TSTP Solution File: SET047+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET047+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 : Tue Jul 19 00:16:41 EDT 2022
% Result : Theorem 2.35s 1.25s
% Output : Proof 3.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET047+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 18:16:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.52/0.59 ____ _
% 0.52/0.59 ___ / __ \_____(_)___ ________ __________
% 0.52/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.59
% 0.52/0.59 A Theorem Prover for First-Order Logic
% 0.52/0.60 (ePrincess v.1.0)
% 0.52/0.60
% 0.52/0.60 (c) Philipp Rümmer, 2009-2015
% 0.52/0.60 (c) Peter Backeman, 2014-2015
% 0.52/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.60 Bug reports to peter@backeman.se
% 0.52/0.60
% 0.52/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.60
% 0.52/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.24/0.89 Prover 0: Preprocessing ...
% 1.38/0.96 Prover 0: Warning: ignoring some quantifiers
% 1.46/0.98 Prover 0: Constructing countermodel ...
% 1.77/1.08 Prover 0: gave up
% 1.77/1.09 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.77/1.10 Prover 1: Preprocessing ...
% 2.09/1.16 Prover 1: Constructing countermodel ...
% 2.35/1.25 Prover 1: proved (168ms)
% 2.35/1.25
% 2.35/1.25 No countermodel exists, formula is valid
% 2.35/1.25 % SZS status Theorem for theBenchmark
% 2.35/1.25
% 2.35/1.25 Generating proof ... found it (size 88)
% 3.04/1.51
% 3.04/1.51 % SZS output start Proof for theBenchmark
% 3.04/1.51 Assumed formulas after preprocessing and simplification:
% 3.04/1.51 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (set_equal(v1, v0) = v3 & set_equal(v0, v1) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (set_equal(v4, v5) = 0) | ~ (element(v6, v4) = v7) | ? [v8] : ( ~ (v8 = 0) & element(v6, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (set_equal(v7, v6) = v5) | ~ (set_equal(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (element(v7, v6) = v5) | ~ (element(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (set_equal(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (element(v7, v5) = v9 & element(v7, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)) & (v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_equal(v4, v5) = 0) | ~ (element(v6, v4) = 0) | element(v6, v5) = 0) & ((v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0))))
% 3.26/1.54 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 3.26/1.54 | (1) set_equal(all_0_2_2, all_0_3_3) = all_0_0_0 & set_equal(all_0_3_3, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_equal(v0, v1) = 0) | ~ (element(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_equal(v3, v2) = v1) | ~ (set_equal(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (set_equal(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (element(v3, v1) = v5 & element(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_equal(v0, v1) = 0) | ~ (element(v2, v0) = 0) | element(v2, v1) = 0) & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))
% 3.26/1.54 |
% 3.26/1.54 | Applying alpha-rule on (1) yields:
% 3.26/1.54 | (2) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))
% 3.26/1.54 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 3.26/1.55 | (4) set_equal(all_0_2_2, all_0_3_3) = all_0_0_0
% 3.26/1.55 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_equal(v0, v1) = 0) | ~ (element(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4))
% 3.26/1.55 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_equal(v0, v1) = 0) | ~ (element(v2, v0) = 0) | element(v2, v1) = 0)
% 3.26/1.55 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_equal(v3, v2) = v1) | ~ (set_equal(v3, v2) = v0))
% 3.26/1.55 | (8) set_equal(all_0_3_3, all_0_2_2) = all_0_1_1
% 3.26/1.55 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (set_equal(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (element(v3, v1) = v5 & element(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 3.34/1.55 |
% 3.34/1.55 | Instantiating formula (9) with all_0_0_0, all_0_3_3, all_0_2_2 and discharging atoms set_equal(all_0_2_2, all_0_3_3) = all_0_0_0, yields:
% 3.34/1.55 | (10) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (element(v0, all_0_2_2) = v1 & element(v0, all_0_3_3) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 3.34/1.55 |
% 3.34/1.55 | Instantiating formula (9) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms set_equal(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 3.34/1.55 | (11) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (element(v0, all_0_2_2) = v2 & element(v0, all_0_3_3) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 3.34/1.55 |
% 3.34/1.55 +-Applying beta-rule and splitting (2), into two cases.
% 3.34/1.55 |-Branch one:
% 3.34/1.55 | (12) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 3.34/1.55 |
% 3.34/1.55 | Applying alpha-rule on (12) yields:
% 3.34/1.55 | (13) all_0_0_0 = 0
% 3.34/1.55 | (14) ~ (all_0_1_1 = 0)
% 3.34/1.55 |
% 3.34/1.55 | From (13) and (4) follows:
% 3.34/1.55 | (15) set_equal(all_0_2_2, all_0_3_3) = 0
% 3.34/1.55 |
% 3.34/1.55 +-Applying beta-rule and splitting (11), into two cases.
% 3.34/1.55 |-Branch one:
% 3.34/1.55 | (16) all_0_1_1 = 0
% 3.34/1.55 |
% 3.34/1.55 | Equations (16) can reduce 14 to:
% 3.34/1.55 | (17) $false
% 3.34/1.55 |
% 3.34/1.56 |-The branch is then unsatisfiable
% 3.34/1.56 |-Branch two:
% 3.34/1.56 | (14) ~ (all_0_1_1 = 0)
% 3.34/1.56 | (19) ? [v0] : ? [v1] : ? [v2] : (element(v0, all_0_2_2) = v2 & element(v0, all_0_3_3) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 3.34/1.56 |
% 3.34/1.56 | Instantiating (19) with all_14_0_4, all_14_1_5, all_14_2_6 yields:
% 3.34/1.56 | (20) element(all_14_2_6, all_0_2_2) = all_14_0_4 & element(all_14_2_6, all_0_3_3) = all_14_1_5 & ( ~ (all_14_0_4 = 0) | ~ (all_14_1_5 = 0)) & (all_14_0_4 = 0 | all_14_1_5 = 0)
% 3.34/1.56 |
% 3.34/1.56 | Applying alpha-rule on (20) yields:
% 3.34/1.56 | (21) element(all_14_2_6, all_0_2_2) = all_14_0_4
% 3.34/1.56 | (22) element(all_14_2_6, all_0_3_3) = all_14_1_5
% 3.34/1.56 | (23) ~ (all_14_0_4 = 0) | ~ (all_14_1_5 = 0)
% 3.34/1.56 | (24) all_14_0_4 = 0 | all_14_1_5 = 0
% 3.34/1.56 |
% 3.34/1.56 | Instantiating formula (3) with all_14_2_6, all_0_3_3, all_14_1_5, all_14_0_4 and discharging atoms element(all_14_2_6, all_0_3_3) = all_14_1_5, yields:
% 3.34/1.56 | (25) all_14_0_4 = all_14_1_5 | ~ (element(all_14_2_6, all_0_3_3) = all_14_0_4)
% 3.34/1.56 |
% 3.34/1.56 | Instantiating formula (5) with all_14_0_4, all_14_2_6, all_0_3_3, all_0_2_2 and discharging atoms set_equal(all_0_2_2, all_0_3_3) = 0, element(all_14_2_6, all_0_2_2) = all_14_0_4, yields:
% 3.34/1.56 | (26) all_14_0_4 = 0 | ? [v0] : ( ~ (v0 = 0) & element(all_14_2_6, all_0_3_3) = v0)
% 3.34/1.56 |
% 3.34/1.56 +-Applying beta-rule and splitting (25), into two cases.
% 3.34/1.56 |-Branch one:
% 3.34/1.56 | (27) ~ (element(all_14_2_6, all_0_3_3) = all_14_0_4)
% 3.34/1.56 |
% 3.34/1.56 | Using (22) and (27) yields:
% 3.34/1.56 | (28) ~ (all_14_0_4 = all_14_1_5)
% 3.34/1.56 |
% 3.34/1.56 +-Applying beta-rule and splitting (23), into two cases.
% 3.34/1.56 |-Branch one:
% 3.34/1.56 | (29) ~ (all_14_0_4 = 0)
% 3.34/1.56 |
% 3.34/1.56 +-Applying beta-rule and splitting (24), into two cases.
% 3.34/1.56 |-Branch one:
% 3.34/1.56 | (30) all_14_0_4 = 0
% 3.34/1.56 |
% 3.34/1.56 | Equations (30) can reduce 29 to:
% 3.34/1.56 | (17) $false
% 3.34/1.56 |
% 3.34/1.56 |-The branch is then unsatisfiable
% 3.34/1.56 |-Branch two:
% 3.34/1.56 | (29) ~ (all_14_0_4 = 0)
% 3.34/1.56 | (33) all_14_1_5 = 0
% 3.34/1.56 |
% 3.34/1.56 | Equations (33) can reduce 28 to:
% 3.34/1.56 | (29) ~ (all_14_0_4 = 0)
% 3.34/1.56 |
% 3.34/1.56 | From (33) and (22) follows:
% 3.34/1.56 | (35) element(all_14_2_6, all_0_3_3) = 0
% 3.34/1.56 |
% 3.34/1.56 +-Applying beta-rule and splitting (26), into two cases.
% 3.34/1.56 |-Branch one:
% 3.34/1.56 | (30) all_14_0_4 = 0
% 3.34/1.56 |
% 3.34/1.56 | Equations (30) can reduce 29 to:
% 3.34/1.56 | (17) $false
% 3.34/1.56 |
% 3.34/1.56 |-The branch is then unsatisfiable
% 3.34/1.56 |-Branch two:
% 3.34/1.56 | (29) ~ (all_14_0_4 = 0)
% 3.34/1.56 | (39) ? [v0] : ( ~ (v0 = 0) & element(all_14_2_6, all_0_3_3) = v0)
% 3.34/1.56 |
% 3.34/1.56 | Instantiating (39) with all_42_0_7 yields:
% 3.34/1.56 | (40) ~ (all_42_0_7 = 0) & element(all_14_2_6, all_0_3_3) = all_42_0_7
% 3.34/1.56 |
% 3.34/1.56 | Applying alpha-rule on (40) yields:
% 3.34/1.56 | (41) ~ (all_42_0_7 = 0)
% 3.34/1.56 | (42) element(all_14_2_6, all_0_3_3) = all_42_0_7
% 3.34/1.56 |
% 3.34/1.56 | Instantiating formula (3) with all_14_2_6, all_0_3_3, 0, all_42_0_7 and discharging atoms element(all_14_2_6, all_0_3_3) = all_42_0_7, element(all_14_2_6, all_0_3_3) = 0, yields:
% 3.34/1.56 | (43) all_42_0_7 = 0
% 3.34/1.56 |
% 3.34/1.56 | Equations (43) can reduce 41 to:
% 3.34/1.56 | (17) $false
% 3.34/1.56 |
% 3.34/1.56 |-The branch is then unsatisfiable
% 3.34/1.56 |-Branch two:
% 3.34/1.56 | (30) all_14_0_4 = 0
% 3.34/1.56 | (46) ~ (all_14_1_5 = 0)
% 3.34/1.56 |
% 3.34/1.56 | From (30) and (21) follows:
% 3.34/1.56 | (47) element(all_14_2_6, all_0_2_2) = 0
% 3.34/1.56 |
% 3.34/1.56 | From (30) and (27) follows:
% 3.34/1.56 | (48) ~ (element(all_14_2_6, all_0_3_3) = 0)
% 3.34/1.56 |
% 3.34/1.56 | Instantiating formula (6) with all_14_2_6, all_0_3_3, all_0_2_2 and discharging atoms set_equal(all_0_2_2, all_0_3_3) = 0, element(all_14_2_6, all_0_2_2) = 0, ~ (element(all_14_2_6, all_0_3_3) = 0), yields:
% 3.34/1.56 | (49) $false
% 3.34/1.56 |
% 3.34/1.56 |-The branch is then unsatisfiable
% 3.34/1.56 |-Branch two:
% 3.34/1.56 | (50) element(all_14_2_6, all_0_3_3) = all_14_0_4
% 3.34/1.56 | (51) all_14_0_4 = all_14_1_5
% 3.34/1.56 |
% 3.34/1.56 +-Applying beta-rule and splitting (23), into two cases.
% 3.34/1.56 |-Branch one:
% 3.34/1.56 | (29) ~ (all_14_0_4 = 0)
% 3.34/1.56 |
% 3.34/1.56 | Equations (51) can reduce 29 to:
% 3.34/1.56 | (46) ~ (all_14_1_5 = 0)
% 3.34/1.56 |
% 3.34/1.56 +-Applying beta-rule and splitting (24), into two cases.
% 3.34/1.56 |-Branch one:
% 3.34/1.56 | (30) all_14_0_4 = 0
% 3.34/1.56 |
% 3.34/1.56 | Combining equations (30,51) yields a new equation:
% 3.34/1.56 | (33) all_14_1_5 = 0
% 3.34/1.56 |
% 3.34/1.57 | Equations (33) can reduce 46 to:
% 3.34/1.57 | (17) $false
% 3.34/1.57 |
% 3.34/1.57 |-The branch is then unsatisfiable
% 3.34/1.57 |-Branch two:
% 3.34/1.57 | (29) ~ (all_14_0_4 = 0)
% 3.34/1.57 | (33) all_14_1_5 = 0
% 3.34/1.57 |
% 3.34/1.57 | Equations (33) can reduce 46 to:
% 3.34/1.57 | (17) $false
% 3.34/1.57 |
% 3.34/1.57 |-The branch is then unsatisfiable
% 3.34/1.57 |-Branch two:
% 3.34/1.57 | (30) all_14_0_4 = 0
% 3.34/1.57 | (46) ~ (all_14_1_5 = 0)
% 3.34/1.57 |
% 3.34/1.57 | Combining equations (30,51) yields a new equation:
% 3.34/1.57 | (33) all_14_1_5 = 0
% 3.34/1.57 |
% 3.34/1.57 | Equations (33) can reduce 46 to:
% 3.34/1.57 | (17) $false
% 3.34/1.57 |
% 3.34/1.57 |-The branch is then unsatisfiable
% 3.34/1.57 |-Branch two:
% 3.34/1.57 | (64) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 3.34/1.57 |
% 3.34/1.57 | Applying alpha-rule on (64) yields:
% 3.34/1.57 | (16) all_0_1_1 = 0
% 3.34/1.57 | (66) ~ (all_0_0_0 = 0)
% 3.34/1.57 |
% 3.34/1.57 | From (16) and (8) follows:
% 3.34/1.57 | (67) set_equal(all_0_3_3, all_0_2_2) = 0
% 3.34/1.57 |
% 3.34/1.57 +-Applying beta-rule and splitting (10), into two cases.
% 3.34/1.57 |-Branch one:
% 3.34/1.57 | (13) all_0_0_0 = 0
% 3.34/1.57 |
% 3.34/1.57 | Equations (13) can reduce 66 to:
% 3.34/1.57 | (17) $false
% 3.34/1.57 |
% 3.34/1.57 |-The branch is then unsatisfiable
% 3.34/1.57 |-Branch two:
% 3.34/1.57 | (66) ~ (all_0_0_0 = 0)
% 3.34/1.57 | (71) ? [v0] : ? [v1] : ? [v2] : (element(v0, all_0_2_2) = v1 & element(v0, all_0_3_3) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 3.34/1.57 |
% 3.34/1.57 | Instantiating (71) with all_14_0_8, all_14_1_9, all_14_2_10 yields:
% 3.34/1.57 | (72) element(all_14_2_10, all_0_2_2) = all_14_1_9 & element(all_14_2_10, all_0_3_3) = all_14_0_8 & ( ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0)) & (all_14_0_8 = 0 | all_14_1_9 = 0)
% 3.34/1.57 |
% 3.34/1.57 | Applying alpha-rule on (72) yields:
% 3.34/1.57 | (73) element(all_14_2_10, all_0_2_2) = all_14_1_9
% 3.34/1.57 | (74) element(all_14_2_10, all_0_3_3) = all_14_0_8
% 3.34/1.57 | (75) ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0)
% 3.34/1.57 | (76) all_14_0_8 = 0 | all_14_1_9 = 0
% 3.34/1.57 |
% 3.34/1.57 | Instantiating formula (3) with all_14_2_10, all_0_3_3, all_14_0_8, all_14_1_9 and discharging atoms element(all_14_2_10, all_0_3_3) = all_14_0_8, yields:
% 3.34/1.57 | (77) all_14_0_8 = all_14_1_9 | ~ (element(all_14_2_10, all_0_3_3) = all_14_1_9)
% 3.34/1.57 |
% 3.34/1.57 | Instantiating formula (5) with all_14_0_8, all_14_2_10, all_0_2_2, all_0_3_3 and discharging atoms set_equal(all_0_3_3, all_0_2_2) = 0, element(all_14_2_10, all_0_3_3) = all_14_0_8, yields:
% 3.34/1.57 | (78) all_14_0_8 = 0 | ? [v0] : ( ~ (v0 = 0) & element(all_14_2_10, all_0_2_2) = v0)
% 3.34/1.57 |
% 3.34/1.57 +-Applying beta-rule and splitting (77), into two cases.
% 3.34/1.57 |-Branch one:
% 3.34/1.57 | (79) ~ (element(all_14_2_10, all_0_3_3) = all_14_1_9)
% 3.34/1.57 |
% 3.34/1.57 | Using (74) and (79) yields:
% 3.34/1.57 | (80) ~ (all_14_0_8 = all_14_1_9)
% 3.34/1.57 |
% 3.34/1.57 +-Applying beta-rule and splitting (75), into two cases.
% 3.34/1.57 |-Branch one:
% 3.34/1.57 | (81) ~ (all_14_0_8 = 0)
% 3.34/1.57 |
% 3.34/1.57 +-Applying beta-rule and splitting (76), into two cases.
% 3.34/1.57 |-Branch one:
% 3.34/1.57 | (82) all_14_0_8 = 0
% 3.34/1.57 |
% 3.34/1.57 | Equations (82) can reduce 81 to:
% 3.34/1.57 | (17) $false
% 3.34/1.57 |
% 3.34/1.57 |-The branch is then unsatisfiable
% 3.34/1.57 |-Branch two:
% 3.34/1.57 | (81) ~ (all_14_0_8 = 0)
% 3.34/1.57 | (85) all_14_1_9 = 0
% 3.34/1.57 |
% 3.34/1.57 | Equations (85) can reduce 80 to:
% 3.34/1.57 | (81) ~ (all_14_0_8 = 0)
% 3.34/1.57 |
% 3.34/1.57 | From (85) and (73) follows:
% 3.34/1.57 | (87) element(all_14_2_10, all_0_2_2) = 0
% 3.34/1.57 |
% 3.34/1.57 +-Applying beta-rule and splitting (78), into two cases.
% 3.34/1.57 |-Branch one:
% 3.34/1.57 | (82) all_14_0_8 = 0
% 3.34/1.57 |
% 3.34/1.57 | Equations (82) can reduce 81 to:
% 3.34/1.57 | (17) $false
% 3.34/1.57 |
% 3.34/1.57 |-The branch is then unsatisfiable
% 3.34/1.57 |-Branch two:
% 3.34/1.57 | (81) ~ (all_14_0_8 = 0)
% 3.34/1.57 | (91) ? [v0] : ( ~ (v0 = 0) & element(all_14_2_10, all_0_2_2) = v0)
% 3.34/1.57 |
% 3.34/1.57 | Instantiating (91) with all_42_0_11 yields:
% 3.34/1.57 | (92) ~ (all_42_0_11 = 0) & element(all_14_2_10, all_0_2_2) = all_42_0_11
% 3.34/1.57 |
% 3.34/1.57 | Applying alpha-rule on (92) yields:
% 3.34/1.57 | (93) ~ (all_42_0_11 = 0)
% 3.34/1.57 | (94) element(all_14_2_10, all_0_2_2) = all_42_0_11
% 3.34/1.57 |
% 3.34/1.57 | Instantiating formula (3) with all_14_2_10, all_0_2_2, 0, all_42_0_11 and discharging atoms element(all_14_2_10, all_0_2_2) = all_42_0_11, element(all_14_2_10, all_0_2_2) = 0, yields:
% 3.34/1.57 | (95) all_42_0_11 = 0
% 3.34/1.57 |
% 3.34/1.57 | Equations (95) can reduce 93 to:
% 3.34/1.57 | (17) $false
% 3.34/1.57 |
% 3.34/1.57 |-The branch is then unsatisfiable
% 3.34/1.57 |-Branch two:
% 3.34/1.57 | (82) all_14_0_8 = 0
% 3.34/1.58 | (98) ~ (all_14_1_9 = 0)
% 3.34/1.58 |
% 3.34/1.58 | Equations (82) can reduce 80 to:
% 3.34/1.58 | (99) ~ (all_14_1_9 = 0)
% 3.34/1.58 |
% 3.34/1.58 | Simplifying 99 yields:
% 3.34/1.58 | (98) ~ (all_14_1_9 = 0)
% 3.34/1.58 |
% 3.34/1.58 | From (82) and (74) follows:
% 3.34/1.58 | (101) element(all_14_2_10, all_0_3_3) = 0
% 3.34/1.58 |
% 3.34/1.58 | Instantiating formula (6) with all_14_2_10, all_0_2_2, all_0_3_3 and discharging atoms set_equal(all_0_3_3, all_0_2_2) = 0, element(all_14_2_10, all_0_3_3) = 0, yields:
% 3.34/1.58 | (87) element(all_14_2_10, all_0_2_2) = 0
% 3.34/1.58 |
% 3.34/1.58 | Instantiating formula (3) with all_14_2_10, all_0_2_2, 0, all_14_1_9 and discharging atoms element(all_14_2_10, all_0_2_2) = all_14_1_9, element(all_14_2_10, all_0_2_2) = 0, yields:
% 3.34/1.58 | (85) all_14_1_9 = 0
% 3.34/1.58 |
% 3.34/1.58 | Equations (85) can reduce 98 to:
% 3.34/1.58 | (17) $false
% 3.34/1.58 |
% 3.34/1.58 |-The branch is then unsatisfiable
% 3.34/1.58 |-Branch two:
% 3.34/1.58 | (105) element(all_14_2_10, all_0_3_3) = all_14_1_9
% 3.34/1.58 | (106) all_14_0_8 = all_14_1_9
% 3.34/1.58 |
% 3.34/1.58 +-Applying beta-rule and splitting (75), into two cases.
% 3.34/1.58 |-Branch one:
% 3.34/1.58 | (81) ~ (all_14_0_8 = 0)
% 3.34/1.58 |
% 3.34/1.58 | Equations (106) can reduce 81 to:
% 3.34/1.58 | (98) ~ (all_14_1_9 = 0)
% 3.34/1.58 |
% 3.34/1.58 +-Applying beta-rule and splitting (76), into two cases.
% 3.34/1.58 |-Branch one:
% 3.34/1.58 | (82) all_14_0_8 = 0
% 3.34/1.58 |
% 3.34/1.58 | Combining equations (82,106) yields a new equation:
% 3.34/1.58 | (85) all_14_1_9 = 0
% 3.34/1.58 |
% 3.34/1.58 | Equations (85) can reduce 98 to:
% 3.34/1.58 | (17) $false
% 3.34/1.58 |
% 3.34/1.58 |-The branch is then unsatisfiable
% 3.34/1.58 |-Branch two:
% 3.34/1.58 | (81) ~ (all_14_0_8 = 0)
% 3.34/1.58 | (85) all_14_1_9 = 0
% 3.34/1.58 |
% 3.34/1.58 | Equations (85) can reduce 98 to:
% 3.34/1.58 | (17) $false
% 3.34/1.58 |
% 3.34/1.58 |-The branch is then unsatisfiable
% 3.34/1.58 |-Branch two:
% 3.34/1.58 | (82) all_14_0_8 = 0
% 3.34/1.58 | (98) ~ (all_14_1_9 = 0)
% 3.34/1.58 |
% 3.34/1.58 | Combining equations (82,106) yields a new equation:
% 3.34/1.58 | (85) all_14_1_9 = 0
% 3.34/1.58 |
% 3.34/1.58 | Equations (85) can reduce 98 to:
% 3.34/1.58 | (17) $false
% 3.34/1.58 |
% 3.34/1.58 |-The branch is then unsatisfiable
% 3.34/1.58 % SZS output end Proof for theBenchmark
% 3.34/1.58
% 3.34/1.58 972ms
%------------------------------------------------------------------------------