% 21.77/5.77 |
% 21.77/5.77 +-Applying beta-rule and splitting (306), into two cases.
% 21.77/5.77 |-Branch one:
% 21.77/5.77 | (307) ~ (all_72_0_362 = all_29_0_34) & apply(x, all_32_2_44) = all_72_0_362
% 21.77/5.77 |
% 21.77/5.77 | Applying alpha-rule on (307) yields:
% 21.77/5.77 | (308) ~ (all_72_0_362 = all_29_0_34)
% 21.77/5.77 | (309) apply(x, all_32_2_44) = all_72_0_362
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (44) with x, all_32_2_44, all_72_0_362, all_29_0_34 and discharging atoms apply(x, all_32_2_44) = all_72_0_362, apply(x, all_32_2_44) = all_29_0_34, yields:
% 21.77/5.77 | (310) all_72_0_362 = all_29_0_34
% 21.77/5.77 |
% 21.77/5.77 | Equations (310) can reduce 308 to:
% 21.77/5.77 | (88) $false
% 21.77/5.77 |
% 21.77/5.77 |-The branch is then unsatisfiable
% 21.77/5.77 |-Branch two:
% 21.77/5.77 | (312) ~ (all_72_0_362 = 0) & injection(x) = all_72_0_362
% 21.77/5.77 |
% 21.77/5.77 | Applying alpha-rule on (312) yields:
% 21.77/5.77 | (313) ~ (all_72_0_362 = 0)
% 21.77/5.77 | (314) injection(x) = all_72_0_362
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (61) with x, all_72_0_362, 0 and discharging atoms injection(x) = all_72_0_362, injection(x) = 0, yields:
% 21.77/5.77 | (315) all_72_0_362 = 0
% 21.77/5.77 |
% 21.77/5.77 | Equations (315) can reduce 313 to:
% 21.77/5.77 | (88) $false
% 21.77/5.77 |
% 21.77/5.77 |-The branch is then unsatisfiable
% 21.77/5.77 |-Branch two:
% 21.77/5.77 | (317) ~ (all_72_0_362 = 0) & element(all_29_1_35, any1) = all_72_0_362
% 21.77/5.77 |
% 21.77/5.77 | Applying alpha-rule on (317) yields:
% 21.77/5.77 | (313) ~ (all_72_0_362 = 0)
% 21.77/5.77 | (319) element(all_29_1_35, any1) = all_72_0_362
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (15) with all_29_1_35, any1, all_72_0_362, all_68_0_361 and discharging atoms element(all_29_1_35, any1) = all_72_0_362, element(all_29_1_35, any1) = all_68_0_361, yields:
% 21.77/5.77 | (320) all_72_0_362 = all_68_0_361
% 21.77/5.77 |
% 21.77/5.77 | Equations (320) can reduce 313 to:
% 21.77/5.77 | (290) ~ (all_68_0_361 = 0)
% 21.77/5.77 |
% 21.77/5.77 | From (320) and (319) follows:
% 21.77/5.77 | (301) element(all_29_1_35, any1) = all_68_0_361
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (19) with all_29_1_35, all_32_2_44, all_32_2_44, any1 and discharging atoms subtract(any1, all_32_2_44, all_32_2_44) = all_29_1_35, yields:
% 21.77/5.77 | (323) ? [v0] : ((v0 = 0 & element(all_29_1_35, any1) = 0) | ( ~ (v0 = 0) & element(all_32_2_44, any1) = v0))
% 21.77/5.77 |
% 21.77/5.77 | Instantiating (323) with all_99_0_372 yields:
% 21.77/5.77 | (324) (all_99_0_372 = 0 & element(all_29_1_35, any1) = 0) | ( ~ (all_99_0_372 = 0) & element(all_32_2_44, any1) = all_99_0_372)
% 21.77/5.77 |
% 21.77/5.77 +-Applying beta-rule and splitting (324), into two cases.
% 21.77/5.77 |-Branch one:
% 21.77/5.77 | (325) all_99_0_372 = 0 & element(all_29_1_35, any1) = 0
% 21.77/5.77 |
% 21.77/5.77 | Applying alpha-rule on (325) yields:
% 21.77/5.77 | (326) all_99_0_372 = 0
% 21.77/5.77 | (327) element(all_29_1_35, any1) = 0
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (15) with all_29_1_35, any1, 0, all_68_0_361 and discharging atoms element(all_29_1_35, any1) = all_68_0_361, element(all_29_1_35, any1) = 0, yields:
% 21.77/5.77 | (292) all_68_0_361 = 0
% 21.77/5.77 |
% 21.77/5.77 | Equations (292) can reduce 290 to:
% 21.77/5.77 | (88) $false
% 21.77/5.77 |
% 21.77/5.77 |-The branch is then unsatisfiable
% 21.77/5.77 |-Branch two:
% 21.77/5.77 | (330) ~ (all_99_0_372 = 0) & element(all_32_2_44, any1) = all_99_0_372
% 21.77/5.77 |
% 21.77/5.77 | Applying alpha-rule on (330) yields:
% 21.77/5.77 | (331) ~ (all_99_0_372 = 0)
% 21.77/5.77 | (332) element(all_32_2_44, any1) = all_99_0_372
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (15) with all_32_2_44, any1, all_99_0_372, 0 and discharging atoms element(all_32_2_44, any1) = all_99_0_372, element(all_32_2_44, any1) = 0, yields:
% 21.77/5.77 | (326) all_99_0_372 = 0
% 21.77/5.77 |
% 21.77/5.77 | Equations (326) can reduce 331 to:
% 21.77/5.77 | (88) $false
% 21.77/5.77 |
% 21.77/5.77 |-The branch is then unsatisfiable
% 21.77/5.77 |-Branch two:
% 21.77/5.77 | (335) all_32_4_46 = 0 & injection_2(x) = 0
% 21.77/5.77 |
% 21.77/5.77 | Applying alpha-rule on (335) yields:
% 21.77/5.77 | (336) all_32_4_46 = 0
% 21.77/5.77 | (83) injection_2(x) = 0
% 21.77/5.77 |
% 21.77/5.77 | Instantiating formula (43) with x, 0, all_0_0_0 and discharging atoms injection_2(x) = all_0_0_0, injection_2(x) = 0, yields:
% 21.77/5.77 | (81) all_0_0_0 = 0
% 21.77/5.77 |
% 21.77/5.77 | Equations (81) can reduce 253 to:
% 21.77/5.77 | (88) $false
% 21.77/5.77 |
% 21.77/5.77 |-The branch is then unsatisfiable
% 21.77/5.77 % SZS output end Proof for theBenchmark
% 21.77/5.77
% 21.77/5.77 5165ms
%------------------------------------------------------------------------------