TSTP Solution File: SYN084+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 21 04:59:50 EDT 2022
% Result : Theorem 2.52s 1.25s
% Output : Proof 4.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 12:37:02 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58 Bug reports to peter@backeman.se
% 0.55/0.58
% 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58
% 0.55/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.62/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.85 Prover 0: Preprocessing ...
% 1.51/0.94 Prover 0: Warning: ignoring some quantifiers
% 1.54/0.95 Prover 0: Constructing countermodel ...
% 2.01/1.09 Prover 0: gave up
% 2.01/1.09 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.01/1.11 Prover 1: Preprocessing ...
% 2.01/1.16 Prover 1: Constructing countermodel ...
% 2.52/1.25 Prover 1: proved (153ms)
% 2.52/1.25
% 2.52/1.25 No countermodel exists, formula is valid
% 2.52/1.25 % SZS status Theorem for theBenchmark
% 2.52/1.25
% 2.52/1.25 Generating proof ... found it (size 86)
% 3.85/1.66
% 3.85/1.66 % SZS output start Proof for theBenchmark
% 3.85/1.66 Assumed formulas after preprocessing and simplification:
% 3.85/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (big_p(a) = v0 & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (f(v9) = v8) | ~ (f(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (big_p(v9) = v8) | ~ (big_p(v9) = v7)) & ((v0 = 0 & ~ (v6 = 0) & f(v3) = v5 & f(v1) = v3 & big_p(v5) = v6 & big_p(v3) = v4 & big_p(v1) = v2 & ! [v7] : ! [v8] : ( ~ (f(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (f(v8) = v10 & big_p(v10) = v11 & big_p(v8) = v9 & ( ~ (v9 = 0) | v11 = 0))) & ! [v7] : ! [v8] : ( ~ (f(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (f(v8) = v10 & big_p(v10) = v11 & big_p(v7) = v9 & (v11 = 0 | v9 = 0))) & ( ~ (v2 = 0) | v4 = 0)) | (v0 = 0 & ~ (v5 = 0) & f(v3) = v4 & f(v1) = v3 & big_p(v4) = v5 & big_p(v3) = v6 & big_p(v1) = v2 & ! [v7] : ! [v8] : ( ~ (f(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (f(v8) = v11 & big_p(v11) = v12 & big_p(v8) = v10 & big_p(v7) = v9 & (v12 = 0 | (v9 = 0 & ~ (v10 = 0))))) & ( ~ (v2 = 0) | v6 = 0))))
% 3.85/1.69 | 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 yields:
% 3.85/1.69 | (1) big_p(a) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ((all_0_6_6 = 0 & ~ (all_0_0_0 = 0) & f(all_0_3_3) = all_0_1_1 & f(all_0_5_5) = all_0_3_3 & big_p(all_0_1_1) = all_0_0_0 & big_p(all_0_3_3) = all_0_2_2 & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (f(v1) = v3 & big_p(v3) = v4 & big_p(v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (f(v1) = v3 & big_p(v3) = v4 & big_p(v0) = v2 & (v4 = 0 | v2 = 0))) & ( ~ (all_0_4_4 = 0) | all_0_2_2 = 0)) | (all_0_6_6 = 0 & ~ (all_0_1_1 = 0) & f(all_0_3_3) = all_0_2_2 & f(all_0_5_5) = all_0_3_3 & big_p(all_0_2_2) = all_0_1_1 & big_p(all_0_3_3) = all_0_0_0 & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (f(v1) = v4 & big_p(v4) = v5 & big_p(v1) = v3 & big_p(v0) = v2 & (v5 = 0 | (v2 = 0 & ~ (v3 = 0))))) & ( ~ (all_0_4_4 = 0) | all_0_0_0 = 0)))
% 3.85/1.69 |
% 3.85/1.69 | Applying alpha-rule on (1) yields:
% 3.85/1.69 | (2) big_p(a) = all_0_6_6
% 3.85/1.69 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 3.85/1.69 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 3.85/1.69 | (5) (all_0_6_6 = 0 & ~ (all_0_0_0 = 0) & f(all_0_3_3) = all_0_1_1 & f(all_0_5_5) = all_0_3_3 & big_p(all_0_1_1) = all_0_0_0 & big_p(all_0_3_3) = all_0_2_2 & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (f(v1) = v3 & big_p(v3) = v4 & big_p(v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (f(v1) = v3 & big_p(v3) = v4 & big_p(v0) = v2 & (v4 = 0 | v2 = 0))) & ( ~ (all_0_4_4 = 0) | all_0_2_2 = 0)) | (all_0_6_6 = 0 & ~ (all_0_1_1 = 0) & f(all_0_3_3) = all_0_2_2 & f(all_0_5_5) = all_0_3_3 & big_p(all_0_2_2) = all_0_1_1 & big_p(all_0_3_3) = all_0_0_0 & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (f(v1) = v4 & big_p(v4) = v5 & big_p(v1) = v3 & big_p(v0) = v2 & (v5 = 0 | (v2 = 0 & ~ (v3 = 0))))) & ( ~ (all_0_4_4 = 0) | all_0_0_0 = 0))
% 3.85/1.70 |
% 3.85/1.70 +-Applying beta-rule and splitting (5), into two cases.
% 3.85/1.70 |-Branch one:
% 3.85/1.70 | (6) all_0_6_6 = 0 & ~ (all_0_0_0 = 0) & f(all_0_3_3) = all_0_1_1 & f(all_0_5_5) = all_0_3_3 & big_p(all_0_1_1) = all_0_0_0 & big_p(all_0_3_3) = all_0_2_2 & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (f(v1) = v3 & big_p(v3) = v4 & big_p(v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (f(v1) = v3 & big_p(v3) = v4 & big_p(v0) = v2 & (v4 = 0 | v2 = 0))) & ( ~ (all_0_4_4 = 0) | all_0_2_2 = 0)
% 3.85/1.70 |
% 3.85/1.70 | Applying alpha-rule on (6) yields:
% 3.85/1.70 | (7) all_0_6_6 = 0
% 3.85/1.70 | (8) big_p(all_0_3_3) = all_0_2_2
% 3.85/1.70 | (9) ~ (all_0_4_4 = 0) | all_0_2_2 = 0
% 3.85/1.70 | (10) big_p(all_0_1_1) = all_0_0_0
% 3.85/1.70 | (11) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (f(v1) = v3 & big_p(v3) = v4 & big_p(v1) = v2 & ( ~ (v2 = 0) | v4 = 0)))
% 3.85/1.70 | (12) f(all_0_5_5) = all_0_3_3
% 3.85/1.70 | (13) big_p(all_0_5_5) = all_0_4_4
% 3.85/1.70 | (14) f(all_0_3_3) = all_0_1_1
% 3.85/1.70 | (15) ~ (all_0_0_0 = 0)
% 3.85/1.70 | (16) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (f(v1) = v3 & big_p(v3) = v4 & big_p(v0) = v2 & (v4 = 0 | v2 = 0)))
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (11) with all_0_1_1, all_0_3_3 and discharging atoms f(all_0_3_3) = all_0_1_1, yields:
% 3.85/1.70 | (17) ? [v0] : ? [v1] : ? [v2] : (f(all_0_1_1) = v1 & big_p(v1) = v2 & big_p(all_0_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0))
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (16) with all_0_1_1, all_0_3_3 and discharging atoms f(all_0_3_3) = all_0_1_1, yields:
% 3.85/1.70 | (18) ? [v0] : ? [v1] : ? [v2] : (f(all_0_1_1) = v1 & big_p(v1) = v2 & big_p(all_0_3_3) = v0 & (v2 = 0 | v0 = 0))
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (11) with all_0_3_3, all_0_5_5 and discharging atoms f(all_0_5_5) = all_0_3_3, yields:
% 3.85/1.70 | (19) ? [v0] : ? [v1] : ? [v2] : (f(all_0_3_3) = v1 & big_p(v1) = v2 & big_p(all_0_3_3) = v0 & ( ~ (v0 = 0) | v2 = 0))
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (16) with all_0_3_3, all_0_5_5 and discharging atoms f(all_0_5_5) = all_0_3_3, yields:
% 3.85/1.70 | (20) ? [v0] : ? [v1] : ? [v2] : (f(all_0_3_3) = v1 & big_p(v1) = v2 & big_p(all_0_5_5) = v0 & (v2 = 0 | v0 = 0))
% 3.85/1.70 |
% 3.85/1.70 | Instantiating (20) with all_16_0_7, all_16_1_8, all_16_2_9 yields:
% 3.85/1.70 | (21) f(all_0_3_3) = all_16_1_8 & big_p(all_16_1_8) = all_16_0_7 & big_p(all_0_5_5) = all_16_2_9 & (all_16_0_7 = 0 | all_16_2_9 = 0)
% 3.85/1.70 |
% 3.85/1.70 | Applying alpha-rule on (21) yields:
% 3.85/1.70 | (22) f(all_0_3_3) = all_16_1_8
% 3.85/1.70 | (23) big_p(all_16_1_8) = all_16_0_7
% 3.85/1.70 | (24) big_p(all_0_5_5) = all_16_2_9
% 3.85/1.70 | (25) all_16_0_7 = 0 | all_16_2_9 = 0
% 3.85/1.70 |
% 3.85/1.70 | Instantiating (19) with all_18_0_10, all_18_1_11, all_18_2_12 yields:
% 3.85/1.70 | (26) f(all_0_3_3) = all_18_1_11 & big_p(all_18_1_11) = all_18_0_10 & big_p(all_0_3_3) = all_18_2_12 & ( ~ (all_18_2_12 = 0) | all_18_0_10 = 0)
% 3.85/1.70 |
% 3.85/1.70 | Applying alpha-rule on (26) yields:
% 3.85/1.70 | (27) f(all_0_3_3) = all_18_1_11
% 3.85/1.70 | (28) big_p(all_18_1_11) = all_18_0_10
% 3.85/1.70 | (29) big_p(all_0_3_3) = all_18_2_12
% 3.85/1.70 | (30) ~ (all_18_2_12 = 0) | all_18_0_10 = 0
% 3.85/1.71 |
% 3.85/1.71 | Instantiating (18) with all_20_0_13, all_20_1_14, all_20_2_15 yields:
% 3.85/1.71 | (31) f(all_0_1_1) = all_20_1_14 & big_p(all_20_1_14) = all_20_0_13 & big_p(all_0_3_3) = all_20_2_15 & (all_20_0_13 = 0 | all_20_2_15 = 0)
% 3.85/1.71 |
% 3.85/1.71 | Applying alpha-rule on (31) yields:
% 3.85/1.71 | (32) f(all_0_1_1) = all_20_1_14
% 3.85/1.71 | (33) big_p(all_20_1_14) = all_20_0_13
% 3.85/1.71 | (34) big_p(all_0_3_3) = all_20_2_15
% 3.85/1.71 | (35) all_20_0_13 = 0 | all_20_2_15 = 0
% 3.85/1.71 |
% 3.85/1.71 | Instantiating (17) with all_22_0_16, all_22_1_17, all_22_2_18 yields:
% 3.85/1.71 | (36) f(all_0_1_1) = all_22_1_17 & big_p(all_22_1_17) = all_22_0_16 & big_p(all_0_1_1) = all_22_2_18 & ( ~ (all_22_2_18 = 0) | all_22_0_16 = 0)
% 3.85/1.71 |
% 3.85/1.71 | Applying alpha-rule on (36) yields:
% 3.85/1.71 | (37) f(all_0_1_1) = all_22_1_17
% 3.85/1.71 | (38) big_p(all_22_1_17) = all_22_0_16
% 3.85/1.71 | (39) big_p(all_0_1_1) = all_22_2_18
% 3.85/1.71 | (40) ~ (all_22_2_18 = 0) | all_22_0_16 = 0
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (3) with all_0_3_3, all_18_1_11, all_0_1_1 and discharging atoms f(all_0_3_3) = all_18_1_11, f(all_0_3_3) = all_0_1_1, yields:
% 3.85/1.71 | (41) all_18_1_11 = all_0_1_1
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (3) with all_0_3_3, all_16_1_8, all_18_1_11 and discharging atoms f(all_0_3_3) = all_18_1_11, f(all_0_3_3) = all_16_1_8, yields:
% 3.85/1.71 | (42) all_18_1_11 = all_16_1_8
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (4) with all_16_1_8, all_16_0_7, all_18_0_10 and discharging atoms big_p(all_16_1_8) = all_16_0_7, yields:
% 3.85/1.71 | (43) all_18_0_10 = all_16_0_7 | ~ (big_p(all_16_1_8) = all_18_0_10)
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (4) with all_0_1_1, all_22_2_18, all_0_0_0 and discharging atoms big_p(all_0_1_1) = all_22_2_18, big_p(all_0_1_1) = all_0_0_0, yields:
% 3.85/1.71 | (44) all_22_2_18 = all_0_0_0
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (4) with all_0_1_1, all_22_2_18, all_16_0_7 and discharging atoms big_p(all_0_1_1) = all_22_2_18, yields:
% 3.85/1.71 | (45) all_22_2_18 = all_16_0_7 | ~ (big_p(all_0_1_1) = all_16_0_7)
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (4) with all_0_3_3, all_20_2_15, all_0_2_2 and discharging atoms big_p(all_0_3_3) = all_20_2_15, big_p(all_0_3_3) = all_0_2_2, yields:
% 3.85/1.71 | (46) all_20_2_15 = all_0_2_2
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (4) with all_0_3_3, all_18_2_12, all_20_2_15 and discharging atoms big_p(all_0_3_3) = all_20_2_15, big_p(all_0_3_3) = all_18_2_12, yields:
% 3.85/1.71 | (47) all_20_2_15 = all_18_2_12
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (4) with all_0_5_5, all_16_2_9, all_0_4_4 and discharging atoms big_p(all_0_5_5) = all_16_2_9, big_p(all_0_5_5) = all_0_4_4, yields:
% 3.85/1.71 | (48) all_16_2_9 = all_0_4_4
% 3.85/1.71 |
% 3.85/1.71 | Combining equations (47,46) yields a new equation:
% 3.85/1.71 | (49) all_18_2_12 = all_0_2_2
% 3.85/1.71 |
% 3.85/1.71 | Simplifying 49 yields:
% 3.85/1.71 | (50) all_18_2_12 = all_0_2_2
% 3.85/1.71 |
% 3.85/1.71 | Combining equations (41,42) yields a new equation:
% 3.85/1.71 | (51) all_16_1_8 = all_0_1_1
% 3.85/1.71 |
% 3.85/1.71 | Combining equations (51,42) yields a new equation:
% 3.85/1.71 | (41) all_18_1_11 = all_0_1_1
% 3.85/1.71 |
% 3.85/1.71 | From (41) and (28) follows:
% 3.85/1.71 | (53) big_p(all_0_1_1) = all_18_0_10
% 3.85/1.71 |
% 3.85/1.71 +-Applying beta-rule and splitting (43), into two cases.
% 3.85/1.71 |-Branch one:
% 3.85/1.71 | (54) ~ (big_p(all_16_1_8) = all_18_0_10)
% 3.85/1.71 |
% 3.85/1.71 | From (51) and (54) follows:
% 3.85/1.71 | (55) ~ (big_p(all_0_1_1) = all_18_0_10)
% 3.85/1.71 |
% 3.85/1.71 | Using (53) and (55) yields:
% 3.85/1.71 | (56) $false
% 3.85/1.71 |
% 3.85/1.71 |-The branch is then unsatisfiable
% 3.85/1.71 |-Branch two:
% 3.85/1.71 | (57) big_p(all_16_1_8) = all_18_0_10
% 3.85/1.71 | (58) all_18_0_10 = all_16_0_7
% 3.85/1.71 |
% 3.85/1.71 | From (58) and (53) follows:
% 3.85/1.71 | (59) big_p(all_0_1_1) = all_16_0_7
% 3.85/1.71 |
% 3.85/1.71 +-Applying beta-rule and splitting (45), into two cases.
% 3.85/1.71 |-Branch one:
% 3.85/1.71 | (60) ~ (big_p(all_0_1_1) = all_16_0_7)
% 3.85/1.71 |
% 3.85/1.71 | Using (59) and (60) yields:
% 3.85/1.71 | (56) $false
% 3.85/1.71 |
% 3.85/1.71 |-The branch is then unsatisfiable
% 3.85/1.71 |-Branch two:
% 3.85/1.71 | (59) big_p(all_0_1_1) = all_16_0_7
% 3.85/1.71 | (63) all_22_2_18 = all_16_0_7
% 3.85/1.71 |
% 3.85/1.71 | Combining equations (63,44) yields a new equation:
% 3.85/1.71 | (64) all_16_0_7 = all_0_0_0
% 3.85/1.71 |
% 3.85/1.71 | Simplifying 64 yields:
% 3.85/1.71 | (65) all_16_0_7 = all_0_0_0
% 3.85/1.71 |
% 3.85/1.71 | Combining equations (65,58) yields a new equation:
% 3.85/1.71 | (66) all_18_0_10 = all_0_0_0
% 3.85/1.71 |
% 3.85/1.71 +-Applying beta-rule and splitting (30), into two cases.
% 3.85/1.71 |-Branch one:
% 3.85/1.71 | (67) ~ (all_18_2_12 = 0)
% 3.85/1.71 |
% 3.85/1.72 | Equations (50) can reduce 67 to:
% 3.85/1.72 | (68) ~ (all_0_2_2 = 0)
% 3.85/1.72 |
% 3.85/1.72 +-Applying beta-rule and splitting (9), into two cases.
% 3.85/1.72 |-Branch one:
% 3.85/1.72 | (69) ~ (all_0_4_4 = 0)
% 3.85/1.72 |
% 3.85/1.72 +-Applying beta-rule and splitting (25), into two cases.
% 3.85/1.72 |-Branch one:
% 3.85/1.72 | (70) all_16_0_7 = 0
% 3.85/1.72 |
% 3.85/1.72 | Combining equations (70,65) yields a new equation:
% 3.85/1.72 | (71) all_0_0_0 = 0
% 3.85/1.72 |
% 3.85/1.72 | Equations (71) can reduce 15 to:
% 3.85/1.72 | (72) $false
% 3.85/1.72 |
% 3.85/1.72 |-The branch is then unsatisfiable
% 3.85/1.72 |-Branch two:
% 3.85/1.72 | (73) ~ (all_16_0_7 = 0)
% 3.85/1.72 | (74) all_16_2_9 = 0
% 3.85/1.72 |
% 3.85/1.72 | Combining equations (74,48) yields a new equation:
% 3.85/1.72 | (75) all_0_4_4 = 0
% 3.85/1.72 |
% 3.85/1.72 | Equations (75) can reduce 69 to:
% 3.85/1.72 | (72) $false
% 3.85/1.72 |
% 3.85/1.72 |-The branch is then unsatisfiable
% 3.85/1.72 |-Branch two:
% 3.85/1.72 | (75) all_0_4_4 = 0
% 3.85/1.72 | (78) all_0_2_2 = 0
% 3.85/1.72 |
% 3.85/1.72 | Equations (78) can reduce 68 to:
% 3.85/1.72 | (72) $false
% 3.85/1.72 |
% 3.85/1.72 |-The branch is then unsatisfiable
% 3.85/1.72 |-Branch two:
% 3.85/1.72 | (80) all_18_2_12 = 0
% 3.85/1.72 | (81) all_18_0_10 = 0
% 3.85/1.72 |
% 3.85/1.72 | Combining equations (81,66) yields a new equation:
% 3.85/1.72 | (71) all_0_0_0 = 0
% 3.85/1.72 |
% 3.85/1.72 | Equations (71) can reduce 15 to:
% 3.85/1.72 | (72) $false
% 3.85/1.72 |
% 3.85/1.72 |-The branch is then unsatisfiable
% 3.85/1.72 |-Branch two:
% 3.85/1.72 | (84) all_0_6_6 = 0 & ~ (all_0_1_1 = 0) & f(all_0_3_3) = all_0_2_2 & f(all_0_5_5) = all_0_3_3 & big_p(all_0_2_2) = all_0_1_1 & big_p(all_0_3_3) = all_0_0_0 & big_p(all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (f(v1) = v4 & big_p(v4) = v5 & big_p(v1) = v3 & big_p(v0) = v2 & (v5 = 0 | (v2 = 0 & ~ (v3 = 0))))) & ( ~ (all_0_4_4 = 0) | all_0_0_0 = 0)
% 3.85/1.72 |
% 3.85/1.72 | Applying alpha-rule on (84) yields:
% 3.85/1.72 | (7) all_0_6_6 = 0
% 3.85/1.72 | (86) f(all_0_3_3) = all_0_2_2
% 3.85/1.72 | (87) ~ (all_0_1_1 = 0)
% 3.85/1.72 | (88) big_p(all_0_3_3) = all_0_0_0
% 3.85/1.72 | (89) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (f(v1) = v4 & big_p(v4) = v5 & big_p(v1) = v3 & big_p(v0) = v2 & (v5 = 0 | (v2 = 0 & ~ (v3 = 0)))))
% 3.85/1.72 | (12) f(all_0_5_5) = all_0_3_3
% 3.85/1.72 | (13) big_p(all_0_5_5) = all_0_4_4
% 3.85/1.72 | (92) big_p(all_0_2_2) = all_0_1_1
% 3.85/1.72 | (93) ~ (all_0_4_4 = 0) | all_0_0_0 = 0
% 3.85/1.72 |
% 3.85/1.72 | Instantiating formula (89) with all_0_2_2, all_0_3_3 and discharging atoms f(all_0_3_3) = all_0_2_2, yields:
% 3.85/1.72 | (94) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (f(all_0_2_2) = v2 & big_p(v2) = v3 & big_p(all_0_2_2) = v1 & big_p(all_0_3_3) = v0 & (v3 = 0 | (v0 = 0 & ~ (v1 = 0))))
% 3.85/1.72 |
% 3.85/1.72 | Instantiating formula (89) with all_0_3_3, all_0_5_5 and discharging atoms f(all_0_5_5) = all_0_3_3, yields:
% 3.85/1.72 | (95) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (f(all_0_3_3) = v2 & big_p(v2) = v3 & big_p(all_0_3_3) = v1 & big_p(all_0_5_5) = v0 & (v3 = 0 | (v0 = 0 & ~ (v1 = 0))))
% 3.85/1.72 |
% 3.85/1.72 | Instantiating (95) with all_16_0_19, all_16_1_20, all_16_2_21, all_16_3_22 yields:
% 3.85/1.72 | (96) f(all_0_3_3) = all_16_1_20 & big_p(all_16_1_20) = all_16_0_19 & big_p(all_0_3_3) = all_16_2_21 & big_p(all_0_5_5) = all_16_3_22 & (all_16_0_19 = 0 | (all_16_3_22 = 0 & ~ (all_16_2_21 = 0)))
% 3.85/1.72 |
% 3.85/1.72 | Applying alpha-rule on (96) yields:
% 3.85/1.72 | (97) f(all_0_3_3) = all_16_1_20
% 3.85/1.72 | (98) big_p(all_0_5_5) = all_16_3_22
% 3.85/1.72 | (99) big_p(all_16_1_20) = all_16_0_19
% 3.85/1.72 | (100) all_16_0_19 = 0 | (all_16_3_22 = 0 & ~ (all_16_2_21 = 0))
% 3.85/1.72 | (101) big_p(all_0_3_3) = all_16_2_21
% 3.85/1.72 |
% 3.85/1.72 | Instantiating (94) with all_18_0_23, all_18_1_24, all_18_2_25, all_18_3_26 yields:
% 3.85/1.72 | (102) f(all_0_2_2) = all_18_1_24 & big_p(all_18_1_24) = all_18_0_23 & big_p(all_0_2_2) = all_18_2_25 & big_p(all_0_3_3) = all_18_3_26 & (all_18_0_23 = 0 | (all_18_3_26 = 0 & ~ (all_18_2_25 = 0)))
% 3.85/1.72 |
% 3.85/1.72 | Applying alpha-rule on (102) yields:
% 3.85/1.72 | (103) all_18_0_23 = 0 | (all_18_3_26 = 0 & ~ (all_18_2_25 = 0))
% 3.85/1.72 | (104) big_p(all_0_2_2) = all_18_2_25
% 3.85/1.73 | (105) f(all_0_2_2) = all_18_1_24
% 3.85/1.73 | (106) big_p(all_18_1_24) = all_18_0_23
% 3.85/1.73 | (107) big_p(all_0_3_3) = all_18_3_26
% 3.85/1.73 |
% 3.85/1.73 | Instantiating formula (3) with all_0_3_3, all_16_1_20, all_0_2_2 and discharging atoms f(all_0_3_3) = all_16_1_20, f(all_0_3_3) = all_0_2_2, yields:
% 3.85/1.73 | (108) all_16_1_20 = all_0_2_2
% 3.85/1.73 |
% 3.85/1.73 | Instantiating formula (4) with all_0_2_2, all_16_0_19, all_0_1_1 and discharging atoms big_p(all_0_2_2) = all_0_1_1, yields:
% 3.85/1.73 | (109) all_16_0_19 = all_0_1_1 | ~ (big_p(all_0_2_2) = all_16_0_19)
% 3.85/1.73 |
% 3.85/1.73 | Instantiating formula (4) with all_0_3_3, all_18_3_26, all_0_0_0 and discharging atoms big_p(all_0_3_3) = all_18_3_26, big_p(all_0_3_3) = all_0_0_0, yields:
% 3.85/1.73 | (110) all_18_3_26 = all_0_0_0
% 3.85/1.73 |
% 3.85/1.73 | Instantiating formula (4) with all_0_3_3, all_16_2_21, all_18_3_26 and discharging atoms big_p(all_0_3_3) = all_18_3_26, big_p(all_0_3_3) = all_16_2_21, yields:
% 3.85/1.73 | (111) all_18_3_26 = all_16_2_21
% 3.85/1.73 |
% 3.85/1.73 | Instantiating formula (4) with all_0_5_5, all_16_3_22, all_0_4_4 and discharging atoms big_p(all_0_5_5) = all_16_3_22, big_p(all_0_5_5) = all_0_4_4, yields:
% 3.85/1.73 | (112) all_16_3_22 = all_0_4_4
% 3.85/1.73 |
% 3.85/1.73 | Combining equations (111,110) yields a new equation:
% 3.85/1.73 | (113) all_16_2_21 = all_0_0_0
% 3.85/1.73 |
% 3.85/1.73 | Simplifying 113 yields:
% 3.85/1.73 | (114) all_16_2_21 = all_0_0_0
% 3.85/1.73 |
% 3.85/1.73 | From (108) and (99) follows:
% 3.85/1.73 | (115) big_p(all_0_2_2) = all_16_0_19
% 3.85/1.73 |
% 3.85/1.73 +-Applying beta-rule and splitting (109), into two cases.
% 3.85/1.73 |-Branch one:
% 3.85/1.73 | (116) ~ (big_p(all_0_2_2) = all_16_0_19)
% 3.85/1.73 |
% 3.85/1.73 | Using (115) and (116) yields:
% 3.85/1.73 | (56) $false
% 3.85/1.73 |
% 3.85/1.73 |-The branch is then unsatisfiable
% 3.85/1.73 |-Branch two:
% 3.85/1.73 | (115) big_p(all_0_2_2) = all_16_0_19
% 3.85/1.73 | (119) all_16_0_19 = all_0_1_1
% 3.85/1.73 |
% 3.85/1.73 +-Applying beta-rule and splitting (100), into two cases.
% 3.85/1.73 |-Branch one:
% 3.85/1.73 | (120) all_16_0_19 = 0
% 3.85/1.73 |
% 3.85/1.73 | Combining equations (119,120) yields a new equation:
% 3.85/1.73 | (121) all_0_1_1 = 0
% 3.85/1.73 |
% 3.85/1.73 | Simplifying 121 yields:
% 3.85/1.73 | (122) all_0_1_1 = 0
% 3.85/1.73 |
% 3.85/1.73 | Equations (122) can reduce 87 to:
% 3.85/1.73 | (72) $false
% 3.85/1.73 |
% 3.85/1.73 |-The branch is then unsatisfiable
% 3.85/1.73 |-Branch two:
% 3.85/1.73 | (124) ~ (all_16_0_19 = 0)
% 3.85/1.73 | (125) all_16_3_22 = 0 & ~ (all_16_2_21 = 0)
% 3.85/1.73 |
% 3.85/1.73 | Applying alpha-rule on (125) yields:
% 3.85/1.73 | (126) all_16_3_22 = 0
% 3.85/1.73 | (127) ~ (all_16_2_21 = 0)
% 3.85/1.73 |
% 3.85/1.73 | Combining equations (126,112) yields a new equation:
% 3.85/1.73 | (75) all_0_4_4 = 0
% 3.85/1.73 |
% 3.85/1.73 | Equations (114) can reduce 127 to:
% 3.85/1.73 | (15) ~ (all_0_0_0 = 0)
% 3.85/1.73 |
% 3.85/1.73 +-Applying beta-rule and splitting (93), into two cases.
% 3.85/1.73 |-Branch one:
% 3.85/1.73 | (69) ~ (all_0_4_4 = 0)
% 3.85/1.73 |
% 3.85/1.73 | Equations (75) can reduce 69 to:
% 3.85/1.73 | (72) $false
% 3.85/1.73 |
% 3.85/1.73 |-The branch is then unsatisfiable
% 3.85/1.73 |-Branch two:
% 3.85/1.73 | (75) all_0_4_4 = 0
% 3.85/1.73 | (71) all_0_0_0 = 0
% 3.85/1.73 |
% 3.85/1.73 | Equations (71) can reduce 15 to:
% 3.85/1.73 | (72) $false
% 3.85/1.73 |
% 3.85/1.73 |-The branch is then unsatisfiable
% 4.22/1.73 % SZS output end Proof for theBenchmark
% 4.22/1.73
% 4.22/1.73 1146ms
%------------------------------------------------------------------------------