TSTP Solution File: KLE035+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE035+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 01:51:02 EDT 2022
% Result : Theorem 22.92s 6.78s
% Output : Proof 37.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE035+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 10:35:54 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.64/0.65 ____ _
% 0.64/0.65 ___ / __ \_____(_)___ ________ __________
% 0.64/0.65 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.64/0.65 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.64/0.65 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.64/0.65
% 0.64/0.65 A Theorem Prover for First-Order Logic
% 0.64/0.65 (ePrincess v.1.0)
% 0.64/0.65
% 0.64/0.65 (c) Philipp Rümmer, 2009-2015
% 0.64/0.65 (c) Peter Backeman, 2014-2015
% 0.64/0.65 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.65 Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.65 Bug reports to peter@backeman.se
% 0.64/0.65
% 0.64/0.65 For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.65
% 0.64/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.46/1.00 Prover 0: Preprocessing ...
% 2.53/1.35 Prover 0: Constructing countermodel ...
% 19.67/5.99 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.67/6.01 Prover 1: Preprocessing ...
% 20.12/6.07 Prover 1: Constructing countermodel ...
% 22.92/6.77 Prover 1: proved (780ms)
% 22.92/6.78 Prover 0: stopped
% 22.92/6.78
% 22.92/6.78 No countermodel exists, formula is valid
% 22.92/6.78 % SZS status Theorem for theBenchmark
% 22.92/6.78
% 22.92/6.78 Generating proof ... found it (size 73)
% 36.91/10.13
% 36.91/10.13 % SZS output start Proof for theBenchmark
% 36.91/10.14 Assumed formulas after preprocessing and simplification:
% 36.91/10.14 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = 0) & c(v3) = v5 & test(v3) = 0 & test(v2) = 0 & leq(v11, zero) = v12 & leq(v8, zero) = 0 & leq(v6, zero) = 0 & multiplication(v10, v5) = v11 & multiplication(v7, v5) = v8 & multiplication(v4, v5) = v6 & multiplication(v2, v9) = v10 & multiplication(v2, v1) = v7 & multiplication(v2, v0) = v4 & addition(v0, v1) = v9 & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (multiplication(v14, v15) = v17) | ~ (multiplication(v13, v15) = v16) | ~ (addition(v16, v17) = v18) | ? [v19] : (multiplication(v19, v15) = v18 & addition(v13, v14) = v19)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (multiplication(v13, v15) = v17) | ~ (multiplication(v13, v14) = v16) | ~ (addition(v16, v17) = v18) | ? [v19] : (multiplication(v13, v19) = v18 & addition(v14, v15) = v19)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (c(v14) = v16) | ~ (c(v13) = v15) | ~ (multiplication(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (c(v20) = v21 & test(v14) = v19 & test(v13) = v18 & addition(v13, v14) = v20 & ( ~ (v19 = 0) | ~ (v18 = 0) | v21 = v17))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (c(v14) = v16) | ~ (c(v13) = v15) | ~ (addition(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (c(v20) = v21 & test(v14) = v19 & test(v13) = v18 & multiplication(v13, v14) = v20 & ( ~ (v19 = 0) | ~ (v18 = 0) | v21 = v17))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (multiplication(v16, v15) = v17) | ~ (multiplication(v13, v14) = v16) | ? [v18] : (multiplication(v14, v15) = v18 & multiplication(v13, v18) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (addition(v16, v13) = v17) | ~ (addition(v15, v14) = v16) | ? [v18] : (addition(v15, v18) = v17 & addition(v14, v13) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (complement(v16, v15) = v14) | ~ (complement(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (leq(v16, v15) = v14) | ~ (leq(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (multiplication(v16, v15) = v14) | ~ (multiplication(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (addition(v16, v15) = v14) | ~ (addition(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (complement(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : (multiplication(v14, v13) = v17 & multiplication(v13, v14) = v16 & addition(v13, v14) = v18 & ( ~ (v18 = one) | ~ (v17 = zero) | ~ (v16 = zero)))) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (leq(v13, v14) = v15) | ? [v16] : ( ~ (v16 = v14) & addition(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (c(v15) = v14) | ~ (c(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (test(v15) = v14) | ~ (test(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (test(v13) = v14) | ~ (complement(v15, v13) = 0)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (complement(v13, v14) = v15) | ? [v16] : ? [v17] : (c(v13) = v17 & test(v13) = v16 & ( ~ (v16 = 0) | (( ~ (v17 = v14) | v15 = 0) & ( ~ (v15 = 0) | v17 = v14))))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (addition(v13, v14) = v15) | addition(v14, v13) = v15) & ! [v13] : ! [v14] : (v14 = v13 | ~ (multiplication(v13, one) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (multiplication(one, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (addition(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (addition(v13, zero) = v14)) & ! [v13] : ! [v14] : (v14 = zero | ~ (multiplication(v13, zero) = v14)) & ! [v13] : ! [v14] : (v14 = zero | ~ (multiplication(zero, v13) = v14)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (test(v13) = v14) | c(v13) = zero) & ! [v13] : ! [v14] : ( ~ (complement(v14, v13) = 0) | (multiplication(v14, v13) = zero & multiplication(v13, v14) = zero & addition(v13, v14) = one)) & ! [v13] : ! [v14] : ( ~ (leq(v13, v14) = 0) | addition(v13, v14) = v14) & ! [v13] : ( ~ (test(v13) = 0) | ? [v14] : complement(v14, v13) = 0))
% 37.02/10.19 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields:
% 37.02/10.19 | (1) ~ (all_0_0_0 = 0) & c(all_0_9_9) = all_0_7_7 & test(all_0_9_9) = 0 & test(all_0_10_10) = 0 & leq(all_0_1_1, zero) = all_0_0_0 & leq(all_0_4_4, zero) = 0 & leq(all_0_6_6, zero) = 0 & multiplication(all_0_2_2, all_0_7_7) = all_0_1_1 & multiplication(all_0_5_5, all_0_7_7) = all_0_4_4 & multiplication(all_0_8_8, all_0_7_7) = all_0_6_6 & multiplication(all_0_10_10, all_0_3_3) = all_0_2_2 & multiplication(all_0_10_10, all_0_11_11) = all_0_5_5 & multiplication(all_0_10_10, all_0_12_12) = all_0_8_8 & addition(all_0_12_12, all_0_11_11) = all_0_3_3 & ! [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] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (multiplication(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (c(v7) = v8 & test(v1) = v6 & test(v0) = v5 & addition(v0, v1) = v7 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (c(v7) = v8 & test(v1) = v6 & test(v0) = v5 & multiplication(v0, v1) = v7 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4))) & ! [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] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (complement(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (multiplication(v1, v0) = v4 & multiplication(v0, v1) = v3 & addition(v0, v1) = v5 & ( ~ (v5 = one) | ~ (v4 = zero) | ~ (v3 = zero)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (test(v0) = v1) | ~ (complement(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0, v1) = v2) | ? [v3] : ? [v4] : (c(v0) = v4 & test(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v1) | v2 = 0) & ( ~ (v2 = 0) | v4 = v1))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (test(v0) = v1) | c(v0) = zero) & ! [v0] : ! [v1] : ( ~ (complement(v1, v0) = 0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ( ~ (test(v0) = 0) | ? [v1] : complement(v1, v0) = 0)
% 37.02/10.21 |
% 37.02/10.21 | Applying alpha-rule on (1) yields:
% 37.02/10.21 | (2) ! [v0] : ! [v1] : ( ~ (complement(v1, v0) = 0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one))
% 37.02/10.21 | (3) ~ (all_0_0_0 = 0)
% 37.02/10.21 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (test(v0) = v1) | ~ (complement(v2, v0) = 0))
% 37.02/10.21 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 37.02/10.21 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 37.02/10.21 | (7) multiplication(all_0_2_2, all_0_7_7) = all_0_1_1
% 37.02/10.21 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (test(v0) = v1) | c(v0) = zero)
% 37.02/10.21 | (9) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 37.02/10.21 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0, v1) = v2) | ? [v3] : ? [v4] : (c(v0) = v4 & test(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v1) | v2 = 0) & ( ~ (v2 = 0) | v4 = v1)))))
% 37.02/10.21 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (complement(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (multiplication(v1, v0) = v4 & multiplication(v0, v1) = v3 & addition(v0, v1) = v5 & ( ~ (v5 = one) | ~ (v4 = zero) | ~ (v3 = zero))))
% 37.02/10.21 | (12) leq(all_0_6_6, zero) = 0
% 37.02/10.21 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 37.02/10.21 | (14) leq(all_0_1_1, zero) = all_0_0_0
% 37.02/10.21 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 37.02/10.21 | (16) ! [v0] : ( ~ (test(v0) = 0) | ? [v1] : complement(v1, v0) = 0)
% 37.02/10.21 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0))
% 37.02/10.21 | (18) ! [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))
% 37.02/10.22 | (19) multiplication(all_0_10_10, all_0_12_12) = all_0_8_8
% 37.02/10.22 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 37.02/10.22 | (21) ! [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))
% 37.02/10.22 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (c(v7) = v8 & test(v1) = v6 & test(v0) = v5 & multiplication(v0, v1) = v7 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4)))
% 37.02/10.22 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (multiplication(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (c(v7) = v8 & test(v1) = v6 & test(v0) = v5 & addition(v0, v1) = v7 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4)))
% 37.02/10.22 | (24) multiplication(all_0_8_8, all_0_7_7) = all_0_6_6
% 37.02/10.22 | (25) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 37.02/10.22 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 37.02/10.22 | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 37.02/10.22 | (28) multiplication(all_0_10_10, all_0_11_11) = all_0_5_5
% 37.02/10.22 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) = v0))
% 37.02/10.22 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 37.02/10.22 | (31) c(all_0_9_9) = all_0_7_7
% 37.02/10.22 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 37.02/10.22 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 37.02/10.22 | (34) addition(all_0_12_12, all_0_11_11) = all_0_3_3
% 37.02/10.22 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 37.02/10.23 | (36) test(all_0_10_10) = 0
% 37.02/10.23 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 37.02/10.23 | (38) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 37.02/10.23 | (39) multiplication(all_0_5_5, all_0_7_7) = all_0_4_4
% 37.02/10.23 | (40) test(all_0_9_9) = 0
% 37.31/10.23 | (41) multiplication(all_0_10_10, all_0_3_3) = all_0_2_2
% 37.31/10.23 | (42) leq(all_0_4_4, zero) = 0
% 37.31/10.23 |
% 37.31/10.23 | Instantiating formula (33) with all_0_0_0, zero, all_0_1_1 and discharging atoms leq(all_0_1_1, zero) = all_0_0_0, yields:
% 37.31/10.23 | (43) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = zero) & addition(all_0_1_1, zero) = v0)
% 37.31/10.23 |
% 37.31/10.23 | Instantiating formula (9) with zero, all_0_4_4 and discharging atoms leq(all_0_4_4, zero) = 0, yields:
% 37.31/10.23 | (44) addition(all_0_4_4, zero) = zero
% 37.31/10.23 |
% 37.31/10.23 | Instantiating formula (9) with zero, all_0_6_6 and discharging atoms leq(all_0_6_6, zero) = 0, yields:
% 37.31/10.23 | (45) addition(all_0_6_6, zero) = zero
% 37.31/10.23 |
% 37.31/10.23 | Instantiating formula (26) with all_0_1_1, all_0_2_2, all_0_7_7, all_0_3_3, all_0_10_10 and discharging atoms multiplication(all_0_2_2, all_0_7_7) = all_0_1_1, multiplication(all_0_10_10, all_0_3_3) = all_0_2_2, yields:
% 37.31/10.23 | (46) ? [v0] : (multiplication(all_0_3_3, all_0_7_7) = v0 & multiplication(all_0_10_10, v0) = all_0_1_1)
% 37.31/10.23 |
% 37.31/10.23 | Instantiating formula (26) with all_0_4_4, all_0_5_5, all_0_7_7, all_0_11_11, all_0_10_10 and discharging atoms multiplication(all_0_5_5, all_0_7_7) = all_0_4_4, multiplication(all_0_10_10, all_0_11_11) = all_0_5_5, yields:
% 37.31/10.23 | (47) ? [v0] : (multiplication(all_0_10_10, v0) = all_0_4_4 & multiplication(all_0_11_11, all_0_7_7) = v0)
% 37.31/10.23 |
% 37.31/10.23 | Instantiating formula (26) with all_0_6_6, all_0_8_8, all_0_7_7, all_0_12_12, all_0_10_10 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_0_6_6, multiplication(all_0_10_10, all_0_12_12) = all_0_8_8, yields:
% 37.31/10.23 | (48) ? [v0] : (multiplication(all_0_10_10, v0) = all_0_6_6 & multiplication(all_0_12_12, all_0_7_7) = v0)
% 37.31/10.23 |
% 37.31/10.23 | Instantiating formula (13) with all_0_3_3, all_0_11_11, all_0_12_12 and discharging atoms addition(all_0_12_12, all_0_11_11) = all_0_3_3, yields:
% 37.31/10.23 | (49) addition(all_0_11_11, all_0_12_12) = all_0_3_3
% 37.31/10.23 |
% 37.31/10.23 | Instantiating (47) with all_9_0_13 yields:
% 37.31/10.23 | (50) multiplication(all_0_10_10, all_9_0_13) = all_0_4_4 & multiplication(all_0_11_11, all_0_7_7) = all_9_0_13
% 37.31/10.23 |
% 37.31/10.23 | Applying alpha-rule on (50) yields:
% 37.31/10.23 | (51) multiplication(all_0_10_10, all_9_0_13) = all_0_4_4
% 37.31/10.23 | (52) multiplication(all_0_11_11, all_0_7_7) = all_9_0_13
% 37.31/10.23 |
% 37.31/10.23 | Instantiating (46) with all_13_0_15 yields:
% 37.31/10.23 | (53) multiplication(all_0_3_3, all_0_7_7) = all_13_0_15 & multiplication(all_0_10_10, all_13_0_15) = all_0_1_1
% 37.31/10.23 |
% 37.31/10.23 | Applying alpha-rule on (53) yields:
% 37.31/10.23 | (54) multiplication(all_0_3_3, all_0_7_7) = all_13_0_15
% 37.31/10.23 | (55) multiplication(all_0_10_10, all_13_0_15) = all_0_1_1
% 37.31/10.23 |
% 37.31/10.23 | Instantiating (48) with all_17_0_17 yields:
% 37.31/10.23 | (56) multiplication(all_0_10_10, all_17_0_17) = all_0_6_6 & multiplication(all_0_12_12, all_0_7_7) = all_17_0_17
% 37.31/10.23 |
% 37.31/10.23 | Applying alpha-rule on (56) yields:
% 37.31/10.23 | (57) multiplication(all_0_10_10, all_17_0_17) = all_0_6_6
% 37.31/10.23 | (58) multiplication(all_0_12_12, all_0_7_7) = all_17_0_17
% 37.31/10.23 |
% 37.31/10.23 +-Applying beta-rule and splitting (43), into two cases.
% 37.31/10.23 |-Branch one:
% 37.31/10.23 | (59) all_0_0_0 = 0
% 37.31/10.23 |
% 37.31/10.23 | Equations (59) can reduce 3 to:
% 37.31/10.24 | (60) $false
% 37.31/10.24 |
% 37.31/10.24 |-The branch is then unsatisfiable
% 37.31/10.24 |-Branch two:
% 37.31/10.24 | (3) ~ (all_0_0_0 = 0)
% 37.31/10.24 | (62) ? [v0] : ( ~ (v0 = zero) & addition(all_0_1_1, zero) = v0)
% 37.31/10.24 |
% 37.31/10.24 | Instantiating (62) with all_23_0_18 yields:
% 37.31/10.24 | (63) ~ (all_23_0_18 = zero) & addition(all_0_1_1, zero) = all_23_0_18
% 37.31/10.24 |
% 37.31/10.24 | Applying alpha-rule on (63) yields:
% 37.31/10.24 | (64) ~ (all_23_0_18 = zero)
% 37.31/10.24 | (65) addition(all_0_1_1, zero) = all_23_0_18
% 37.31/10.24 |
% 37.31/10.24 | Instantiating formula (35) with all_23_0_18, all_0_1_1 and discharging atoms addition(all_0_1_1, zero) = all_23_0_18, yields:
% 37.31/10.24 | (66) all_23_0_18 = all_0_1_1
% 37.31/10.24 |
% 37.31/10.24 | Instantiating formula (35) with zero, all_0_4_4 and discharging atoms addition(all_0_4_4, zero) = zero, yields:
% 37.31/10.24 | (67) all_0_4_4 = zero
% 37.31/10.24 |
% 37.31/10.24 | Instantiating formula (35) with zero, all_0_6_6 and discharging atoms addition(all_0_6_6, zero) = zero, yields:
% 37.31/10.24 | (68) all_0_6_6 = zero
% 37.31/10.24 |
% 37.31/10.24 | Equations (66) can reduce 64 to:
% 37.31/10.24 | (69) ~ (all_0_1_1 = zero)
% 37.31/10.24 |
% 37.31/10.24 | From (67) and (39) follows:
% 37.31/10.24 | (70) multiplication(all_0_5_5, all_0_7_7) = zero
% 37.31/10.24 |
% 37.31/10.24 | From (68) and (24) follows:
% 37.31/10.24 | (71) multiplication(all_0_8_8, all_0_7_7) = zero
% 37.31/10.24 |
% 37.31/10.24 | From (68) and (57) follows:
% 37.31/10.24 | (72) multiplication(all_0_10_10, all_17_0_17) = zero
% 37.31/10.24 |
% 37.31/10.24 | From (67) and (51) follows:
% 37.31/10.24 | (73) multiplication(all_0_10_10, all_9_0_13) = zero
% 37.31/10.24 |
% 37.31/10.24 | From (68) and (45) follows:
% 37.31/10.24 | (74) addition(zero, zero) = zero
% 37.31/10.24 |
% 37.31/10.24 | Instantiating formula (18) with zero, zero, zero, all_0_7_7, all_0_8_8, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_7_7) = zero, multiplication(all_0_8_8, all_0_7_7) = zero, addition(zero, zero) = zero, yields:
% 37.31/10.24 | (75) ? [v0] : (multiplication(v0, all_0_7_7) = zero & addition(all_0_5_5, all_0_8_8) = v0)
% 37.31/10.24 |
% 37.31/10.24 | Instantiating formula (21) with zero, zero, zero, all_17_0_17, all_17_0_17, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_17_0_17) = zero, addition(zero, zero) = zero, yields:
% 37.31/10.24 | (76) ? [v0] : (multiplication(all_0_10_10, v0) = zero & addition(all_17_0_17, all_17_0_17) = v0)
% 37.31/10.24 |
% 37.31/10.24 | Instantiating formula (21) with zero, zero, zero, all_17_0_17, all_9_0_13, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_17_0_17) = zero, multiplication(all_0_10_10, all_9_0_13) = zero, addition(zero, zero) = zero, yields:
% 37.31/10.24 | (77) ? [v0] : (multiplication(all_0_10_10, v0) = zero & addition(all_9_0_13, all_17_0_17) = v0)
% 37.31/10.24 |
% 37.31/10.24 | Instantiating formula (21) with zero, zero, zero, all_9_0_13, all_17_0_17, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_17_0_17) = zero, multiplication(all_0_10_10, all_9_0_13) = zero, addition(zero, zero) = zero, yields:
% 37.31/10.24 | (78) ? [v0] : (multiplication(all_0_10_10, v0) = zero & addition(all_17_0_17, all_9_0_13) = v0)
% 37.31/10.24 |
% 37.31/10.24 | Instantiating (77) with all_105_0_20 yields:
% 37.31/10.24 | (79) multiplication(all_0_10_10, all_105_0_20) = zero & addition(all_9_0_13, all_17_0_17) = all_105_0_20
% 37.31/10.24 |
% 37.31/10.24 | Applying alpha-rule on (79) yields:
% 37.31/10.24 | (80) multiplication(all_0_10_10, all_105_0_20) = zero
% 37.31/10.24 | (81) addition(all_9_0_13, all_17_0_17) = all_105_0_20
% 37.31/10.24 |
% 37.31/10.24 | Instantiating (76) with all_111_0_23 yields:
% 37.31/10.24 | (82) multiplication(all_0_10_10, all_111_0_23) = zero & addition(all_17_0_17, all_17_0_17) = all_111_0_23
% 37.31/10.24 |
% 37.31/10.24 | Applying alpha-rule on (82) yields:
% 37.31/10.24 | (83) multiplication(all_0_10_10, all_111_0_23) = zero
% 37.31/10.24 | (84) addition(all_17_0_17, all_17_0_17) = all_111_0_23
% 37.31/10.24 |
% 37.31/10.24 | Instantiating (78) with all_113_0_24 yields:
% 37.31/10.24 | (85) multiplication(all_0_10_10, all_113_0_24) = zero & addition(all_17_0_17, all_9_0_13) = all_113_0_24
% 37.31/10.24 |
% 37.31/10.24 | Applying alpha-rule on (85) yields:
% 37.31/10.24 | (86) multiplication(all_0_10_10, all_113_0_24) = zero
% 37.31/10.24 | (87) addition(all_17_0_17, all_9_0_13) = all_113_0_24
% 37.31/10.24 |
% 37.31/10.24 | Instantiating (75) with all_121_0_29 yields:
% 37.31/10.24 | (88) multiplication(all_121_0_29, all_0_7_7) = zero & addition(all_0_5_5, all_0_8_8) = all_121_0_29
% 37.31/10.24 |
% 37.31/10.24 | Applying alpha-rule on (88) yields:
% 37.31/10.24 | (89) multiplication(all_121_0_29, all_0_7_7) = zero
% 37.31/10.24 | (90) addition(all_0_5_5, all_0_8_8) = all_121_0_29
% 37.31/10.24 |
% 37.31/10.24 | Instantiating formula (37) with all_0_10_10, all_113_0_24, zero, all_0_1_1 and discharging atoms multiplication(all_0_10_10, all_113_0_24) = zero, yields:
% 37.31/10.24 | (91) all_0_1_1 = zero | ~ (multiplication(all_0_10_10, all_113_0_24) = all_0_1_1)
% 37.31/10.24 |
% 37.31/10.24 | Instantiating formula (5) with all_111_0_23, all_17_0_17 and discharging atoms addition(all_17_0_17, all_17_0_17) = all_111_0_23, yields:
% 37.31/10.24 | (92) all_111_0_23 = all_17_0_17
% 37.31/10.25 |
% 37.31/10.25 | From (92) and (84) follows:
% 37.31/10.25 | (93) addition(all_17_0_17, all_17_0_17) = all_17_0_17
% 37.31/10.25 |
% 37.31/10.25 | Instantiating formula (30) with all_113_0_24, all_17_0_17, all_17_0_17, all_17_0_17, all_9_0_13 and discharging atoms addition(all_17_0_17, all_17_0_17) = all_17_0_17, addition(all_17_0_17, all_9_0_13) = all_113_0_24, yields:
% 37.31/10.25 | (94) ? [v0] : (addition(all_17_0_17, v0) = all_113_0_24 & addition(all_17_0_17, all_9_0_13) = v0)
% 37.31/10.25 |
% 37.31/10.25 | Instantiating formula (18) with all_105_0_20, all_17_0_17, all_9_0_13, all_0_7_7, all_0_12_12, all_0_11_11 and discharging atoms multiplication(all_0_11_11, all_0_7_7) = all_9_0_13, multiplication(all_0_12_12, all_0_7_7) = all_17_0_17, addition(all_9_0_13, all_17_0_17) = all_105_0_20, yields:
% 37.31/10.25 | (95) ? [v0] : (multiplication(v0, all_0_7_7) = all_105_0_20 & addition(all_0_11_11, all_0_12_12) = v0)
% 37.31/10.25 |
% 37.31/10.25 | Instantiating formula (13) with all_105_0_20, all_17_0_17, all_9_0_13 and discharging atoms addition(all_9_0_13, all_17_0_17) = all_105_0_20, yields:
% 37.31/10.25 | (96) addition(all_17_0_17, all_9_0_13) = all_105_0_20
% 37.31/10.25 |
% 37.31/10.25 | Instantiating formula (21) with all_121_0_29, all_0_8_8, all_0_5_5, all_0_12_12, all_0_11_11, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_0_11_11) = all_0_5_5, multiplication(all_0_10_10, all_0_12_12) = all_0_8_8, addition(all_0_5_5, all_0_8_8) = all_121_0_29, yields:
% 37.31/10.25 | (97) ? [v0] : (multiplication(all_0_10_10, v0) = all_121_0_29 & addition(all_0_11_11, all_0_12_12) = v0)
% 37.31/10.25 |
% 37.31/10.25 | Instantiating (95) with all_375_0_41 yields:
% 37.31/10.25 | (98) multiplication(all_375_0_41, all_0_7_7) = all_105_0_20 & addition(all_0_11_11, all_0_12_12) = all_375_0_41
% 37.31/10.25 |
% 37.31/10.25 | Applying alpha-rule on (98) yields:
% 37.31/10.25 | (99) multiplication(all_375_0_41, all_0_7_7) = all_105_0_20
% 37.31/10.25 | (100) addition(all_0_11_11, all_0_12_12) = all_375_0_41
% 37.31/10.25 |
% 37.31/10.25 | Instantiating (97) with all_413_0_63 yields:
% 37.31/10.25 | (101) multiplication(all_0_10_10, all_413_0_63) = all_121_0_29 & addition(all_0_11_11, all_0_12_12) = all_413_0_63
% 37.31/10.25 |
% 37.31/10.25 | Applying alpha-rule on (101) yields:
% 37.31/10.25 | (102) multiplication(all_0_10_10, all_413_0_63) = all_121_0_29
% 37.31/10.25 | (103) addition(all_0_11_11, all_0_12_12) = all_413_0_63
% 37.31/10.25 |
% 37.31/10.25 | Instantiating (94) with all_417_0_65 yields:
% 37.31/10.25 | (104) addition(all_17_0_17, all_417_0_65) = all_113_0_24 & addition(all_17_0_17, all_9_0_13) = all_417_0_65
% 37.31/10.25 |
% 37.31/10.25 | Applying alpha-rule on (104) yields:
% 37.31/10.25 | (105) addition(all_17_0_17, all_417_0_65) = all_113_0_24
% 37.31/10.25 | (106) addition(all_17_0_17, all_9_0_13) = all_417_0_65
% 37.31/10.25 |
% 37.31/10.25 | Instantiating formula (37) with all_0_3_3, all_0_7_7, all_113_0_24, all_13_0_15 and discharging atoms multiplication(all_0_3_3, all_0_7_7) = all_13_0_15, yields:
% 37.31/10.25 | (107) all_113_0_24 = all_13_0_15 | ~ (multiplication(all_0_3_3, all_0_7_7) = all_113_0_24)
% 37.31/10.25 |
% 37.31/10.25 | Instantiating formula (6) with all_17_0_17, all_9_0_13, all_417_0_65, all_113_0_24 and discharging atoms addition(all_17_0_17, all_9_0_13) = all_417_0_65, addition(all_17_0_17, all_9_0_13) = all_113_0_24, yields:
% 37.31/10.25 | (108) all_417_0_65 = all_113_0_24
% 37.31/10.25 |
% 37.31/10.25 | Instantiating formula (6) with all_17_0_17, all_9_0_13, all_105_0_20, all_417_0_65 and discharging atoms addition(all_17_0_17, all_9_0_13) = all_417_0_65, addition(all_17_0_17, all_9_0_13) = all_105_0_20, yields:
% 37.31/10.25 | (109) all_417_0_65 = all_105_0_20
% 37.31/10.25 |
% 37.31/10.25 | Instantiating formula (6) with all_0_11_11, all_0_12_12, all_413_0_63, all_0_3_3 and discharging atoms addition(all_0_11_11, all_0_12_12) = all_413_0_63, addition(all_0_11_11, all_0_12_12) = all_0_3_3, yields:
% 37.31/10.25 | (110) all_413_0_63 = all_0_3_3
% 37.31/10.25 |
% 37.31/10.25 | Instantiating formula (6) with all_0_11_11, all_0_12_12, all_375_0_41, all_413_0_63 and discharging atoms addition(all_0_11_11, all_0_12_12) = all_413_0_63, addition(all_0_11_11, all_0_12_12) = all_375_0_41, yields:
% 37.31/10.25 | (111) all_413_0_63 = all_375_0_41
% 37.31/10.25 |
% 37.31/10.25 | Combining equations (109,108) yields a new equation:
% 37.31/10.25 | (112) all_113_0_24 = all_105_0_20
% 37.31/10.25 |
% 37.31/10.25 | Combining equations (111,110) yields a new equation:
% 37.31/10.25 | (113) all_375_0_41 = all_0_3_3
% 37.31/10.25 |
% 37.31/10.25 | Simplifying 113 yields:
% 37.31/10.25 | (114) all_375_0_41 = all_0_3_3
% 37.31/10.25 |
% 37.31/10.25 | From (114) and (99) follows:
% 37.31/10.25 | (115) multiplication(all_0_3_3, all_0_7_7) = all_105_0_20
% 37.31/10.25 |
% 37.31/10.25 +-Applying beta-rule and splitting (107), into two cases.
% 37.31/10.25 |-Branch one:
% 37.31/10.25 | (116) ~ (multiplication(all_0_3_3, all_0_7_7) = all_113_0_24)
% 37.31/10.25 |
% 37.31/10.25 | From (112) and (116) follows:
% 37.31/10.25 | (117) ~ (multiplication(all_0_3_3, all_0_7_7) = all_105_0_20)
% 37.31/10.25 |
% 37.31/10.25 | Using (115) and (117) yields:
% 37.31/10.25 | (118) $false
% 37.31/10.25 |
% 37.31/10.25 |-The branch is then unsatisfiable
% 37.31/10.25 |-Branch two:
% 37.31/10.25 | (119) multiplication(all_0_3_3, all_0_7_7) = all_113_0_24
% 37.31/10.25 | (120) all_113_0_24 = all_13_0_15
% 37.31/10.25 |
% 37.31/10.25 +-Applying beta-rule and splitting (91), into two cases.
% 37.31/10.25 |-Branch one:
% 37.31/10.25 | (121) ~ (multiplication(all_0_10_10, all_113_0_24) = all_0_1_1)
% 37.31/10.25 |
% 37.31/10.25 | From (120) and (121) follows:
% 37.31/10.25 | (122) ~ (multiplication(all_0_10_10, all_13_0_15) = all_0_1_1)
% 37.31/10.25 |
% 37.31/10.25 | Using (55) and (122) yields:
% 37.31/10.25 | (118) $false
% 37.31/10.25 |
% 37.31/10.25 |-The branch is then unsatisfiable
% 37.31/10.25 |-Branch two:
% 37.31/10.25 | (124) multiplication(all_0_10_10, all_113_0_24) = all_0_1_1
% 37.31/10.25 | (125) all_0_1_1 = zero
% 37.31/10.25 |
% 37.31/10.25 | Equations (125) can reduce 69 to:
% 37.31/10.25 | (60) $false
% 37.31/10.25 |
% 37.31/10.25 |-The branch is then unsatisfiable
% 37.31/10.25 % SZS output end Proof for theBenchmark
% 37.31/10.25
% 37.31/10.25 9591ms
%------------------------------------------------------------------------------