TSTP Solution File: ALG042+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG042+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 : Thu Jul 14 15:33:52 EDT 2022
% Result : Theorem 3.78s 1.50s
% Output : Proof 7.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG042+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n024.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 : Wed Jun 8 14:42:19 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.19/0.57 ____ _
% 0.19/0.57 ___ / __ \_____(_)___ ________ __________
% 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.57
% 0.19/0.57 A Theorem Prover for First-Order Logic
% 0.19/0.57 (ePrincess v.1.0)
% 0.19/0.57
% 0.19/0.57 (c) Philipp Rümmer, 2009-2015
% 0.19/0.57 (c) Peter Backeman, 2014-2015
% 0.19/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.57 Bug reports to peter@backeman.se
% 0.19/0.57
% 0.19/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.57
% 0.19/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.65/0.96 Prover 0: Preprocessing ...
% 2.50/1.20 Prover 0: Constructing countermodel ...
% 3.78/1.50 Prover 0: proved (875ms)
% 3.78/1.50
% 3.78/1.50 No countermodel exists, formula is valid
% 3.78/1.50 % SZS status Theorem for theBenchmark
% 3.78/1.50
% 3.78/1.50 Generating proof ... found it (size 134)
% 6.72/2.12
% 6.72/2.12 % SZS output start Proof for theBenchmark
% 6.72/2.12 Assumed formulas after preprocessing and simplification:
% 6.72/2.12 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(v3, v3) = v0 & op2(v3, v2) = v1 & op2(v3, v1) = v2 & op2(v3, v0) = v3 & op2(v2, v3) = v1 & op2(v2, v2) = v0 & op2(v2, v1) = v3 & op2(v2, v0) = v2 & op2(v1, v3) = v2 & op2(v1, v2) = v3 & op2(v1, v1) = v0 & op2(v1, v0) = v1 & op2(v0, v3) = v3 & op2(v0, v2) = v2 & op2(v0, v1) = v1 & op2(v0, v0) = v0 & op2(e23, e23) = e20 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e23) = e21 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e20 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e23) = e22 & op2(e21, e22) = e20 & op2(e21, e20) = e21 & op2(e21, e21) = e23 & op1(v7, v7) = v4 & op1(v7, v6) = v5 & op1(v7, v5) = v6 & op1(v7, v4) = v7 & op1(v6, v7) = v5 & op1(v6, v6) = v7 & op1(v6, v5) = v4 & op1(v6, v4) = v6 & op1(v5, v7) = v6 & op1(v5, v6) = v4 & op1(v5, v5) = v7 & op1(v5, v4) = v5 & op1(v4, v7) = v7 & op1(v4, v6) = v6 & op1(v4, v5) = v5 & op1(v4, v4) = v4 & op1(e13, e13) = e10 & op1(e13, e12) = e11 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e13) = e11 & op1(e12, e12) = e10 & op1(e12, e10) = e12 & op1(e12, e11) = e13 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e13) = e12 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & h(v7) = e23 & h(v6) = e22 & h(v5) = e21 & h(v4) = e20 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e23) = v7 & j(e22) = v6 & j(e20) = v4 & j(e21) = v5 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (op2(v11, v10) = v9) | ~ (op2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (op1(v11, v10) = v9) | ~ (op1(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (h(v10) = v9) | ~ (h(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (j(v10) = v9) | ~ (j(v10) = v8)) & (v7 = e13 | v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e13 | v6 = e12 | v6 = e10 | v6 = e11) & (v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 = e13 | v4 = e12 | v4 = e10 | v4 = e11) & (v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21))
% 6.82/2.16 | 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 yields:
% 6.82/2.16 | (1) ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(all_0_4_4, all_0_4_4) = all_0_7_7 & op2(all_0_4_4, all_0_5_5) = all_0_6_6 & op2(all_0_4_4, all_0_6_6) = all_0_5_5 & op2(all_0_4_4, all_0_7_7) = all_0_4_4 & op2(all_0_5_5, all_0_4_4) = all_0_6_6 & op2(all_0_5_5, all_0_5_5) = all_0_7_7 & op2(all_0_5_5, all_0_6_6) = all_0_4_4 & op2(all_0_5_5, all_0_7_7) = all_0_5_5 & op2(all_0_6_6, all_0_4_4) = all_0_5_5 & op2(all_0_6_6, all_0_5_5) = all_0_4_4 & op2(all_0_6_6, all_0_6_6) = all_0_7_7 & op2(all_0_6_6, all_0_7_7) = all_0_6_6 & op2(all_0_7_7, all_0_4_4) = all_0_4_4 & op2(all_0_7_7, all_0_5_5) = all_0_5_5 & op2(all_0_7_7, all_0_6_6) = all_0_6_6 & op2(all_0_7_7, all_0_7_7) = all_0_7_7 & op2(e23, e23) = e20 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e23) = e21 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e20 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e23) = e22 & op2(e21, e22) = e20 & op2(e21, e20) = e21 & op2(e21, e21) = e23 & op1(all_0_0_0, all_0_0_0) = all_0_3_3 & op1(all_0_0_0, all_0_1_1) = all_0_2_2 & op1(all_0_0_0, all_0_2_2) = all_0_1_1 & op1(all_0_0_0, all_0_3_3) = all_0_0_0 & op1(all_0_1_1, all_0_0_0) = all_0_2_2 & op1(all_0_1_1, all_0_1_1) = all_0_0_0 & op1(all_0_1_1, all_0_2_2) = all_0_3_3 & op1(all_0_1_1, all_0_3_3) = all_0_1_1 & op1(all_0_2_2, all_0_0_0) = all_0_1_1 & op1(all_0_2_2, all_0_1_1) = all_0_3_3 & op1(all_0_2_2, all_0_2_2) = all_0_0_0 & op1(all_0_2_2, all_0_3_3) = all_0_2_2 & op1(all_0_3_3, all_0_0_0) = all_0_0_0 & op1(all_0_3_3, all_0_1_1) = all_0_1_1 & op1(all_0_3_3, all_0_2_2) = all_0_2_2 & op1(all_0_3_3, all_0_3_3) = all_0_3_3 & op1(e13, e13) = e10 & op1(e13, e12) = e11 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e13) = e11 & op1(e12, e12) = e10 & op1(e12, e10) = e12 & op1(e12, e11) = e13 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e13) = e12 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & h(all_0_0_0) = e23 & h(all_0_1_1) = e22 & h(all_0_2_2) = e21 & h(all_0_3_3) = e20 & h(e13) = all_0_4_4 & h(e12) = all_0_5_5 & h(e10) = all_0_7_7 & h(e11) = all_0_6_6 & j(all_0_4_4) = e13 & j(all_0_5_5) = e12 & j(all_0_6_6) = e11 & j(all_0_7_7) = e10 & j(e23) = all_0_0_0 & j(e22) = all_0_1_1 & j(e20) = all_0_3_3 & j(e21) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) & (all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11) & (all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11) & (all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11) & (all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11) & (all_0_4_4 = e23 | all_0_4_4 = e22 | all_0_4_4 = e20 | all_0_4_4 = e21) & (all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21) & (all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21) & (all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21)
% 6.82/2.17 |
% 6.82/2.17 | Applying alpha-rule on (1) yields:
% 6.82/2.17 | (2) h(all_0_0_0) = e23
% 6.82/2.17 | (3) op1(all_0_3_3, all_0_1_1) = all_0_1_1
% 6.82/2.17 | (4) op1(all_0_2_2, all_0_3_3) = all_0_2_2
% 6.82/2.17 | (5) ~ (e23 = e20)
% 6.82/2.17 | (6) op1(e11, e13) = e12
% 6.82/2.17 | (7) h(all_0_3_3) = e20
% 6.82/2.17 | (8) ~ (e23 = e13)
% 6.82/2.17 | (9) op1(e10, e13) = e13
% 6.82/2.17 | (10) ~ (e21 = e11)
% 6.82/2.17 | (11) op1(all_0_0_0, all_0_2_2) = all_0_1_1
% 6.82/2.17 | (12) op1(e13, e12) = e11
% 6.82/2.17 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 6.82/2.17 | (14) op1(e12, e13) = e11
% 6.82/2.17 | (15) op1(all_0_0_0, all_0_1_1) = all_0_2_2
% 6.82/2.17 | (16) all_0_4_4 = e23 | all_0_4_4 = e22 | all_0_4_4 = e20 | all_0_4_4 = e21
% 6.82/2.17 | (17) op1(all_0_3_3, all_0_2_2) = all_0_2_2
% 6.82/2.17 | (18) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 6.82/2.17 | (19) op1(all_0_1_1, all_0_2_2) = all_0_3_3
% 6.82/2.17 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 6.82/2.17 | (21) op1(all_0_2_2, all_0_2_2) = all_0_0_0
% 6.82/2.17 | (22) op1(all_0_0_0, all_0_3_3) = all_0_0_0
% 6.82/2.17 | (23) op1(e13, e11) = e12
% 6.82/2.17 | (24) ~ (e20 = e13)
% 6.82/2.17 | (25) ~ (e20 = e10)
% 6.82/2.17 | (26) j(all_0_7_7) = e10
% 6.82/2.17 | (27) op2(all_0_4_4, all_0_6_6) = all_0_5_5
% 6.82/2.17 | (28) op2(e22, e20) = e22
% 6.82/2.17 | (29) op1(e13, e13) = e10
% 6.82/2.17 | (30) ~ (e13 = e11)
% 6.82/2.17 | (31) h(e13) = all_0_4_4
% 6.82/2.17 | (32) ~ (e22 = e20)
% 6.82/2.17 | (33) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 6.82/2.17 | (34) ~ (e23 = e10)
% 6.82/2.17 | (35) op1(e12, e10) = e12
% 6.82/2.17 | (36) j(e20) = all_0_3_3
% 6.82/2.17 | (37) op2(all_0_6_6, all_0_7_7) = all_0_6_6
% 6.82/2.17 | (38) op2(all_0_7_7, all_0_7_7) = all_0_7_7
% 6.82/2.17 | (39) op2(all_0_7_7, all_0_5_5) = all_0_5_5
% 6.82/2.17 | (40) h(all_0_2_2) = e21
% 6.82/2.18 | (41) op2(all_0_7_7, all_0_6_6) = all_0_6_6
% 6.82/2.18 | (42) ~ (e21 = e10)
% 6.82/2.18 | (43) all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11
% 6.82/2.18 | (44) op1(e10, e10) = e10
% 6.82/2.18 | (45) op2(all_0_4_4, all_0_4_4) = all_0_7_7
% 6.82/2.18 | (46) ~ (e22 = e21)
% 6.82/2.18 | (47) op2(all_0_4_4, all_0_7_7) = all_0_4_4
% 6.82/2.18 | (48) op1(e11, e10) = e11
% 6.82/2.18 | (49) op1(e11, e11) = e10
% 6.82/2.18 | (50) op1(all_0_2_2, all_0_0_0) = all_0_1_1
% 6.82/2.18 | (51) j(e22) = all_0_1_1
% 6.82/2.18 | (52) op2(e20, e22) = e22
% 6.82/2.18 | (53) j(e21) = all_0_2_2
% 6.82/2.18 | (54) op2(all_0_5_5, all_0_4_4) = all_0_6_6
% 6.82/2.18 | (55) h(all_0_1_1) = e22
% 6.82/2.18 | (56) op2(e20, e23) = e23
% 6.82/2.18 | (57) op2(e22, e22) = e23
% 6.82/2.18 | (58) h(e12) = all_0_5_5
% 6.82/2.18 | (59) j(all_0_4_4) = e13
% 6.82/2.18 | (60) ~ (e20 = e12)
% 6.82/2.18 | (61) op2(all_0_6_6, all_0_5_5) = all_0_4_4
% 6.82/2.18 | (62) ~ (e22 = e12)
% 6.82/2.18 | (63) ~ (e23 = e21)
% 6.82/2.18 | (64) op1(e12, e12) = e10
% 6.82/2.18 | (65) j(e23) = all_0_0_0
% 6.82/2.18 | (66) ~ (e13 = e12)
% 6.82/2.18 | (67) op1(all_0_3_3, all_0_3_3) = all_0_3_3
% 6.82/2.18 | (68) j(all_0_5_5) = e12
% 6.82/2.18 | (69) ~ (e22 = e10)
% 6.82/2.18 | (70) ~ (e10 = e11)
% 6.82/2.18 | (71) ~ (e13 = e10)
% 6.82/2.18 | (72) op1(all_0_3_3, all_0_0_0) = all_0_0_0
% 6.82/2.18 | (73) op2(e21, e22) = e20
% 6.82/2.18 | (74) op2(e21, e21) = e23
% 6.82/2.18 | (75) all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 6.82/2.18 | (76) op2(e20, e20) = e20
% 6.82/2.18 | (77) j(all_0_6_6) = e11
% 6.82/2.18 | (78) ~ (e20 = e11)
% 6.82/2.18 | (79) op2(e23, e23) = e20
% 6.82/2.18 | (80) h(e11) = all_0_6_6
% 6.82/2.18 | (81) ~ (e23 = e22)
% 6.82/2.18 | (82) op2(all_0_5_5, all_0_6_6) = all_0_4_4
% 6.82/2.18 | (83) op1(e12, e11) = e13
% 6.82/2.18 | (84) op1(all_0_0_0, all_0_0_0) = all_0_3_3
% 6.82/2.18 | (85) op2(all_0_5_5, all_0_7_7) = all_0_5_5
% 6.82/2.18 | (86) ~ (e23 = e11)
% 6.82/2.18 | (87) op1(e13, e10) = e13
% 6.82/2.18 | (88) ~ (e22 = e11)
% 6.82/2.18 | (89) op1(e10, e12) = e12
% 6.82/2.18 | (90) all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11
% 6.82/2.18 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 6.82/2.18 | (92) ~ (e22 = e13)
% 6.82/2.18 | (93) op2(e20, e21) = e21
% 6.82/2.18 | (94) all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 6.82/2.18 | (95) op2(all_0_4_4, all_0_5_5) = all_0_6_6
% 6.82/2.18 | (96) op2(e22, e21) = e20
% 6.82/2.18 | (97) ~ (e23 = e12)
% 6.82/2.18 | (98) h(e10) = all_0_7_7
% 6.82/2.18 | (99) ~ (e20 = e21)
% 6.82/2.18 | (100) op2(e21, e23) = e22
% 6.82/2.18 | (101) op2(all_0_5_5, all_0_5_5) = all_0_7_7
% 6.82/2.18 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 6.82/2.18 | (103) op1(all_0_1_1, all_0_0_0) = all_0_2_2
% 6.82/2.19 | (104) op2(e23, e20) = e23
% 6.82/2.19 | (105) op2(all_0_7_7, all_0_4_4) = all_0_4_4
% 6.82/2.19 | (106) op2(e22, e23) = e21
% 6.82/2.19 | (107) op2(e23, e21) = e22
% 6.82/2.19 | (108) ~ (e21 = e13)
% 6.82/2.19 | (109) ~ (e21 = e12)
% 6.82/2.19 | (110) op1(all_0_1_1, all_0_1_1) = all_0_0_0
% 6.82/2.19 | (111) op2(all_0_6_6, all_0_4_4) = all_0_5_5
% 6.82/2.19 | (112) op1(all_0_1_1, all_0_3_3) = all_0_1_1
% 6.82/2.19 | (113) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 6.82/2.19 | (114) op1(all_0_2_2, all_0_1_1) = all_0_3_3
% 6.82/2.19 | (115) op2(e21, e20) = e21
% 6.82/2.19 | (116) ~ (e12 = e10)
% 6.82/2.19 | (117) op1(e11, e12) = e13
% 6.82/2.19 | (118) op2(e23, e22) = e21
% 6.82/2.19 | (119) op1(e10, e11) = e11
% 6.82/2.19 | (120) op2(all_0_6_6, all_0_6_6) = all_0_7_7
% 6.82/2.19 | (121) ~ (e12 = e11)
% 6.82/2.19 |
% 6.82/2.19 +-Applying beta-rule and splitting (33), into two cases.
% 6.82/2.19 |-Branch one:
% 6.82/2.19 | (122) all_0_0_0 = e13
% 6.82/2.19 |
% 6.82/2.19 | From (122)(122) and (84) follows:
% 6.82/2.19 | (123) op1(e13, e13) = all_0_3_3
% 6.82/2.19 |
% 6.82/2.19 | From (122) and (2) follows:
% 6.82/2.19 | (124) h(e13) = e23
% 6.82/2.19 |
% 6.82/2.19 | Instantiating formula (13) with e13, e13, all_0_3_3, e10 and discharging atoms op1(e13, e13) = all_0_3_3, op1(e13, e13) = e10, yields:
% 6.82/2.19 | (125) all_0_3_3 = e10
% 6.82/2.19 |
% 6.82/2.19 | Instantiating formula (20) with e13, e23, all_0_4_4 and discharging atoms h(e13) = all_0_4_4, h(e13) = e23, yields:
% 6.82/2.19 | (126) all_0_4_4 = e23
% 6.82/2.19 |
% 6.82/2.19 | From (125) and (7) follows:
% 6.82/2.19 | (127) h(e10) = e20
% 6.82/2.19 |
% 6.82/2.19 | From (126) and (59) follows:
% 6.82/2.19 | (128) j(e23) = e13
% 6.82/2.19 |
% 6.82/2.19 | Instantiating formula (20) with e10, e20, all_0_7_7 and discharging atoms h(e10) = all_0_7_7, h(e10) = e20, yields:
% 6.82/2.19 | (129) all_0_7_7 = e20
% 6.82/2.19 |
% 6.82/2.19 | From (129) and (120) follows:
% 6.82/2.19 | (130) op2(all_0_6_6, all_0_6_6) = e20
% 6.82/2.19 |
% 6.82/2.19 | From (129) and (26) follows:
% 6.82/2.19 | (131) j(e20) = e10
% 6.82/2.19 |
% 6.82/2.19 +-Applying beta-rule and splitting (113), into two cases.
% 6.82/2.19 |-Branch one:
% 6.82/2.19 | (132) all_0_6_6 = e23
% 6.82/2.19 |
% 6.82/2.19 | From (132) and (77) follows:
% 6.82/2.19 | (133) j(e23) = e11
% 6.82/2.19 |
% 6.82/2.19 | Instantiating formula (91) with e23, e11, e13 and discharging atoms j(e23) = e13, j(e23) = e11, yields:
% 6.82/2.19 | (134) e13 = e11
% 6.82/2.19 |
% 6.82/2.20 | Equations (134) can reduce 30 to:
% 6.82/2.20 | (135) $false
% 6.82/2.20 |
% 6.82/2.20 |-The branch is then unsatisfiable
% 6.82/2.20 |-Branch two:
% 6.82/2.20 | (136) ~ (all_0_6_6 = e23)
% 6.82/2.20 | (137) all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 6.82/2.20 |
% 6.82/2.20 +-Applying beta-rule and splitting (137), into two cases.
% 6.82/2.20 |-Branch one:
% 6.82/2.20 | (138) all_0_6_6 = e22
% 6.82/2.20 |
% 6.82/2.20 | From (138)(138) and (130) follows:
% 6.82/2.20 | (139) op2(e22, e22) = e20
% 6.82/2.20 |
% 6.82/2.20 | Instantiating formula (102) with e22, e22, e20, e23 and discharging atoms op2(e22, e22) = e23, op2(e22, e22) = e20, yields:
% 6.82/2.20 | (140) e23 = e20
% 6.82/2.20 |
% 6.82/2.20 | Equations (140) can reduce 5 to:
% 6.82/2.20 | (135) $false
% 6.82/2.20 |
% 6.82/2.20 |-The branch is then unsatisfiable
% 6.82/2.20 |-Branch two:
% 6.82/2.20 | (142) ~ (all_0_6_6 = e22)
% 6.82/2.20 | (143) all_0_6_6 = e20 | all_0_6_6 = e21
% 6.82/2.20 |
% 6.82/2.20 +-Applying beta-rule and splitting (143), into two cases.
% 6.82/2.20 |-Branch one:
% 6.82/2.20 | (144) all_0_6_6 = e20
% 6.82/2.20 |
% 6.82/2.20 | From (144) and (77) follows:
% 6.82/2.20 | (145) j(e20) = e11
% 6.82/2.20 |
% 6.82/2.20 | Instantiating formula (91) with e20, e11, e10 and discharging atoms j(e20) = e10, j(e20) = e11, yields:
% 6.82/2.20 | (146) e10 = e11
% 6.82/2.20 |
% 6.82/2.20 | Equations (146) can reduce 70 to:
% 6.82/2.20 | (135) $false
% 6.82/2.20 |
% 6.82/2.20 |-The branch is then unsatisfiable
% 6.82/2.20 |-Branch two:
% 6.82/2.20 | (148) ~ (all_0_6_6 = e20)
% 6.82/2.20 | (149) all_0_6_6 = e21
% 6.82/2.20 |
% 6.82/2.20 | From (149)(149) and (130) follows:
% 6.82/2.20 | (150) op2(e21, e21) = e20
% 6.82/2.20 |
% 6.82/2.20 | Instantiating formula (102) with e21, e21, e20, e23 and discharging atoms op2(e21, e21) = e23, op2(e21, e21) = e20, yields:
% 6.82/2.20 | (140) e23 = e20
% 6.82/2.20 |
% 6.82/2.20 | Equations (140) can reduce 5 to:
% 6.82/2.20 | (135) $false
% 6.82/2.20 |
% 6.82/2.20 |-The branch is then unsatisfiable
% 6.82/2.20 |-Branch two:
% 6.82/2.20 | (153) ~ (all_0_0_0 = e13)
% 6.82/2.20 | (154) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 6.82/2.20 |
% 6.82/2.20 +-Applying beta-rule and splitting (18), into two cases.
% 6.82/2.20 |-Branch one:
% 6.82/2.20 | (155) all_0_7_7 = e23
% 6.82/2.20 |
% 6.82/2.20 | From (155)(155)(155) and (38) follows:
% 6.82/2.20 | (156) op2(e23, e23) = e23
% 6.82/2.20 |
% 6.82/2.20 | Instantiating formula (102) with e23, e23, e23, e20 and discharging atoms op2(e23, e23) = e23, op2(e23, e23) = e20, yields:
% 6.82/2.20 | (140) e23 = e20
% 6.82/2.20 |
% 6.82/2.20 | Equations (140) can reduce 5 to:
% 6.82/2.20 | (135) $false
% 6.82/2.20 |
% 6.82/2.20 |-The branch is then unsatisfiable
% 6.82/2.20 |-Branch two:
% 6.82/2.20 | (159) ~ (all_0_7_7 = e23)
% 6.82/2.20 | (160) all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 6.82/2.20 |
% 6.82/2.20 +-Applying beta-rule and splitting (75), into two cases.
% 6.82/2.20 |-Branch one:
% 6.82/2.20 | (161) all_0_1_1 = e13
% 6.82/2.20 |
% 6.82/2.20 | From (161)(161) and (110) follows:
% 6.82/2.20 | (162) op1(e13, e13) = all_0_0_0
% 6.82/2.20 |
% 6.82/2.20 | Instantiating formula (13) with e13, e13, all_0_0_0, e10 and discharging atoms op1(e13, e13) = all_0_0_0, op1(e13, e13) = e10, yields:
% 6.82/2.20 | (163) all_0_0_0 = e10
% 6.82/2.20 |
% 6.82/2.20 | From (163) and (2) follows:
% 6.82/2.20 | (164) h(e10) = e23
% 6.82/2.20 |
% 6.82/2.20 | Instantiating formula (20) with e10, e23, all_0_7_7 and discharging atoms h(e10) = all_0_7_7, h(e10) = e23, yields:
% 6.82/2.20 | (155) all_0_7_7 = e23
% 6.82/2.20 |
% 6.82/2.20 | Equations (155) can reduce 159 to:
% 6.82/2.20 | (135) $false
% 6.82/2.20 |
% 6.82/2.20 |-The branch is then unsatisfiable
% 6.82/2.20 |-Branch two:
% 6.82/2.20 | (167) ~ (all_0_1_1 = e13)
% 6.82/2.21 | (168) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 6.82/2.21 |
% 6.82/2.21 +-Applying beta-rule and splitting (113), into two cases.
% 6.82/2.21 |-Branch one:
% 6.82/2.21 | (132) all_0_6_6 = e23
% 6.82/2.21 |
% 6.82/2.21 | From (132)(132) and (120) follows:
% 6.82/2.21 | (170) op2(e23, e23) = all_0_7_7
% 6.82/2.21 |
% 6.82/2.21 | From (132) and (77) follows:
% 6.82/2.21 | (133) j(e23) = e11
% 6.82/2.21 |
% 6.82/2.21 | Instantiating formula (102) with e23, e23, all_0_7_7, e20 and discharging atoms op2(e23, e23) = all_0_7_7, op2(e23, e23) = e20, yields:
% 6.82/2.21 | (129) all_0_7_7 = e20
% 6.82/2.21 |
% 6.82/2.21 | Instantiating formula (91) with e23, e11, all_0_0_0 and discharging atoms j(e23) = all_0_0_0, j(e23) = e11, yields:
% 6.82/2.21 | (173) all_0_0_0 = e11
% 6.82/2.21 |
% 6.82/2.21 | From (173)(173) and (84) follows:
% 6.82/2.21 | (174) op1(e11, e11) = all_0_3_3
% 6.82/2.21 |
% 6.82/2.21 | From (173) and (15) follows:
% 6.82/2.21 | (175) op1(e11, all_0_1_1) = all_0_2_2
% 6.82/2.21 |
% 6.82/2.21 | From (173)(173) and (22) follows:
% 6.82/2.21 | (176) op1(e11, all_0_3_3) = e11
% 6.82/2.21 |
% 6.82/2.21 | From (173) and (110) follows:
% 6.82/2.21 | (177) op1(all_0_1_1, all_0_1_1) = e11
% 6.82/2.21 |
% 6.82/2.21 | From (129) and (26) follows:
% 6.82/2.21 | (131) j(e20) = e10
% 6.82/2.21 |
% 6.82/2.21 | Instantiating formula (91) with e20, e10, all_0_3_3 and discharging atoms j(e20) = all_0_3_3, j(e20) = e10, yields:
% 6.82/2.21 | (125) all_0_3_3 = e10
% 6.82/2.21 |
% 6.82/2.21 | From (125) and (19) follows:
% 6.82/2.21 | (180) op1(all_0_1_1, all_0_2_2) = e10
% 6.82/2.21 |
% 6.82/2.21 | From (125) and (17) follows:
% 6.82/2.21 | (181) op1(e10, all_0_2_2) = all_0_2_2
% 6.82/2.21 |
% 6.82/2.21 | From (125) and (176) follows:
% 6.82/2.21 | (48) op1(e11, e10) = e11
% 6.82/2.21 |
% 6.82/2.21 | From (125) and (174) follows:
% 6.82/2.21 | (49) op1(e11, e11) = e10
% 6.82/2.21 |
% 6.82/2.21 +-Applying beta-rule and splitting (168), into two cases.
% 6.82/2.21 |-Branch one:
% 6.82/2.21 | (184) all_0_1_1 = e12
% 6.82/2.21 |
% 6.82/2.21 | From (184)(184) and (177) follows:
% 6.82/2.21 | (185) op1(e12, e12) = e11
% 6.82/2.21 |
% 6.82/2.21 | Instantiating formula (13) with e12, e12, e11, e10 and discharging atoms op1(e12, e12) = e10, op1(e12, e12) = e11, yields:
% 6.82/2.21 | (146) e10 = e11
% 6.82/2.21 |
% 6.82/2.21 | Equations (146) can reduce 70 to:
% 6.82/2.21 | (135) $false
% 6.82/2.21 |
% 6.82/2.21 |-The branch is then unsatisfiable
% 6.82/2.21 |-Branch two:
% 6.82/2.21 | (188) ~ (all_0_1_1 = e12)
% 6.82/2.21 | (189) all_0_1_1 = e10 | all_0_1_1 = e11
% 6.82/2.21 |
% 6.82/2.21 +-Applying beta-rule and splitting (189), into two cases.
% 6.82/2.21 |-Branch one:
% 6.82/2.21 | (190) all_0_1_1 = e10
% 6.82/2.21 |
% 6.82/2.21 | From (190) and (180) follows:
% 6.82/2.21 | (191) op1(e10, all_0_2_2) = e10
% 6.82/2.21 |
% 6.82/2.21 | From (190) and (175) follows:
% 6.82/2.21 | (192) op1(e11, e10) = all_0_2_2
% 6.82/2.21 |
% 6.82/2.21 | Instantiating formula (13) with e10, all_0_2_2, e10, all_0_2_2 and discharging atoms op1(e10, all_0_2_2) = all_0_2_2, op1(e10, all_0_2_2) = e10, yields:
% 6.82/2.21 | (193) all_0_2_2 = e10
% 6.82/2.21 |
% 6.82/2.21 | Instantiating formula (13) with e11, e10, all_0_2_2, e11 and discharging atoms op1(e11, e10) = all_0_2_2, op1(e11, e10) = e11, yields:
% 6.82/2.22 | (194) all_0_2_2 = e11
% 6.82/2.22 |
% 6.82/2.22 | Combining equations (194,193) yields a new equation:
% 6.82/2.22 | (146) e10 = e11
% 6.82/2.22 |
% 6.82/2.22 | Equations (146) can reduce 70 to:
% 6.82/2.22 | (135) $false
% 6.82/2.22 |
% 6.82/2.22 |-The branch is then unsatisfiable
% 6.82/2.22 |-Branch two:
% 6.82/2.22 | (197) ~ (all_0_1_1 = e10)
% 6.82/2.22 | (198) all_0_1_1 = e11
% 6.82/2.22 |
% 6.82/2.22 | Equations (198) can reduce 197 to:
% 6.82/2.22 | (199) ~ (e10 = e11)
% 6.82/2.22 |
% 6.82/2.22 | Simplifying 199 yields:
% 6.82/2.22 | (70) ~ (e10 = e11)
% 6.82/2.22 |
% 6.82/2.22 | From (198)(198) and (177) follows:
% 6.82/2.22 | (201) op1(e11, e11) = e11
% 6.82/2.22 |
% 6.82/2.22 | From (198) and (175) follows:
% 6.82/2.22 | (202) op1(e11, e11) = all_0_2_2
% 6.82/2.22 |
% 6.82/2.22 | Instantiating formula (13) with e11, e11, all_0_2_2, e10 and discharging atoms op1(e11, e11) = all_0_2_2, op1(e11, e11) = e10, yields:
% 6.82/2.22 | (193) all_0_2_2 = e10
% 6.82/2.22 |
% 6.82/2.22 | Instantiating formula (13) with e11, e11, e11, all_0_2_2 and discharging atoms op1(e11, e11) = all_0_2_2, op1(e11, e11) = e11, yields:
% 6.82/2.22 | (194) all_0_2_2 = e11
% 7.19/2.22 |
% 7.19/2.22 | Combining equations (194,193) yields a new equation:
% 7.19/2.22 | (146) e10 = e11
% 7.19/2.22 |
% 7.19/2.22 | Equations (146) can reduce 70 to:
% 7.19/2.22 | (135) $false
% 7.19/2.22 |
% 7.19/2.22 |-The branch is then unsatisfiable
% 7.19/2.22 |-Branch two:
% 7.19/2.22 | (136) ~ (all_0_6_6 = e23)
% 7.19/2.22 | (137) all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 7.19/2.22 |
% 7.19/2.22 +-Applying beta-rule and splitting (94), into two cases.
% 7.19/2.22 |-Branch one:
% 7.19/2.22 | (209) all_0_5_5 = e23
% 7.19/2.22 |
% 7.19/2.22 | From (209)(209) and (101) follows:
% 7.19/2.22 | (170) op2(e23, e23) = all_0_7_7
% 7.19/2.22 |
% 7.19/2.22 | From (209) and (68) follows:
% 7.19/2.22 | (211) j(e23) = e12
% 7.19/2.22 |
% 7.19/2.22 | Instantiating formula (102) with e23, e23, all_0_7_7, e20 and discharging atoms op2(e23, e23) = all_0_7_7, op2(e23, e23) = e20, yields:
% 7.19/2.22 | (129) all_0_7_7 = e20
% 7.19/2.22 |
% 7.19/2.22 | Instantiating formula (91) with e23, e12, all_0_0_0 and discharging atoms j(e23) = all_0_0_0, j(e23) = e12, yields:
% 7.19/2.22 | (213) all_0_0_0 = e12
% 7.19/2.22 |
% 7.19/2.22 | From (213)(213) and (84) follows:
% 7.19/2.22 | (214) op1(e12, e12) = all_0_3_3
% 7.19/2.22 |
% 7.19/2.22 | From (213) and (15) follows:
% 7.19/2.22 | (215) op1(e12, all_0_1_1) = all_0_2_2
% 7.19/2.22 |
% 7.19/2.22 | From (213) and (103) follows:
% 7.19/2.22 | (216) op1(all_0_1_1, e12) = all_0_2_2
% 7.19/2.22 |
% 7.19/2.22 | From (213) and (110) follows:
% 7.19/2.22 | (217) op1(all_0_1_1, all_0_1_1) = e12
% 7.19/2.22 |
% 7.19/2.22 | From (213)(213) and (72) follows:
% 7.19/2.22 | (218) op1(all_0_3_3, e12) = e12
% 7.19/2.22 |
% 7.19/2.22 | From (129) and (26) follows:
% 7.19/2.22 | (131) j(e20) = e10
% 7.19/2.22 |
% 7.19/2.22 | Instantiating formula (91) with e20, e10, all_0_3_3 and discharging atoms j(e20) = all_0_3_3, j(e20) = e10, yields:
% 7.19/2.23 | (125) all_0_3_3 = e10
% 7.19/2.23 |
% 7.19/2.23 | From (125) and (19) follows:
% 7.19/2.23 | (180) op1(all_0_1_1, all_0_2_2) = e10
% 7.19/2.23 |
% 7.19/2.23 | From (125) and (17) follows:
% 7.19/2.23 | (181) op1(e10, all_0_2_2) = all_0_2_2
% 7.19/2.23 |
% 7.19/2.23 | From (125) and (218) follows:
% 7.19/2.23 | (89) op1(e10, e12) = e12
% 7.19/2.23 |
% 7.19/2.23 | From (125) and (214) follows:
% 7.19/2.23 | (64) op1(e12, e12) = e10
% 7.19/2.23 |
% 7.19/2.23 +-Applying beta-rule and splitting (168), into two cases.
% 7.19/2.23 |-Branch one:
% 7.19/2.23 | (184) all_0_1_1 = e12
% 7.19/2.23 |
% 7.19/2.23 | From (184)(184) and (217) follows:
% 7.19/2.23 | (226) op1(e12, e12) = e12
% 7.19/2.23 |
% 7.19/2.23 | From (184) and (215) follows:
% 7.19/2.23 | (227) op1(e12, e12) = all_0_2_2
% 7.19/2.23 |
% 7.19/2.23 | Instantiating formula (13) with e12, e12, all_0_2_2, e10 and discharging atoms op1(e12, e12) = all_0_2_2, op1(e12, e12) = e10, yields:
% 7.19/2.23 | (193) all_0_2_2 = e10
% 7.19/2.23 |
% 7.19/2.23 | Instantiating formula (13) with e12, e12, e12, all_0_2_2 and discharging atoms op1(e12, e12) = all_0_2_2, op1(e12, e12) = e12, yields:
% 7.19/2.23 | (229) all_0_2_2 = e12
% 7.19/2.23 |
% 7.19/2.23 | Combining equations (229,193) yields a new equation:
% 7.19/2.23 | (230) e12 = e10
% 7.19/2.23 |
% 7.19/2.23 | Simplifying 230 yields:
% 7.19/2.23 | (231) e12 = e10
% 7.19/2.23 |
% 7.19/2.23 | Equations (231) can reduce 116 to:
% 7.19/2.23 | (135) $false
% 7.19/2.23 |
% 7.19/2.23 |-The branch is then unsatisfiable
% 7.19/2.23 |-Branch two:
% 7.19/2.23 | (188) ~ (all_0_1_1 = e12)
% 7.19/2.23 | (189) all_0_1_1 = e10 | all_0_1_1 = e11
% 7.19/2.23 |
% 7.19/2.23 +-Applying beta-rule and splitting (189), into two cases.
% 7.19/2.23 |-Branch one:
% 7.19/2.23 | (190) all_0_1_1 = e10
% 7.19/2.23 |
% 7.19/2.23 | Equations (190) can reduce 188 to:
% 7.19/2.23 | (236) ~ (e12 = e10)
% 7.19/2.23 |
% 7.19/2.23 | Simplifying 236 yields:
% 7.19/2.23 | (116) ~ (e12 = e10)
% 7.19/2.23 |
% 7.19/2.23 | From (190) and (180) follows:
% 7.19/2.23 | (191) op1(e10, all_0_2_2) = e10
% 7.19/2.23 |
% 7.19/2.23 | From (190) and (216) follows:
% 7.19/2.23 | (239) op1(e10, e12) = all_0_2_2
% 7.19/2.23 |
% 7.19/2.23 | Instantiating formula (13) with e10, all_0_2_2, e10, all_0_2_2 and discharging atoms op1(e10, all_0_2_2) = all_0_2_2, op1(e10, all_0_2_2) = e10, yields:
% 7.19/2.23 | (193) all_0_2_2 = e10
% 7.19/2.23 |
% 7.19/2.23 | Instantiating formula (13) with e10, e12, all_0_2_2, e12 and discharging atoms op1(e10, e12) = all_0_2_2, op1(e10, e12) = e12, yields:
% 7.19/2.23 | (229) all_0_2_2 = e12
% 7.19/2.23 |
% 7.19/2.23 | Combining equations (229,193) yields a new equation:
% 7.19/2.23 | (230) e12 = e10
% 7.19/2.23 |
% 7.19/2.23 | Simplifying 230 yields:
% 7.19/2.23 | (231) e12 = e10
% 7.19/2.23 |
% 7.19/2.23 | Equations (231) can reduce 116 to:
% 7.19/2.23 | (135) $false
% 7.19/2.23 |
% 7.19/2.23 |-The branch is then unsatisfiable
% 7.19/2.23 |-Branch two:
% 7.19/2.23 | (197) ~ (all_0_1_1 = e10)
% 7.19/2.23 | (198) all_0_1_1 = e11
% 7.19/2.23 |
% 7.19/2.23 | From (198)(198) and (217) follows:
% 7.19/2.23 | (247) op1(e11, e11) = e12
% 7.19/2.23 |
% 7.19/2.23 | Instantiating formula (13) with e11, e11, e12, e10 and discharging atoms op1(e11, e11) = e12, op1(e11, e11) = e10, yields:
% 7.19/2.23 | (231) e12 = e10
% 7.19/2.23 |
% 7.19/2.23 | Equations (231) can reduce 116 to:
% 7.19/2.23 | (135) $false
% 7.19/2.23 |
% 7.19/2.23 |-The branch is then unsatisfiable
% 7.19/2.23 |-Branch two:
% 7.19/2.23 | (250) ~ (all_0_5_5 = e23)
% 7.19/2.23 | (251) all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 7.19/2.23 |
% 7.19/2.23 +-Applying beta-rule and splitting (154), into two cases.
% 7.19/2.23 |-Branch one:
% 7.19/2.23 | (213) all_0_0_0 = e12
% 7.19/2.23 |
% 7.19/2.23 | From (213) and (2) follows:
% 7.19/2.23 | (253) h(e12) = e23
% 7.19/2.23 |
% 7.19/2.23 | Instantiating formula (20) with e12, e23, all_0_5_5 and discharging atoms h(e12) = all_0_5_5, h(e12) = e23, yields:
% 7.19/2.23 | (209) all_0_5_5 = e23
% 7.19/2.23 |
% 7.19/2.23 | Equations (209) can reduce 250 to:
% 7.19/2.23 | (135) $false
% 7.19/2.23 |
% 7.19/2.23 |-The branch is then unsatisfiable
% 7.19/2.23 |-Branch two:
% 7.19/2.23 | (256) ~ (all_0_0_0 = e12)
% 7.19/2.23 | (257) all_0_0_0 = e10 | all_0_0_0 = e11
% 7.19/2.23 |
% 7.19/2.23 +-Applying beta-rule and splitting (257), into two cases.
% 7.19/2.23 |-Branch one:
% 7.19/2.23 | (163) all_0_0_0 = e10
% 7.19/2.23 |
% 7.19/2.23 | From (163) and (2) follows:
% 7.19/2.23 | (164) h(e10) = e23
% 7.19/2.23 |
% 7.19/2.23 | Instantiating formula (20) with e10, e23, all_0_7_7 and discharging atoms h(e10) = all_0_7_7, h(e10) = e23, yields:
% 7.19/2.23 | (155) all_0_7_7 = e23
% 7.19/2.23 |
% 7.19/2.23 | Equations (155) can reduce 159 to:
% 7.19/2.23 | (135) $false
% 7.19/2.23 |
% 7.19/2.23 |-The branch is then unsatisfiable
% 7.19/2.23 |-Branch two:
% 7.19/2.23 | (262) ~ (all_0_0_0 = e10)
% 7.19/2.23 | (173) all_0_0_0 = e11
% 7.19/2.23 |
% 7.19/2.23 | From (173) and (2) follows:
% 7.19/2.23 | (264) h(e11) = e23
% 7.19/2.23 |
% 7.19/2.23 | Instantiating formula (20) with e11, e23, all_0_6_6 and discharging atoms h(e11) = all_0_6_6, h(e11) = e23, yields:
% 7.19/2.23 | (132) all_0_6_6 = e23
% 7.19/2.23 |
% 7.19/2.23 | Equations (132) can reduce 136 to:
% 7.19/2.23 | (135) $false
% 7.19/2.23 |
% 7.19/2.23 |-The branch is then unsatisfiable
% 7.19/2.23 % SZS output end Proof for theBenchmark
% 7.19/2.23
% 7.19/2.23 1651ms
%------------------------------------------------------------------------------