TSTP Solution File: KLE022+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE022+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 01:50:56 EDT 2022
% Result : Theorem 2.64s 1.33s
% Output : Proof 4.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE022+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 16 16:18:53 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.68/0.92 Prover 0: Preprocessing ...
% 2.45/1.18 Prover 0: Constructing countermodel ...
% 2.64/1.32 Prover 0: proved (698ms)
% 2.64/1.33
% 2.64/1.33 No countermodel exists, formula is valid
% 2.64/1.33 % SZS status Theorem for theBenchmark
% 2.64/1.33
% 2.64/1.33 Generating proof ... found it (size 19)
% 3.90/1.60
% 3.90/1.60 % SZS output start Proof for theBenchmark
% 3.90/1.60 Assumed formulas after preprocessing and simplification:
% 3.90/1.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v0) & 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)))
% 4.28/1.64 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 4.28/1.64 | (1) ~ (all_0_0_0 = all_0_5_5) & 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))
% 4.28/1.66 |
% 4.28/1.66 | Applying alpha-rule on (1) yields:
% 4.28/1.66 | (2) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero))))
% 4.28/1.66 | (3) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 4.28/1.66 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one))
% 4.28/1.66 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one))
% 4.28/1.66 | (6) c(all_0_4_4) = all_0_2_2
% 4.28/1.66 | (7) multiplication(all_0_5_5, all_0_2_2) = all_0_1_1
% 4.28/1.66 | (8) ~ (all_0_0_0 = all_0_5_5)
% 4.28/1.66 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0))
% 4.28/1.66 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0))
% 4.28/1.66 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 4.28/1.66 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 4.28/1.66 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 4.28/1.66 | (14) ! [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))
% 4.28/1.66 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0))
% 4.28/1.66 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero))
% 4.28/1.66 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 4.28/1.66 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 4.28/1.66 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 4.28/1.66 | (20) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 4.28/1.66 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 4.28/1.67 | (22) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero))))
% 4.28/1.67 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 4.28/1.67 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 4.28/1.67 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 4.28/1.67 | (26) ! [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))
% 4.28/1.67 | (27) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero))))
% 4.28/1.67 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 4.28/1.67 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0))
% 4.28/1.67 | (30) ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0))
% 4.28/1.67 | (31) ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1))
% 4.28/1.67 | (32) test(all_0_4_4)
% 4.28/1.67 | (33) ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0))
% 4.28/1.67 | (34) ! [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))
% 4.28/1.67 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1))
% 4.28/1.67 | (36) addition(all_0_3_3, all_0_1_1) = all_0_0_0
% 4.28/1.67 | (37) multiplication(all_0_5_5, all_0_4_4) = all_0_3_3
% 4.28/1.67 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0))
% 4.28/1.67 | (39) ! [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))
% 4.28/1.67 | (40) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 4.28/1.67 | (41) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0))
% 4.28/1.67 | (42) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 4.28/1.67 |
% 4.28/1.67 | Instantiating formula (14) 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:
% 4.28/1.67 | (43) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = v0)
% 4.28/1.68 |
% 4.28/1.68 | Instantiating formula (24) 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:
% 4.28/1.68 | (44) addition(all_0_1_1, all_0_3_3) = all_0_0_0
% 4.28/1.68 |
% 4.28/1.68 | Instantiating formula (31) 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:
% 4.28/1.68 | (45) complement(all_0_4_4, all_0_2_2)
% 4.28/1.68 |
% 4.28/1.68 | Instantiating (43) with all_11_0_7 yields:
% 4.28/1.68 | (46) multiplication(all_0_5_5, all_11_0_7) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = all_11_0_7
% 4.28/1.68 |
% 4.28/1.68 | Applying alpha-rule on (46) yields:
% 4.28/1.68 | (47) multiplication(all_0_5_5, all_11_0_7) = all_0_0_0
% 4.28/1.68 | (48) addition(all_0_4_4, all_0_2_2) = all_11_0_7
% 4.28/1.68 |
% 4.28/1.68 | Instantiating formula (14) 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:
% 4.28/1.68 | (49) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = v0)
% 4.28/1.68 |
% 4.28/1.68 | Instantiating formula (24) with all_11_0_7, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_4_4, all_0_2_2) = all_11_0_7, yields:
% 4.28/1.68 | (50) addition(all_0_2_2, all_0_4_4) = all_11_0_7
% 4.28/1.68 |
% 4.28/1.68 | Instantiating (49) with all_19_0_8 yields:
% 4.28/1.68 | (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
% 4.28/1.68 |
% 4.28/1.68 | Applying alpha-rule on (51) yields:
% 4.28/1.68 | (52) multiplication(all_0_5_5, all_19_0_8) = all_0_0_0
% 4.28/1.68 | (53) addition(all_0_2_2, all_0_4_4) = all_19_0_8
% 4.28/1.68 |
% 4.28/1.68 | Instantiating formula (29) 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:
% 4.28/1.68 | (54) all_19_0_8 = one
% 4.28/1.68 |
% 4.28/1.68 | Instantiating formula (21) with all_0_2_2, all_0_4_4, all_11_0_7, 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_11_0_7, yields:
% 4.28/1.68 | (55) all_19_0_8 = all_11_0_7
% 4.28/1.68 |
% 4.28/1.68 | Combining equations (55,54) yields a new equation:
% 4.28/1.68 | (56) all_11_0_7 = one
% 4.28/1.68 |
% 4.28/1.68 | Simplifying 56 yields:
% 4.28/1.68 | (57) all_11_0_7 = one
% 4.28/1.68 |
% 4.28/1.68 | From (57) and (47) follows:
% 4.28/1.68 | (58) multiplication(all_0_5_5, one) = all_0_0_0
% 4.28/1.68 |
% 4.28/1.68 | Instantiating formula (40) with all_0_0_0, all_0_5_5 and discharging atoms multiplication(all_0_5_5, one) = all_0_0_0, yields:
% 4.28/1.68 | (59) all_0_0_0 = all_0_5_5
% 4.28/1.68 |
% 4.28/1.68 | Equations (59) can reduce 8 to:
% 4.28/1.68 | (60) $false
% 4.28/1.68 |
% 4.28/1.68 |-The branch is then unsatisfiable
% 4.28/1.68 % SZS output end Proof for theBenchmark
% 4.28/1.68
% 4.28/1.68 1097ms
%------------------------------------------------------------------------------