TSTP Solution File: KLE022+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE022+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 01:50:57 EDT 2022
% Result : Theorem 9.25s 2.83s
% Output : Proof 17.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE022+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n004.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 : Thu Jun 16 13:42:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.60 ____ _
% 0.57/0.60 ___ / __ \_____(_)___ ________ __________
% 0.57/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.60
% 0.57/0.60 A Theorem Prover for First-Order Logic
% 0.57/0.60 (ePrincess v.1.0)
% 0.57/0.60
% 0.57/0.60 (c) Philipp Rümmer, 2009-2015
% 0.57/0.60 (c) Peter Backeman, 2014-2015
% 0.57/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.60 Bug reports to peter@backeman.se
% 0.57/0.60
% 0.57/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.60
% 0.57/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.78/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.72/0.94 Prover 0: Preprocessing ...
% 2.37/1.20 Prover 0: Constructing countermodel ...
% 9.25/2.83 Prover 0: proved (2181ms)
% 9.25/2.83
% 9.25/2.83 No countermodel exists, formula is valid
% 9.25/2.83 % SZS status Theorem for theBenchmark
% 9.25/2.83
% 9.25/2.83 Generating proof ... found it (size 149)
% 16.66/4.62
% 16.66/4.62 % SZS output start Proof for theBenchmark
% 16.66/4.62 Assumed formulas after preprocessing and simplification:
% 16.66/4.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (c(v1) = v3 & multiplication(v0, v3) = v4 & multiplication(v0, v1) = v2 & addition(v2, v4) = v5 & test(v1) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (multiplication(v7, v8) = v10) | ~ (multiplication(v6, v8) = v9) | ~ (addition(v9, v10) = v11) | ? [v12] : (multiplication(v12, v8) = v11 & addition(v6, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (multiplication(v6, v8) = v10) | ~ (multiplication(v6, v7) = v9) | ~ (addition(v9, v10) = v11) | ? [v12] : (multiplication(v6, v12) = v11 & addition(v7, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v9, v8) = v10) | ~ (multiplication(v6, v7) = v9) | ? [v11] : (multiplication(v7, v8) = v11 & multiplication(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v9, v8) = v10) | ~ (addition(v6, v7) = v9) | ? [v11] : ? [v12] : (multiplication(v7, v8) = v12 & multiplication(v6, v8) = v11 & addition(v11, v12) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v7, v8) = v9) | ~ (multiplication(v6, v9) = v10) | ? [v11] : (multiplication(v11, v8) = v10 & multiplication(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v6, v9) = v10) | ~ (addition(v7, v8) = v9) | ? [v11] : ? [v12] : (multiplication(v6, v8) = v12 & multiplication(v6, v7) = v11 & addition(v11, v12) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v9, v6) = v10) | ~ (addition(v8, v7) = v9) | ? [v11] : (addition(v8, v11) = v10 & addition(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v8, v9) = v10) | ~ (addition(v7, v6) = v9) | ? [v11] : (addition(v11, v6) = v10 & addition(v8, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (multiplication(v9, v8) = v7) | ~ (multiplication(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (addition(v9, v8) = v7) | ~ (addition(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (c(v6) = v8) | ~ complement(v6, v7) | ~ test(v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (addition(v6, v7) = v8) | ~ leq(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : (v8 = one | ~ (addition(v6, v7) = v8) | ~ complement(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = zero | ~ (multiplication(v7, v6) = v8) | ~ complement(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = zero | ~ (multiplication(v6, v7) = v8) | ~ complement(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (c(v8) = v7) | ~ (c(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v7, v6) = v8) | ~ complement(v7, v6) | (multiplication(v6, v7) = zero & addition(v6, v7) = one)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v6, v7) = v8) | ~ complement(v7, v6) | (multiplication(v7, v6) = zero & addition(v6, v7) = one)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v7, v6) = v8) | addition(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | ~ complement(v7, v6) | (multiplication(v7, v6) = zero & multiplication(v6, v7) = zero)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | addition(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = v6 | ~ (multiplication(v6, one) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (multiplication(one, v6) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v6, v6) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v6, zero) = v7)) & ! [v6] : ! [v7] : (v7 = zero | ~ (c(v6) = v7) | test(v6)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(v6, zero) = v7)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(zero, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (c(v6) = v7) | ~ test(v6) | complement(v6, v7)) & ! [v6] : ! [v7] : ( ~ (multiplication(v7, v6) = zero) | complement(v7, v6) | ? [v8] : ? [v9] : (multiplication(v6, v7) = v8 & addition(v6, v7) = v9 & ( ~ (v9 = one) | ~ (v8 = zero)))) & ! [v6] : ! [v7] : ( ~ (multiplication(v6, v7) = zero) | complement(v7, v6) | ? [v8] : ? [v9] : (multiplication(v7, v6) = v8 & addition(v6, v7) = v9 & ( ~ (v9 = one) | ~ (v8 = zero)))) & ! [v6] : ! [v7] : ( ~ (addition(v6, v7) = v7) | leq(v6, v7)) & ! [v6] : ! [v7] : ( ~ (addition(v6, v7) = one) | complement(v7, v6) | ? [v8] : ? [v9] : (multiplication(v7, v6) = v9 & multiplication(v6, v7) = v8 & ( ~ (v9 = zero) | ~ (v8 = zero)))) & ! [v6] : ! [v7] : ( ~ complement(v7, v6) | test(v6)) & ! [v6] : ( ~ test(v6) | ? [v7] : complement(v7, v6)) & ( ~ leq(v5, v0) | ~ leq(v0, v5)))
% 16.81/4.66 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 16.81/4.66 | (1) c(all_0_4_4) = all_0_2_2 & multiplication(all_0_5_5, all_0_2_2) = all_0_1_1 & multiplication(all_0_5_5, all_0_4_4) = all_0_3_3 & addition(all_0_3_3, all_0_1_1) = all_0_0_0 & test(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) & ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) & ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) & ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) & ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) & ( ~ leq(all_0_0_0, all_0_5_5) | ~ leq(all_0_5_5, all_0_0_0))
% 16.81/4.68 |
% 16.81/4.68 | Applying alpha-rule on (1) yields:
% 16.81/4.68 | (2) addition(all_0_3_3, all_0_1_1) = all_0_0_0
% 16.81/4.68 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6))
% 16.81/4.68 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 16.81/4.68 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 16.81/4.68 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0))
% 16.81/4.68 | (7) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero))))
% 16.81/4.68 | (8) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 16.81/4.68 | (9) test(all_0_4_4)
% 16.81/4.68 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 16.81/4.68 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 16.81/4.68 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 16.81/4.68 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4))
% 16.81/4.68 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 16.81/4.68 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0))
% 16.81/4.68 | (16) multiplication(all_0_5_5, all_0_2_2) = all_0_1_1
% 16.81/4.68 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 16.81/4.68 | (18) ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1))
% 16.81/4.68 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero))
% 16.81/4.68 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 16.81/4.68 | (21) ~ leq(all_0_0_0, all_0_5_5) | ~ leq(all_0_5_5, all_0_0_0)
% 16.81/4.68 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4))
% 16.81/4.68 | (23) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 16.81/4.68 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0))
% 16.81/4.68 | (25) multiplication(all_0_5_5, all_0_4_4) = all_0_3_3
% 16.81/4.68 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0))
% 16.81/4.68 | (27) ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0))
% 16.81/4.68 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0))
% 16.81/4.68 | (29) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0))
% 16.81/4.68 | (30) ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0))
% 16.81/4.68 | (31) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 16.81/4.68 | (32) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero))))
% 16.81/4.68 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 16.81/4.68 | (34) c(all_0_4_4) = all_0_2_2
% 16.81/4.68 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one))
% 16.81/4.68 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one))
% 16.81/4.68 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 16.81/4.68 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 16.81/4.68 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1))
% 16.81/4.69 | (40) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero))))
% 16.81/4.69 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 16.81/4.69 | (42) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (3) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 16.81/4.69 | (43) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = v0)
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (12) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 16.81/4.69 | (44) addition(all_0_1_1, all_0_3_3) = all_0_0_0
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (18) with all_0_2_2, all_0_4_4 and discharging atoms c(all_0_4_4) = all_0_2_2, test(all_0_4_4), yields:
% 16.81/4.69 | (45) complement(all_0_4_4, all_0_2_2)
% 16.81/4.69 |
% 16.81/4.69 | Instantiating (43) with all_9_0_6 yields:
% 16.81/4.69 | (46) multiplication(all_0_5_5, all_9_0_6) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = all_9_0_6
% 16.81/4.69 |
% 16.81/4.69 | Applying alpha-rule on (46) yields:
% 16.81/4.69 | (47) multiplication(all_0_5_5, all_9_0_6) = all_0_0_0
% 16.81/4.69 | (48) addition(all_0_4_4, all_0_2_2) = all_9_0_6
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (3) with all_0_0_0, all_0_3_3, all_0_1_1, all_0_4_4, all_0_2_2, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, addition(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 16.81/4.69 | (49) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = v0)
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (12) with all_9_0_6, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_4_4, all_0_2_2) = all_9_0_6, yields:
% 16.81/4.69 | (50) addition(all_0_2_2, all_0_4_4) = all_9_0_6
% 16.81/4.69 |
% 16.81/4.69 | Instantiating (49) with all_19_0_8 yields:
% 16.81/4.69 | (51) multiplication(all_0_5_5, all_19_0_8) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = all_19_0_8
% 16.81/4.69 |
% 16.81/4.69 | Applying alpha-rule on (51) yields:
% 16.81/4.69 | (52) multiplication(all_0_5_5, all_19_0_8) = all_0_0_0
% 16.81/4.69 | (53) addition(all_0_2_2, all_0_4_4) = all_19_0_8
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (24) with all_19_0_8, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_4_4) = all_19_0_8, complement(all_0_4_4, all_0_2_2), yields:
% 16.81/4.69 | (54) all_19_0_8 = one
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (14) with all_0_2_2, all_0_4_4, all_9_0_6, all_19_0_8 and discharging atoms addition(all_0_2_2, all_0_4_4) = all_19_0_8, addition(all_0_2_2, all_0_4_4) = all_9_0_6, yields:
% 16.81/4.69 | (55) all_19_0_8 = all_9_0_6
% 16.81/4.69 |
% 16.81/4.69 | Combining equations (54,55) yields a new equation:
% 16.81/4.69 | (56) all_9_0_6 = one
% 16.81/4.69 |
% 16.81/4.69 | From (56) and (47) follows:
% 16.81/4.69 | (57) multiplication(all_0_5_5, one) = all_0_0_0
% 16.81/4.69 |
% 16.81/4.69 | From (56) and (50) follows:
% 16.81/4.69 | (58) addition(all_0_2_2, all_0_4_4) = one
% 16.81/4.69 |
% 16.81/4.69 | From (56) and (48) follows:
% 16.81/4.69 | (59) addition(all_0_4_4, all_0_2_2) = one
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (5) with all_0_0_0, all_0_5_5 and discharging atoms multiplication(all_0_5_5, one) = all_0_0_0, yields:
% 16.81/4.69 | (60) all_0_0_0 = all_0_5_5
% 16.81/4.69 |
% 16.81/4.69 | From (60) and (57) follows:
% 16.81/4.69 | (61) multiplication(all_0_5_5, one) = all_0_5_5
% 16.81/4.69 |
% 16.81/4.69 | From (60) and (44) follows:
% 16.81/4.69 | (62) addition(all_0_1_1, all_0_3_3) = all_0_5_5
% 16.81/4.69 |
% 16.81/4.69 | From (60) and (2) follows:
% 16.81/4.69 | (63) addition(all_0_3_3, all_0_1_1) = all_0_5_5
% 16.81/4.69 |
% 16.81/4.69 +-Applying beta-rule and splitting (21), into two cases.
% 16.81/4.69 |-Branch one:
% 16.81/4.69 | (64) ~ leq(all_0_0_0, all_0_5_5)
% 16.81/4.69 |
% 16.81/4.69 | From (60) and (64) follows:
% 16.81/4.69 | (65) ~ leq(all_0_5_5, all_0_5_5)
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (41) with all_0_1_1, all_0_5_5, all_0_2_2, one, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, multiplication(all_0_5_5, one) = all_0_5_5, yields:
% 16.81/4.69 | (66) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_1_1 & multiplication(one, all_0_2_2) = v0)
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (41) with all_0_3_3, all_0_5_5, all_0_4_4, one, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, multiplication(all_0_5_5, one) = all_0_5_5, yields:
% 16.81/4.69 | (67) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_3_3 & multiplication(one, all_0_4_4) = v0)
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (22) with all_0_1_1, all_0_5_5, all_0_2_2, all_0_3_3, all_0_1_1 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, addition(all_0_1_1, all_0_3_3) = all_0_5_5, yields:
% 16.81/4.69 | (68) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_2_2) = v0 & multiplication(all_0_3_3, all_0_2_2) = v1 & addition(v0, v1) = all_0_1_1)
% 16.81/4.69 |
% 16.81/4.69 | Instantiating formula (22) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_3_3, all_0_1_1 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, addition(all_0_1_1, all_0_3_3) = all_0_5_5, yields:
% 16.81/4.69 | (69) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_4_4) = v0 & multiplication(all_0_3_3, all_0_4_4) = v1 & addition(v0, v1) = all_0_3_3)
% 16.81/4.70 |
% 16.81/4.70 | Instantiating formula (19) with one, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_4_4) = one, complement(all_0_4_4, all_0_2_2), yields:
% 16.81/4.70 | (70) multiplication(all_0_2_2, all_0_4_4) = zero & multiplication(all_0_4_4, all_0_2_2) = zero
% 16.81/4.70 |
% 16.81/4.70 | Applying alpha-rule on (70) yields:
% 16.81/4.70 | (71) multiplication(all_0_2_2, all_0_4_4) = zero
% 16.81/4.70 | (72) multiplication(all_0_4_4, all_0_2_2) = zero
% 16.81/4.70 |
% 16.81/4.70 | Instantiating formula (22) with all_0_1_1, all_0_5_5, all_0_2_2, all_0_1_1, all_0_3_3 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, addition(all_0_3_3, all_0_1_1) = all_0_5_5, yields:
% 16.81/4.70 | (73) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_2_2) = v1 & multiplication(all_0_3_3, all_0_2_2) = v0 & addition(v0, v1) = all_0_1_1)
% 16.81/4.70 |
% 16.81/4.70 | Instantiating formula (22) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_1_1, all_0_3_3 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_5_5, yields:
% 16.81/4.70 | (74) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_4_4) = v1 & multiplication(all_0_3_3, all_0_4_4) = v0 & addition(v0, v1) = all_0_3_3)
% 16.81/4.70 |
% 16.81/4.70 | Instantiating (73) with all_45_0_14, all_45_1_15 yields:
% 16.81/4.70 | (75) multiplication(all_0_1_1, all_0_2_2) = all_45_0_14 & multiplication(all_0_3_3, all_0_2_2) = all_45_1_15 & addition(all_45_1_15, all_45_0_14) = all_0_1_1
% 16.81/4.70 |
% 16.81/4.70 | Applying alpha-rule on (75) yields:
% 16.81/4.70 | (76) multiplication(all_0_1_1, all_0_2_2) = all_45_0_14
% 16.81/4.70 | (77) multiplication(all_0_3_3, all_0_2_2) = all_45_1_15
% 16.81/4.70 | (78) addition(all_45_1_15, all_45_0_14) = all_0_1_1
% 16.81/4.70 |
% 16.81/4.70 | Instantiating (69) with all_47_0_16, all_47_1_17 yields:
% 16.81/4.70 | (79) multiplication(all_0_1_1, all_0_4_4) = all_47_1_17 & multiplication(all_0_3_3, all_0_4_4) = all_47_0_16 & addition(all_47_1_17, all_47_0_16) = all_0_3_3
% 16.81/4.70 |
% 16.81/4.70 | Applying alpha-rule on (79) yields:
% 16.81/4.70 | (80) multiplication(all_0_1_1, all_0_4_4) = all_47_1_17
% 16.81/4.70 | (81) multiplication(all_0_3_3, all_0_4_4) = all_47_0_16
% 16.81/4.70 | (82) addition(all_47_1_17, all_47_0_16) = all_0_3_3
% 16.81/4.70 |
% 16.81/4.70 | Instantiating (68) with all_49_0_18, all_49_1_19 yields:
% 16.81/4.70 | (83) multiplication(all_0_1_1, all_0_2_2) = all_49_1_19 & multiplication(all_0_3_3, all_0_2_2) = all_49_0_18 & addition(all_49_1_19, all_49_0_18) = all_0_1_1
% 16.81/4.70 |
% 16.81/4.70 | Applying alpha-rule on (83) yields:
% 16.81/4.70 | (84) multiplication(all_0_1_1, all_0_2_2) = all_49_1_19
% 16.81/4.70 | (85) multiplication(all_0_3_3, all_0_2_2) = all_49_0_18
% 16.81/4.70 | (86) addition(all_49_1_19, all_49_0_18) = all_0_1_1
% 16.81/4.70 |
% 16.81/4.70 | Instantiating (67) with all_51_0_20 yields:
% 16.81/4.70 | (87) multiplication(all_0_5_5, all_51_0_20) = all_0_3_3 & multiplication(one, all_0_4_4) = all_51_0_20
% 16.81/4.70 |
% 16.81/4.70 | Applying alpha-rule on (87) yields:
% 16.81/4.70 | (88) multiplication(all_0_5_5, all_51_0_20) = all_0_3_3
% 16.81/4.70 | (89) multiplication(one, all_0_4_4) = all_51_0_20
% 16.81/4.70 |
% 16.81/4.70 | Instantiating (66) with all_53_0_21 yields:
% 16.81/4.70 | (90) multiplication(all_0_5_5, all_53_0_21) = all_0_1_1 & multiplication(one, all_0_2_2) = all_53_0_21
% 16.81/4.70 |
% 16.81/4.70 | Applying alpha-rule on (90) yields:
% 16.81/4.70 | (91) multiplication(all_0_5_5, all_53_0_21) = all_0_1_1
% 16.81/4.70 | (92) multiplication(one, all_0_2_2) = all_53_0_21
% 16.81/4.70 |
% 16.81/4.70 | Instantiating (74) with all_55_0_22, all_55_1_23 yields:
% 16.81/4.70 | (93) multiplication(all_0_1_1, all_0_4_4) = all_55_0_22 & multiplication(all_0_3_3, all_0_4_4) = all_55_1_23 & addition(all_55_1_23, all_55_0_22) = all_0_3_3
% 16.81/4.70 |
% 16.81/4.70 | Applying alpha-rule on (93) yields:
% 16.81/4.70 | (94) multiplication(all_0_1_1, all_0_4_4) = all_55_0_22
% 16.81/4.70 | (95) multiplication(all_0_3_3, all_0_4_4) = all_55_1_23
% 16.81/4.70 | (96) addition(all_55_1_23, all_55_0_22) = all_0_3_3
% 16.81/4.70 |
% 16.81/4.70 | Instantiating formula (17) with all_0_1_1, all_0_2_2, all_45_0_14, all_49_1_19 and discharging atoms multiplication(all_0_1_1, all_0_2_2) = all_49_1_19, multiplication(all_0_1_1, all_0_2_2) = all_45_0_14, yields:
% 16.81/4.70 | (97) all_49_1_19 = all_45_0_14
% 16.81/4.70 |
% 16.81/4.70 | Instantiating formula (17) with all_0_1_1, all_0_4_4, all_47_1_17, all_55_0_22 and discharging atoms multiplication(all_0_1_1, all_0_4_4) = all_55_0_22, multiplication(all_0_1_1, all_0_4_4) = all_47_1_17, yields:
% 16.81/4.70 | (98) all_55_0_22 = all_47_1_17
% 16.81/4.70 |
% 16.81/4.70 | Instantiating formula (17) with all_0_3_3, all_0_2_2, all_45_1_15, all_49_0_18 and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_49_0_18, multiplication(all_0_3_3, all_0_2_2) = all_45_1_15, yields:
% 16.81/4.70 | (99) all_49_0_18 = all_45_1_15
% 16.81/4.70 |
% 16.81/4.70 | Instantiating formula (17) with all_0_3_3, all_0_4_4, all_47_0_16, all_55_1_23 and discharging atoms multiplication(all_0_3_3, all_0_4_4) = all_55_1_23, multiplication(all_0_3_3, all_0_4_4) = all_47_0_16, yields:
% 16.81/4.70 | (100) all_55_1_23 = all_47_0_16
% 16.81/4.70 |
% 16.81/4.70 | Instantiating formula (23) with all_53_0_21, all_0_2_2 and discharging atoms multiplication(one, all_0_2_2) = all_53_0_21, yields:
% 16.81/4.70 | (101) all_53_0_21 = all_0_2_2
% 16.81/4.70 |
% 16.81/4.70 | Instantiating formula (23) with all_51_0_20, all_0_4_4 and discharging atoms multiplication(one, all_0_4_4) = all_51_0_20, yields:
% 16.81/4.70 | (102) all_51_0_20 = all_0_4_4
% 16.81/4.70 |
% 16.81/4.70 | From (98) and (94) follows:
% 16.81/4.70 | (80) multiplication(all_0_1_1, all_0_4_4) = all_47_1_17
% 16.81/4.70 |
% 16.81/4.70 | From (99) and (85) follows:
% 16.81/4.70 | (77) multiplication(all_0_3_3, all_0_2_2) = all_45_1_15
% 16.81/4.70 |
% 16.81/4.70 | From (100) and (95) follows:
% 16.81/4.70 | (81) multiplication(all_0_3_3, all_0_4_4) = all_47_0_16
% 16.81/4.70 |
% 16.81/4.70 | From (101) and (91) follows:
% 16.81/4.70 | (16) multiplication(all_0_5_5, all_0_2_2) = all_0_1_1
% 16.81/4.70 |
% 16.81/4.70 | From (102) and (88) follows:
% 16.81/4.70 | (25) multiplication(all_0_5_5, all_0_4_4) = all_0_3_3
% 16.81/4.70 |
% 16.81/4.70 | From (101) and (92) follows:
% 16.81/4.70 | (108) multiplication(one, all_0_2_2) = all_0_2_2
% 16.81/4.70 |
% 16.81/4.70 | From (102) and (89) follows:
% 16.81/4.70 | (109) multiplication(one, all_0_4_4) = all_0_4_4
% 16.81/4.70 |
% 16.81/4.70 | From (100)(98) and (96) follows:
% 16.81/4.70 | (110) addition(all_47_0_16, all_47_1_17) = all_0_3_3
% 16.81/4.70 |
% 16.81/4.70 | From (97)(99) and (86) follows:
% 16.81/4.70 | (111) addition(all_45_0_14, all_45_1_15) = all_0_1_1
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (41) with all_47_1_17, all_0_1_1, all_0_4_4, all_0_2_2, all_0_5_5 and discharging atoms multiplication(all_0_1_1, all_0_4_4) = all_47_1_17, multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, yields:
% 16.81/4.71 | (112) ? [v0] : (multiplication(all_0_2_2, all_0_4_4) = v0 & multiplication(all_0_5_5, v0) = all_47_1_17)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (41) with all_45_1_15, all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_45_1_15, multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 16.81/4.71 | (113) ? [v0] : (multiplication(all_0_4_4, all_0_2_2) = v0 & multiplication(all_0_5_5, v0) = all_45_1_15)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (41) with zero, all_0_2_2, all_0_4_4, all_0_2_2, one and discharging atoms multiplication(all_0_2_2, all_0_4_4) = zero, multiplication(one, all_0_2_2) = all_0_2_2, yields:
% 16.81/4.71 | (114) ? [v0] : (multiplication(all_0_2_2, all_0_4_4) = v0 & multiplication(one, v0) = zero)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (22) with all_0_2_2, one, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms multiplication(one, all_0_2_2) = all_0_2_2, addition(all_0_2_2, all_0_4_4) = one, yields:
% 16.81/4.71 | (115) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_2_2) = v0 & multiplication(all_0_4_4, all_0_2_2) = v1 & addition(v0, v1) = all_0_2_2)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (22) with all_0_2_2, one, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms multiplication(one, all_0_2_2) = all_0_2_2, addition(all_0_4_4, all_0_2_2) = one, yields:
% 16.81/4.71 | (116) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_2_2) = v1 & multiplication(all_0_4_4, all_0_2_2) = v0 & addition(v0, v1) = all_0_2_2)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (41) with zero, all_0_4_4, all_0_2_2, all_0_4_4, one and discharging atoms multiplication(all_0_4_4, all_0_2_2) = zero, multiplication(one, all_0_4_4) = all_0_4_4, yields:
% 16.81/4.71 | (117) ? [v0] : (multiplication(all_0_4_4, all_0_2_2) = v0 & multiplication(one, v0) = zero)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (22) with all_0_4_4, one, all_0_4_4, all_0_4_4, all_0_2_2 and discharging atoms multiplication(one, all_0_4_4) = all_0_4_4, addition(all_0_2_2, all_0_4_4) = one, yields:
% 16.81/4.71 | (118) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_4_4) = v0 & multiplication(all_0_4_4, all_0_4_4) = v1 & addition(v0, v1) = all_0_4_4)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (22) with all_0_4_4, one, all_0_4_4, all_0_2_2, all_0_4_4 and discharging atoms multiplication(one, all_0_4_4) = all_0_4_4, addition(all_0_4_4, all_0_2_2) = one, yields:
% 16.81/4.71 | (119) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_4_4) = v1 & multiplication(all_0_4_4, all_0_4_4) = v0 & addition(v0, v1) = all_0_4_4)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (22) with all_47_0_16, all_0_3_3, all_0_4_4, all_47_1_17, all_47_0_16 and discharging atoms multiplication(all_0_3_3, all_0_4_4) = all_47_0_16, addition(all_47_0_16, all_47_1_17) = all_0_3_3, yields:
% 16.81/4.71 | (120) ? [v0] : ? [v1] : (multiplication(all_47_0_16, all_0_4_4) = v0 & multiplication(all_47_1_17, all_0_4_4) = v1 & addition(v0, v1) = all_47_0_16)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (22) with all_47_0_16, all_0_3_3, all_0_4_4, all_47_0_16, all_47_1_17 and discharging atoms multiplication(all_0_3_3, all_0_4_4) = all_47_0_16, addition(all_47_1_17, all_47_0_16) = all_0_3_3, yields:
% 16.81/4.71 | (121) ? [v0] : ? [v1] : (multiplication(all_47_0_16, all_0_4_4) = v1 & multiplication(all_47_1_17, all_0_4_4) = v0 & addition(v0, v1) = all_47_0_16)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (22) with all_47_1_17, all_0_1_1, all_0_4_4, all_45_1_15, all_45_0_14 and discharging atoms multiplication(all_0_1_1, all_0_4_4) = all_47_1_17, addition(all_45_0_14, all_45_1_15) = all_0_1_1, yields:
% 16.81/4.71 | (122) ? [v0] : ? [v1] : (multiplication(all_45_0_14, all_0_4_4) = v0 & multiplication(all_45_1_15, all_0_4_4) = v1 & addition(v0, v1) = all_47_1_17)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating formula (22) with all_47_1_17, all_0_1_1, all_0_4_4, all_45_0_14, all_45_1_15 and discharging atoms multiplication(all_0_1_1, all_0_4_4) = all_47_1_17, addition(all_45_1_15, all_45_0_14) = all_0_1_1, yields:
% 16.81/4.71 | (123) ? [v0] : ? [v1] : (multiplication(all_45_0_14, all_0_4_4) = v1 & multiplication(all_45_1_15, all_0_4_4) = v0 & addition(v0, v1) = all_47_1_17)
% 16.81/4.71 |
% 16.81/4.71 | Instantiating (122) with all_76_0_28, all_76_1_29 yields:
% 16.81/4.71 | (124) multiplication(all_45_0_14, all_0_4_4) = all_76_1_29 & multiplication(all_45_1_15, all_0_4_4) = all_76_0_28 & addition(all_76_1_29, all_76_0_28) = all_47_1_17
% 16.81/4.71 |
% 16.81/4.71 | Applying alpha-rule on (124) yields:
% 16.81/4.71 | (125) multiplication(all_45_0_14, all_0_4_4) = all_76_1_29
% 16.81/4.71 | (126) multiplication(all_45_1_15, all_0_4_4) = all_76_0_28
% 16.81/4.71 | (127) addition(all_76_1_29, all_76_0_28) = all_47_1_17
% 16.81/4.71 |
% 16.81/4.71 | Instantiating (117) with all_84_0_36 yields:
% 16.81/4.71 | (128) multiplication(all_0_4_4, all_0_2_2) = all_84_0_36 & multiplication(one, all_84_0_36) = zero
% 16.81/4.71 |
% 16.81/4.71 | Applying alpha-rule on (128) yields:
% 16.81/4.71 | (129) multiplication(all_0_4_4, all_0_2_2) = all_84_0_36
% 16.81/4.71 | (130) multiplication(one, all_84_0_36) = zero
% 16.81/4.71 |
% 16.81/4.71 | Instantiating (121) with all_90_0_39, all_90_1_40 yields:
% 16.81/4.71 | (131) multiplication(all_47_0_16, all_0_4_4) = all_90_0_39 & multiplication(all_47_1_17, all_0_4_4) = all_90_1_40 & addition(all_90_1_40, all_90_0_39) = all_47_0_16
% 16.81/4.71 |
% 16.81/4.71 | Applying alpha-rule on (131) yields:
% 16.81/4.71 | (132) multiplication(all_47_0_16, all_0_4_4) = all_90_0_39
% 16.81/4.71 | (133) multiplication(all_47_1_17, all_0_4_4) = all_90_1_40
% 16.81/4.71 | (134) addition(all_90_1_40, all_90_0_39) = all_47_0_16
% 16.81/4.71 |
% 16.81/4.71 | Instantiating (123) with all_96_0_43, all_96_1_44 yields:
% 16.81/4.71 | (135) multiplication(all_45_0_14, all_0_4_4) = all_96_0_43 & multiplication(all_45_1_15, all_0_4_4) = all_96_1_44 & addition(all_96_1_44, all_96_0_43) = all_47_1_17
% 16.81/4.71 |
% 16.81/4.71 | Applying alpha-rule on (135) yields:
% 16.81/4.71 | (136) multiplication(all_45_0_14, all_0_4_4) = all_96_0_43
% 16.81/4.71 | (137) multiplication(all_45_1_15, all_0_4_4) = all_96_1_44
% 16.81/4.71 | (138) addition(all_96_1_44, all_96_0_43) = all_47_1_17
% 16.81/4.71 |
% 16.81/4.71 | Instantiating (116) with all_112_0_55, all_112_1_56 yields:
% 16.81/4.71 | (139) multiplication(all_0_2_2, all_0_2_2) = all_112_0_55 & multiplication(all_0_4_4, all_0_2_2) = all_112_1_56 & addition(all_112_1_56, all_112_0_55) = all_0_2_2
% 16.81/4.71 |
% 16.81/4.71 | Applying alpha-rule on (139) yields:
% 16.81/4.71 | (140) multiplication(all_0_2_2, all_0_2_2) = all_112_0_55
% 16.81/4.71 | (141) multiplication(all_0_4_4, all_0_2_2) = all_112_1_56
% 16.81/4.72 | (142) addition(all_112_1_56, all_112_0_55) = all_0_2_2
% 16.81/4.72 |
% 16.81/4.72 | Instantiating (112) with all_120_0_61 yields:
% 16.81/4.72 | (143) multiplication(all_0_2_2, all_0_4_4) = all_120_0_61 & multiplication(all_0_5_5, all_120_0_61) = all_47_1_17
% 16.81/4.72 |
% 16.81/4.72 | Applying alpha-rule on (143) yields:
% 16.81/4.72 | (144) multiplication(all_0_2_2, all_0_4_4) = all_120_0_61
% 16.81/4.72 | (145) multiplication(all_0_5_5, all_120_0_61) = all_47_1_17
% 16.81/4.72 |
% 16.81/4.72 | Instantiating (115) with all_122_0_62, all_122_1_63 yields:
% 16.81/4.72 | (146) multiplication(all_0_2_2, all_0_2_2) = all_122_1_63 & multiplication(all_0_4_4, all_0_2_2) = all_122_0_62 & addition(all_122_1_63, all_122_0_62) = all_0_2_2
% 16.81/4.72 |
% 16.81/4.72 | Applying alpha-rule on (146) yields:
% 16.81/4.72 | (147) multiplication(all_0_2_2, all_0_2_2) = all_122_1_63
% 16.81/4.72 | (148) multiplication(all_0_4_4, all_0_2_2) = all_122_0_62
% 16.81/4.72 | (149) addition(all_122_1_63, all_122_0_62) = all_0_2_2
% 16.81/4.72 |
% 16.81/4.72 | Instantiating (113) with all_128_0_66 yields:
% 16.81/4.72 | (150) multiplication(all_0_4_4, all_0_2_2) = all_128_0_66 & multiplication(all_0_5_5, all_128_0_66) = all_45_1_15
% 16.81/4.72 |
% 16.81/4.72 | Applying alpha-rule on (150) yields:
% 16.81/4.72 | (151) multiplication(all_0_4_4, all_0_2_2) = all_128_0_66
% 16.81/4.72 | (152) multiplication(all_0_5_5, all_128_0_66) = all_45_1_15
% 16.81/4.72 |
% 16.81/4.72 | Instantiating (119) with all_134_0_71, all_134_1_72 yields:
% 16.81/4.72 | (153) multiplication(all_0_2_2, all_0_4_4) = all_134_0_71 & multiplication(all_0_4_4, all_0_4_4) = all_134_1_72 & addition(all_134_1_72, all_134_0_71) = all_0_4_4
% 16.81/4.72 |
% 16.81/4.72 | Applying alpha-rule on (153) yields:
% 16.81/4.72 | (154) multiplication(all_0_2_2, all_0_4_4) = all_134_0_71
% 16.81/4.72 | (155) multiplication(all_0_4_4, all_0_4_4) = all_134_1_72
% 16.81/4.72 | (156) addition(all_134_1_72, all_134_0_71) = all_0_4_4
% 16.81/4.72 |
% 16.81/4.72 | Instantiating (120) with all_136_0_73, all_136_1_74 yields:
% 16.81/4.72 | (157) multiplication(all_47_0_16, all_0_4_4) = all_136_1_74 & multiplication(all_47_1_17, all_0_4_4) = all_136_0_73 & addition(all_136_1_74, all_136_0_73) = all_47_0_16
% 16.81/4.72 |
% 16.81/4.72 | Applying alpha-rule on (157) yields:
% 16.81/4.72 | (158) multiplication(all_47_0_16, all_0_4_4) = all_136_1_74
% 16.81/4.72 | (159) multiplication(all_47_1_17, all_0_4_4) = all_136_0_73
% 16.81/4.72 | (160) addition(all_136_1_74, all_136_0_73) = all_47_0_16
% 16.81/4.72 |
% 16.81/4.72 | Instantiating (114) with all_140_0_76 yields:
% 16.81/4.72 | (161) multiplication(all_0_2_2, all_0_4_4) = all_140_0_76 & multiplication(one, all_140_0_76) = zero
% 16.81/4.72 |
% 16.81/4.72 | Applying alpha-rule on (161) yields:
% 16.81/4.72 | (162) multiplication(all_0_2_2, all_0_4_4) = all_140_0_76
% 16.81/4.72 | (163) multiplication(one, all_140_0_76) = zero
% 16.81/4.72 |
% 16.81/4.72 | Instantiating (118) with all_148_0_83, all_148_1_84 yields:
% 16.81/4.72 | (164) multiplication(all_0_2_2, all_0_4_4) = all_148_1_84 & multiplication(all_0_4_4, all_0_4_4) = all_148_0_83 & addition(all_148_1_84, all_148_0_83) = all_0_4_4
% 16.81/4.72 |
% 16.81/4.72 | Applying alpha-rule on (164) yields:
% 16.81/4.72 | (165) multiplication(all_0_2_2, all_0_4_4) = all_148_1_84
% 16.81/4.72 | (166) multiplication(all_0_4_4, all_0_4_4) = all_148_0_83
% 16.81/4.72 | (167) addition(all_148_1_84, all_148_0_83) = all_0_4_4
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (17) with all_47_1_17, all_0_4_4, all_90_1_40, all_136_0_73 and discharging atoms multiplication(all_47_1_17, all_0_4_4) = all_136_0_73, multiplication(all_47_1_17, all_0_4_4) = all_90_1_40, yields:
% 16.81/4.72 | (168) all_136_0_73 = all_90_1_40
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (17) with all_45_0_14, all_0_4_4, all_76_1_29, all_96_0_43 and discharging atoms multiplication(all_45_0_14, all_0_4_4) = all_96_0_43, multiplication(all_45_0_14, all_0_4_4) = all_76_1_29, yields:
% 16.81/4.72 | (169) all_96_0_43 = all_76_1_29
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (17) with all_45_1_15, all_0_4_4, all_76_0_28, all_96_1_44 and discharging atoms multiplication(all_45_1_15, all_0_4_4) = all_96_1_44, multiplication(all_45_1_15, all_0_4_4) = all_76_0_28, yields:
% 16.81/4.72 | (170) all_96_1_44 = all_76_0_28
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (15) with all_148_1_84, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_148_1_84, complement(all_0_4_4, all_0_2_2), yields:
% 16.81/4.72 | (171) all_148_1_84 = zero
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (17) with all_0_2_2, all_0_4_4, all_140_0_76, all_148_1_84 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_148_1_84, multiplication(all_0_2_2, all_0_4_4) = all_140_0_76, yields:
% 16.81/4.72 | (172) all_148_1_84 = all_140_0_76
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (17) with all_0_2_2, all_0_4_4, all_134_0_71, all_148_1_84 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_148_1_84, multiplication(all_0_2_2, all_0_4_4) = all_134_0_71, yields:
% 16.81/4.72 | (173) all_148_1_84 = all_134_0_71
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (17) with all_0_2_2, all_0_4_4, all_120_0_61, all_134_0_71 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_134_0_71, multiplication(all_0_2_2, all_0_4_4) = all_120_0_61, yields:
% 16.81/4.72 | (174) all_134_0_71 = all_120_0_61
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (17) with all_0_4_4, all_0_2_2, all_122_0_62, all_128_0_66 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_128_0_66, multiplication(all_0_4_4, all_0_2_2) = all_122_0_62, yields:
% 16.81/4.72 | (175) all_128_0_66 = all_122_0_62
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (17) with all_0_4_4, all_0_2_2, all_112_1_56, all_122_0_62 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_122_0_62, multiplication(all_0_4_4, all_0_2_2) = all_112_1_56, yields:
% 16.81/4.72 | (176) all_122_0_62 = all_112_1_56
% 16.81/4.72 |
% 16.81/4.72 | Instantiating formula (28) with all_112_1_56, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_112_1_56, complement(all_0_4_4, all_0_2_2), yields:
% 16.81/4.73 | (177) all_112_1_56 = zero
% 16.81/4.73 |
% 16.81/4.73 | Instantiating formula (17) with all_0_4_4, all_0_2_2, all_84_0_36, all_128_0_66 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_128_0_66, multiplication(all_0_4_4, all_0_2_2) = all_84_0_36, yields:
% 16.81/4.73 | (178) all_128_0_66 = all_84_0_36
% 16.81/4.73 |
% 16.81/4.73 | Combining equations (171,172) yields a new equation:
% 16.81/4.73 | (179) all_140_0_76 = zero
% 16.81/4.73 |
% 16.81/4.73 | Combining equations (173,172) yields a new equation:
% 16.81/4.73 | (180) all_140_0_76 = all_134_0_71
% 16.81/4.73 |
% 16.81/4.73 | Combining equations (180,179) yields a new equation:
% 16.81/4.73 | (181) all_134_0_71 = zero
% 16.81/4.73 |
% 16.81/4.73 | Simplifying 181 yields:
% 16.81/4.73 | (182) all_134_0_71 = zero
% 16.81/4.73 |
% 16.81/4.73 | Combining equations (174,182) yields a new equation:
% 16.81/4.73 | (183) all_120_0_61 = zero
% 16.81/4.73 |
% 16.81/4.73 | Simplifying 183 yields:
% 16.81/4.73 | (184) all_120_0_61 = zero
% 16.81/4.73 |
% 16.81/4.73 | Combining equations (175,178) yields a new equation:
% 16.81/4.73 | (185) all_122_0_62 = all_84_0_36
% 16.81/4.73 |
% 16.81/4.73 | Simplifying 185 yields:
% 16.81/4.73 | (186) all_122_0_62 = all_84_0_36
% 16.81/4.73 |
% 16.81/4.73 | Combining equations (176,186) yields a new equation:
% 16.81/4.73 | (187) all_112_1_56 = all_84_0_36
% 16.81/4.73 |
% 16.81/4.73 | Simplifying 187 yields:
% 16.81/4.73 | (188) all_112_1_56 = all_84_0_36
% 16.81/4.73 |
% 16.81/4.73 | Combining equations (177,188) yields a new equation:
% 16.81/4.73 | (189) all_84_0_36 = zero
% 16.81/4.73 |
% 16.81/4.73 | Combining equations (189,178) yields a new equation:
% 16.81/4.73 | (190) all_128_0_66 = zero
% 16.81/4.73 |
% 16.81/4.73 | From (168) and (159) follows:
% 16.81/4.73 | (133) multiplication(all_47_1_17, all_0_4_4) = all_90_1_40
% 16.81/4.73 |
% 16.81/4.73 | From (170) and (137) follows:
% 16.81/4.73 | (126) multiplication(all_45_1_15, all_0_4_4) = all_76_0_28
% 17.28/4.73 |
% 17.28/4.73 | From (190) and (152) follows:
% 17.28/4.73 | (193) multiplication(all_0_5_5, zero) = all_45_1_15
% 17.28/4.73 |
% 17.28/4.73 | From (184) and (145) follows:
% 17.28/4.73 | (194) multiplication(all_0_5_5, zero) = all_47_1_17
% 17.28/4.73 |
% 17.28/4.73 | From (170)(169) and (138) follows:
% 17.28/4.73 | (195) addition(all_76_0_28, all_76_1_29) = all_47_1_17
% 17.28/4.73 |
% 17.28/4.73 | Instantiating formula (42) with all_47_1_17, all_0_5_5 and discharging atoms multiplication(all_0_5_5, zero) = all_47_1_17, yields:
% 17.28/4.73 | (196) all_47_1_17 = zero
% 17.28/4.73 |
% 17.28/4.73 | Instantiating formula (17) with all_0_5_5, zero, all_45_1_15, all_47_1_17 and discharging atoms multiplication(all_0_5_5, zero) = all_47_1_17, multiplication(all_0_5_5, zero) = all_45_1_15, yields:
% 17.28/4.73 | (197) all_47_1_17 = all_45_1_15
% 17.28/4.73 |
% 17.28/4.73 | Combining equations (197,196) yields a new equation:
% 17.28/4.73 | (198) all_45_1_15 = zero
% 17.28/4.73 |
% 17.28/4.73 | Simplifying 198 yields:
% 17.28/4.73 | (199) all_45_1_15 = zero
% 17.28/4.73 |
% 17.28/4.73 | From (196) and (133) follows:
% 17.28/4.73 | (200) multiplication(zero, all_0_4_4) = all_90_1_40
% 17.28/4.73 |
% 17.28/4.73 | From (199) and (126) follows:
% 17.28/4.73 | (201) multiplication(zero, all_0_4_4) = all_76_0_28
% 17.28/4.73 |
% 17.28/4.73 | From (199) and (193) follows:
% 17.28/4.73 | (202) multiplication(all_0_5_5, zero) = zero
% 17.28/4.73 |
% 17.28/4.73 | From (196) and (195) follows:
% 17.28/4.73 | (203) addition(all_76_0_28, all_76_1_29) = zero
% 17.28/4.73 |
% 17.28/4.73 | From (196) and (127) follows:
% 17.28/4.73 | (204) addition(all_76_1_29, all_76_0_28) = zero
% 17.28/4.73 |
% 17.28/4.73 | Instantiating formula (31) with all_90_1_40, all_0_4_4 and discharging atoms multiplication(zero, all_0_4_4) = all_90_1_40, yields:
% 17.28/4.73 | (205) all_90_1_40 = zero
% 17.28/4.73 |
% 17.28/4.73 | Instantiating formula (17) with zero, all_0_4_4, all_76_0_28, all_90_1_40 and discharging atoms multiplication(zero, all_0_4_4) = all_90_1_40, multiplication(zero, all_0_4_4) = all_76_0_28, yields:
% 17.28/4.73 | (206) all_90_1_40 = all_76_0_28
% 17.28/4.73 |
% 17.28/4.74 | Combining equations (205,206) yields a new equation:
% 17.28/4.74 | (207) all_76_0_28 = zero
% 17.28/4.74 |
% 17.28/4.74 | From (207) and (203) follows:
% 17.28/4.74 | (208) addition(zero, all_76_1_29) = zero
% 17.28/4.74 |
% 17.28/4.74 | From (207) and (204) follows:
% 17.28/4.74 | (209) addition(all_76_1_29, zero) = zero
% 17.28/4.74 |
% 17.28/4.74 | Instantiating formula (38) with zero, all_76_1_29 and discharging atoms addition(all_76_1_29, zero) = zero, yields:
% 17.28/4.74 | (210) all_76_1_29 = zero
% 17.28/4.74 |
% 17.28/4.74 | From (210) and (208) follows:
% 17.28/4.74 | (211) addition(zero, zero) = zero
% 17.28/4.74 |
% 17.28/4.74 | Instantiating formula (4) with zero, zero, zero, zero, all_0_5_5, all_0_5_5 and discharging atoms multiplication(all_0_5_5, zero) = zero, addition(zero, zero) = zero, yields:
% 17.28/4.74 | (212) ? [v0] : (multiplication(v0, zero) = zero & addition(all_0_5_5, all_0_5_5) = v0)
% 17.28/4.74 |
% 17.28/4.74 | Instantiating (212) with all_256_0_138 yields:
% 17.28/4.74 | (213) multiplication(all_256_0_138, zero) = zero & addition(all_0_5_5, all_0_5_5) = all_256_0_138
% 17.28/4.74 |
% 17.28/4.74 | Applying alpha-rule on (213) yields:
% 17.28/4.74 | (214) multiplication(all_256_0_138, zero) = zero
% 17.28/4.74 | (215) addition(all_0_5_5, all_0_5_5) = all_256_0_138
% 17.28/4.74 |
% 17.28/4.74 | Instantiating formula (10) with all_256_0_138, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_5_5) = all_256_0_138, yields:
% 17.28/4.74 | (216) all_256_0_138 = all_0_5_5
% 17.28/4.74 |
% 17.28/4.74 | From (216) and (215) follows:
% 17.28/4.74 | (217) addition(all_0_5_5, all_0_5_5) = all_0_5_5
% 17.28/4.74 |
% 17.28/4.74 | Instantiating formula (8) with all_0_5_5, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_5_5) = all_0_5_5, ~ leq(all_0_5_5, all_0_5_5), yields:
% 17.28/4.74 | (218) $false
% 17.28/4.74 |
% 17.28/4.74 |-The branch is then unsatisfiable
% 17.28/4.74 |-Branch two:
% 17.28/4.74 | (219) leq(all_0_0_0, all_0_5_5)
% 17.28/4.74 | (220) ~ leq(all_0_5_5, all_0_0_0)
% 17.28/4.74 |
% 17.28/4.74 | From (60) and (219) follows:
% 17.28/4.74 | (221) leq(all_0_5_5, all_0_5_5)
% 17.28/4.74 |
% 17.28/4.74 | From (60) and (220) follows:
% 17.28/4.74 | (65) ~ leq(all_0_5_5, all_0_5_5)
% 17.28/4.74 |
% 17.28/4.74 | Using (221) and (65) yields:
% 17.28/4.74 | (218) $false
% 17.28/4.74 |
% 17.28/4.74 |-The branch is then unsatisfiable
% 17.28/4.74 % SZS output end Proof for theBenchmark
% 17.28/4.74
% 17.28/4.74 4130ms
%------------------------------------------------------------------------------