TSTP Solution File: SYN067+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 04:59:37 EDT 2022
% Result : Theorem 2.74s 1.40s
% Output : Proof 4.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 14:44:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.19/0.56 ____ _
% 0.19/0.56 ___ / __ \_____(_)___ ________ __________
% 0.19/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.56
% 0.19/0.56 A Theorem Prover for First-Order Logic
% 0.19/0.56 (ePrincess v.1.0)
% 0.19/0.56
% 0.19/0.56 (c) Philipp Rümmer, 2009-2015
% 0.19/0.56 (c) Peter Backeman, 2014-2015
% 0.19/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.56 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.56 Bug reports to peter@backeman.se
% 0.19/0.56
% 0.19/0.56 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.56
% 0.19/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.23/0.87 Prover 0: Preprocessing ...
% 1.41/0.95 Prover 0: Warning: ignoring some quantifiers
% 1.41/0.97 Prover 0: Constructing countermodel ...
% 1.52/1.05 Prover 0: gave up
% 1.52/1.05 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.80/1.09 Prover 1: Preprocessing ...
% 2.08/1.20 Prover 1: Constructing countermodel ...
% 2.74/1.40 Prover 1: proved (350ms)
% 2.74/1.40
% 2.74/1.40 No countermodel exists, formula is valid
% 2.74/1.40 % SZS status Theorem for theBenchmark
% 2.74/1.40
% 2.74/1.40 Generating proof ... found it (size 62)
% 4.14/1.82
% 4.14/1.82 % SZS output start Proof for theBenchmark
% 4.14/1.82 Assumed formulas after preprocessing and simplification:
% 4.14/1.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (big_p(a) = v0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (big_r(v9, v8) = v7) | ~ (big_r(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (big_p(v8) = v7) | ~ (big_p(v8) = v6)) & ((v0 = 0 & big_p(v1) = v2 & ! [v6] : ! [v7] : ! [v8] : ( ~ (big_r(v6, v8) = 0) | ~ (big_p(v6) = v7) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & big_r(v10, v9) = 0 & big_r(v6, v10) = 0 & big_p(v9) = 0) | ( ~ (v9 = 0) & big_p(v8) = v9))) & ! [v6] : ! [v7] : (v7 = 0 | ~ (big_p(v6) = v7) | ? [v8] : ? [v9] : (big_r(v9, v8) = 0 & big_r(v6, v9) = 0 & big_p(v8) = 0)) & ! [v6] : ! [v7] : ( ~ (big_r(v1, v7) = 0) | ~ (big_p(v6) = 0) | ? [v8] : ( ~ (v8 = 0) & big_r(v7, v6) = v8)) & ( ~ (v2 = 0) | (v5 = 0 & v4 = 0 & big_r(v1, v3) = 0 & big_p(v3) = 0))) | (v0 = 0 & big_p(v1) = v2 & ! [v6] : ! [v7] : (v7 = 0 | ~ (big_p(v6) = v7) | ? [v8] : ? [v9] : (big_r(v9, v8) = 0 & big_r(v6, v9) = 0 & big_p(v8) = 0)) & ! [v6] : ! [v7] : ( ~ (big_r(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & big_r(v9, v8) = 0 & big_r(v6, v9) = 0 & big_p(v8) = 0) | ( ~ (v8 = 0) & big_p(v7) = v8))) & ! [v6] : ! [v7] : ( ~ (big_r(v1, v7) = 0) | ~ (big_p(v6) = 0) | ? [v8] : ( ~ (v8 = 0) & big_r(v7, v6) = v8)) & ( ~ (v2 = 0) | (v5 = 0 & v4 = 0 & big_r(v1, v3) = 0 & big_p(v3) = 0)))))
% 4.14/1.85 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 4.14/1.85 | (1) big_p(a) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_r(v3, v2) = v1) | ~ (big_r(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ((all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_r(v0, v2) = 0) | ~ (big_p(v0) = v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v3 = 0) & big_p(v2) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0))) | (all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v2 = 0) & big_p(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0))))
% 4.14/1.85 |
% 4.14/1.85 | Applying alpha-rule on (1) yields:
% 4.14/1.86 | (2) big_p(a) = all_0_5_5
% 4.14/1.86 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_r(v3, v2) = v1) | ~ (big_r(v3, v2) = v0))
% 4.14/1.86 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 4.14/1.86 | (5) (all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_r(v0, v2) = 0) | ~ (big_p(v0) = v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v3 = 0) & big_p(v2) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0))) | (all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v2 = 0) & big_p(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0)))
% 4.14/1.86 |
% 4.14/1.86 +-Applying beta-rule and splitting (5), into two cases.
% 4.14/1.86 |-Branch one:
% 4.14/1.86 | (6) all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ( ~ (big_r(v0, v2) = 0) | ~ (big_p(v0) = v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v3 = 0) & big_p(v2) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0))
% 4.14/1.86 |
% 4.14/1.86 | Applying alpha-rule on (6) yields:
% 4.14/1.86 | (7) all_0_5_5 = 0
% 4.14/1.86 | (8) ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0)
% 4.14/1.86 | (9) big_p(all_0_4_4) = all_0_3_3
% 4.14/1.86 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0))
% 4.14/1.86 | (11) ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2))
% 4.14/1.86 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (big_r(v0, v2) = 0) | ~ (big_p(v0) = v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & big_r(v4, v3) = 0 & big_r(v0, v4) = 0 & big_p(v3) = 0) | ( ~ (v3 = 0) & big_p(v2) = v3)))
% 4.14/1.86 |
% 4.14/1.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4 and discharging atoms big_p(all_0_4_4) = all_0_3_3, yields:
% 4.14/1.86 | (13) all_0_3_3 = 0 | ? [v0] : ? [v1] : (big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0)
% 4.14/1.86 |
% 4.14/1.86 +-Applying beta-rule and splitting (8), into two cases.
% 4.14/1.86 |-Branch one:
% 4.14/1.86 | (14) ~ (all_0_3_3 = 0)
% 4.14/1.86 |
% 4.14/1.86 +-Applying beta-rule and splitting (13), into two cases.
% 4.14/1.86 |-Branch one:
% 4.14/1.86 | (15) all_0_3_3 = 0
% 4.14/1.86 |
% 4.14/1.86 | Equations (15) can reduce 14 to:
% 4.14/1.86 | (16) $false
% 4.14/1.86 |
% 4.14/1.86 |-The branch is then unsatisfiable
% 4.14/1.86 |-Branch two:
% 4.14/1.86 | (14) ~ (all_0_3_3 = 0)
% 4.14/1.87 | (18) ? [v0] : ? [v1] : (big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0)
% 4.14/1.87 |
% 4.14/1.87 | Instantiating (18) with all_22_0_6, all_22_1_7 yields:
% 4.14/1.87 | (19) big_r(all_22_0_6, all_22_1_7) = 0 & big_r(all_0_4_4, all_22_0_6) = 0 & big_p(all_22_1_7) = 0
% 4.14/1.87 |
% 4.14/1.87 | Applying alpha-rule on (19) yields:
% 4.14/1.87 | (20) big_r(all_22_0_6, all_22_1_7) = 0
% 4.14/1.87 | (21) big_r(all_0_4_4, all_22_0_6) = 0
% 4.14/1.87 | (22) big_p(all_22_1_7) = 0
% 4.14/1.87 |
% 4.14/1.87 | Instantiating formula (11) with all_22_0_6, all_22_1_7 and discharging atoms big_r(all_0_4_4, all_22_0_6) = 0, big_p(all_22_1_7) = 0, yields:
% 4.14/1.87 | (23) ? [v0] : ( ~ (v0 = 0) & big_r(all_22_0_6, all_22_1_7) = v0)
% 4.14/1.87 |
% 4.14/1.87 | Instantiating (23) with all_29_0_8 yields:
% 4.14/1.87 | (24) ~ (all_29_0_8 = 0) & big_r(all_22_0_6, all_22_1_7) = all_29_0_8
% 4.14/1.87 |
% 4.14/1.87 | Applying alpha-rule on (24) yields:
% 4.14/1.87 | (25) ~ (all_29_0_8 = 0)
% 4.14/1.87 | (26) big_r(all_22_0_6, all_22_1_7) = all_29_0_8
% 4.14/1.87 |
% 4.14/1.87 | Instantiating formula (3) with all_22_0_6, all_22_1_7, all_29_0_8, 0 and discharging atoms big_r(all_22_0_6, all_22_1_7) = all_29_0_8, big_r(all_22_0_6, all_22_1_7) = 0, yields:
% 4.14/1.87 | (27) all_29_0_8 = 0
% 4.14/1.87 |
% 4.14/1.87 | Equations (27) can reduce 25 to:
% 4.14/1.87 | (16) $false
% 4.14/1.87 |
% 4.14/1.87 |-The branch is then unsatisfiable
% 4.14/1.87 |-Branch two:
% 4.14/1.87 | (15) all_0_3_3 = 0
% 4.14/1.87 | (30) all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0
% 4.14/1.87 |
% 4.14/1.87 | Applying alpha-rule on (30) yields:
% 4.14/1.87 | (31) all_0_0_0 = 0
% 4.14/1.87 | (32) all_0_1_1 = 0
% 4.14/1.87 | (33) big_r(all_0_4_4, all_0_2_2) = 0
% 4.14/1.87 | (34) big_p(all_0_2_2) = 0
% 4.14/1.87 |
% 4.14/1.87 | From (15) and (9) follows:
% 4.14/1.87 | (35) big_p(all_0_4_4) = 0
% 4.14/1.87 |
% 4.14/1.87 | Instantiating formula (12) with all_0_2_2, 0, all_0_4_4 and discharging atoms big_r(all_0_4_4, all_0_2_2) = 0, big_p(all_0_4_4) = 0, yields:
% 4.14/1.87 | (36) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0) | ( ~ (v0 = 0) & big_p(all_0_2_2) = v0))
% 4.14/1.87 |
% 4.14/1.87 | Instantiating (36) with all_27_0_17, all_27_1_18, all_27_2_19, all_27_3_20, all_27_4_21 yields:
% 4.14/1.87 | (37) (all_27_0_17 = 0 & all_27_1_18 = 0 & all_27_2_19 = 0 & big_r(all_27_3_20, all_27_4_21) = 0 & big_r(all_0_4_4, all_27_3_20) = 0 & big_p(all_27_4_21) = 0) | ( ~ (all_27_4_21 = 0) & big_p(all_0_2_2) = all_27_4_21)
% 4.14/1.87 |
% 4.14/1.87 +-Applying beta-rule and splitting (37), into two cases.
% 4.14/1.87 |-Branch one:
% 4.14/1.87 | (38) all_27_0_17 = 0 & all_27_1_18 = 0 & all_27_2_19 = 0 & big_r(all_27_3_20, all_27_4_21) = 0 & big_r(all_0_4_4, all_27_3_20) = 0 & big_p(all_27_4_21) = 0
% 4.14/1.87 |
% 4.14/1.87 | Applying alpha-rule on (38) yields:
% 4.14/1.87 | (39) big_r(all_0_4_4, all_27_3_20) = 0
% 4.14/1.87 | (40) all_27_2_19 = 0
% 4.14/1.87 | (41) big_r(all_27_3_20, all_27_4_21) = 0
% 4.14/1.87 | (42) all_27_1_18 = 0
% 4.14/1.87 | (43) big_p(all_27_4_21) = 0
% 4.14/1.87 | (44) all_27_0_17 = 0
% 4.14/1.87 |
% 4.14/1.87 | Instantiating formula (11) with all_27_3_20, all_27_4_21 and discharging atoms big_r(all_0_4_4, all_27_3_20) = 0, big_p(all_27_4_21) = 0, yields:
% 4.14/1.87 | (45) ? [v0] : ( ~ (v0 = 0) & big_r(all_27_3_20, all_27_4_21) = v0)
% 4.14/1.87 |
% 4.14/1.87 | Instantiating (45) with all_39_0_23 yields:
% 4.14/1.87 | (46) ~ (all_39_0_23 = 0) & big_r(all_27_3_20, all_27_4_21) = all_39_0_23
% 4.14/1.87 |
% 4.14/1.87 | Applying alpha-rule on (46) yields:
% 4.14/1.87 | (47) ~ (all_39_0_23 = 0)
% 4.14/1.87 | (48) big_r(all_27_3_20, all_27_4_21) = all_39_0_23
% 4.14/1.87 |
% 4.14/1.87 | Instantiating formula (3) with all_27_3_20, all_27_4_21, all_39_0_23, 0 and discharging atoms big_r(all_27_3_20, all_27_4_21) = all_39_0_23, big_r(all_27_3_20, all_27_4_21) = 0, yields:
% 4.14/1.87 | (49) all_39_0_23 = 0
% 4.14/1.87 |
% 4.14/1.87 | Equations (49) can reduce 47 to:
% 4.14/1.87 | (16) $false
% 4.14/1.87 |
% 4.14/1.87 |-The branch is then unsatisfiable
% 4.14/1.87 |-Branch two:
% 4.14/1.87 | (51) ~ (all_27_4_21 = 0) & big_p(all_0_2_2) = all_27_4_21
% 4.14/1.87 |
% 4.14/1.87 | Applying alpha-rule on (51) yields:
% 4.14/1.87 | (52) ~ (all_27_4_21 = 0)
% 4.14/1.87 | (53) big_p(all_0_2_2) = all_27_4_21
% 4.14/1.87 |
% 4.14/1.87 | Instantiating formula (4) with all_0_2_2, all_27_4_21, 0 and discharging atoms big_p(all_0_2_2) = all_27_4_21, big_p(all_0_2_2) = 0, yields:
% 4.14/1.87 | (54) all_27_4_21 = 0
% 4.14/1.87 |
% 4.14/1.87 | Equations (54) can reduce 52 to:
% 4.14/1.87 | (16) $false
% 4.14/1.87 |
% 4.14/1.87 |-The branch is then unsatisfiable
% 4.14/1.87 |-Branch two:
% 4.14/1.87 | (56) all_0_5_5 = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (big_r(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v2 = 0) & big_p(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2)) & ( ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0))
% 4.14/1.88 |
% 4.14/1.88 | Applying alpha-rule on (56) yields:
% 4.14/1.88 | (7) all_0_5_5 = 0
% 4.14/1.88 | (8) ~ (all_0_3_3 = 0) | (all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0)
% 4.14/1.88 | (9) big_p(all_0_4_4) = all_0_3_3
% 4.14/1.88 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ? [v3] : (big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0))
% 4.14/1.88 | (61) ! [v0] : ! [v1] : ( ~ (big_r(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & big_r(v3, v2) = 0 & big_r(v0, v3) = 0 & big_p(v2) = 0) | ( ~ (v2 = 0) & big_p(v1) = v2)))
% 4.14/1.88 | (11) ! [v0] : ! [v1] : ( ~ (big_r(all_0_4_4, v1) = 0) | ~ (big_p(v0) = 0) | ? [v2] : ( ~ (v2 = 0) & big_r(v1, v0) = v2))
% 4.14/1.88 |
% 4.14/1.88 | Instantiating formula (10) with all_0_3_3, all_0_4_4 and discharging atoms big_p(all_0_4_4) = all_0_3_3, yields:
% 4.14/1.88 | (13) all_0_3_3 = 0 | ? [v0] : ? [v1] : (big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0)
% 4.14/1.88 |
% 4.14/1.88 +-Applying beta-rule and splitting (8), into two cases.
% 4.14/1.88 |-Branch one:
% 4.14/1.88 | (14) ~ (all_0_3_3 = 0)
% 4.14/1.88 |
% 4.14/1.88 +-Applying beta-rule and splitting (13), into two cases.
% 4.14/1.88 |-Branch one:
% 4.14/1.88 | (15) all_0_3_3 = 0
% 4.14/1.88 |
% 4.14/1.88 | Equations (15) can reduce 14 to:
% 4.14/1.88 | (16) $false
% 4.14/1.88 |
% 4.14/1.88 |-The branch is then unsatisfiable
% 4.14/1.88 |-Branch two:
% 4.14/1.88 | (14) ~ (all_0_3_3 = 0)
% 4.14/1.88 | (18) ? [v0] : ? [v1] : (big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0)
% 4.14/1.88 |
% 4.14/1.88 | Instantiating (18) with all_22_0_33, all_22_1_34 yields:
% 4.14/1.88 | (69) big_r(all_22_0_33, all_22_1_34) = 0 & big_r(all_0_4_4, all_22_0_33) = 0 & big_p(all_22_1_34) = 0
% 4.14/1.88 |
% 4.14/1.88 | Applying alpha-rule on (69) yields:
% 4.14/1.88 | (70) big_r(all_22_0_33, all_22_1_34) = 0
% 4.14/1.88 | (71) big_r(all_0_4_4, all_22_0_33) = 0
% 4.14/1.88 | (72) big_p(all_22_1_34) = 0
% 4.14/1.88 |
% 4.14/1.88 | Instantiating formula (11) with all_22_0_33, all_22_1_34 and discharging atoms big_r(all_0_4_4, all_22_0_33) = 0, big_p(all_22_1_34) = 0, yields:
% 4.14/1.88 | (73) ? [v0] : ( ~ (v0 = 0) & big_r(all_22_0_33, all_22_1_34) = v0)
% 4.14/1.88 |
% 4.14/1.88 | Instantiating (73) with all_29_0_35 yields:
% 4.14/1.88 | (74) ~ (all_29_0_35 = 0) & big_r(all_22_0_33, all_22_1_34) = all_29_0_35
% 4.14/1.88 |
% 4.14/1.88 | Applying alpha-rule on (74) yields:
% 4.14/1.88 | (75) ~ (all_29_0_35 = 0)
% 4.14/1.88 | (76) big_r(all_22_0_33, all_22_1_34) = all_29_0_35
% 4.14/1.88 |
% 4.14/1.88 | Instantiating formula (3) with all_22_0_33, all_22_1_34, all_29_0_35, 0 and discharging atoms big_r(all_22_0_33, all_22_1_34) = all_29_0_35, big_r(all_22_0_33, all_22_1_34) = 0, yields:
% 4.14/1.88 | (77) all_29_0_35 = 0
% 4.14/1.88 |
% 4.14/1.88 | Equations (77) can reduce 75 to:
% 4.14/1.88 | (16) $false
% 4.14/1.88 |
% 4.14/1.88 |-The branch is then unsatisfiable
% 4.14/1.88 |-Branch two:
% 4.14/1.88 | (15) all_0_3_3 = 0
% 4.14/1.88 | (30) all_0_0_0 = 0 & all_0_1_1 = 0 & big_r(all_0_4_4, all_0_2_2) = 0 & big_p(all_0_2_2) = 0
% 4.14/1.88 |
% 4.14/1.88 | Applying alpha-rule on (30) yields:
% 4.14/1.88 | (31) all_0_0_0 = 0
% 4.14/1.88 | (32) all_0_1_1 = 0
% 4.14/1.88 | (33) big_r(all_0_4_4, all_0_2_2) = 0
% 4.14/1.88 | (34) big_p(all_0_2_2) = 0
% 4.14/1.88 |
% 4.14/1.88 | Instantiating formula (61) with all_0_2_2, all_0_4_4 and discharging atoms big_r(all_0_4_4, all_0_2_2) = 0, yields:
% 4.14/1.88 | (36) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & big_r(v1, v0) = 0 & big_r(all_0_4_4, v1) = 0 & big_p(v0) = 0) | ( ~ (v0 = 0) & big_p(all_0_2_2) = v0))
% 4.14/1.88 |
% 4.14/1.88 | Instantiating (36) with all_27_0_49, all_27_1_50, all_27_2_51, all_27_3_52, all_27_4_53 yields:
% 4.14/1.88 | (86) (all_27_0_49 = 0 & all_27_1_50 = 0 & all_27_2_51 = 0 & big_r(all_27_3_52, all_27_4_53) = 0 & big_r(all_0_4_4, all_27_3_52) = 0 & big_p(all_27_4_53) = 0) | ( ~ (all_27_4_53 = 0) & big_p(all_0_2_2) = all_27_4_53)
% 4.14/1.88 |
% 4.14/1.88 +-Applying beta-rule and splitting (86), into two cases.
% 4.14/1.88 |-Branch one:
% 4.14/1.88 | (87) all_27_0_49 = 0 & all_27_1_50 = 0 & all_27_2_51 = 0 & big_r(all_27_3_52, all_27_4_53) = 0 & big_r(all_0_4_4, all_27_3_52) = 0 & big_p(all_27_4_53) = 0
% 4.14/1.88 |
% 4.14/1.88 | Applying alpha-rule on (87) yields:
% 4.14/1.88 | (88) big_r(all_27_3_52, all_27_4_53) = 0
% 4.14/1.88 | (89) all_27_2_51 = 0
% 4.14/1.88 | (90) all_27_0_49 = 0
% 4.14/1.88 | (91) all_27_1_50 = 0
% 4.14/1.88 | (92) big_p(all_27_4_53) = 0
% 4.14/1.88 | (93) big_r(all_0_4_4, all_27_3_52) = 0
% 4.14/1.89 |
% 4.14/1.89 | Instantiating formula (11) with all_27_3_52, all_27_4_53 and discharging atoms big_r(all_0_4_4, all_27_3_52) = 0, big_p(all_27_4_53) = 0, yields:
% 4.14/1.89 | (94) ? [v0] : ( ~ (v0 = 0) & big_r(all_27_3_52, all_27_4_53) = v0)
% 4.14/1.89 |
% 4.14/1.89 | Instantiating (94) with all_39_0_55 yields:
% 4.14/1.89 | (95) ~ (all_39_0_55 = 0) & big_r(all_27_3_52, all_27_4_53) = all_39_0_55
% 4.14/1.89 |
% 4.14/1.89 | Applying alpha-rule on (95) yields:
% 4.14/1.89 | (96) ~ (all_39_0_55 = 0)
% 4.14/1.89 | (97) big_r(all_27_3_52, all_27_4_53) = all_39_0_55
% 4.14/1.89 |
% 4.14/1.89 | Instantiating formula (3) with all_27_3_52, all_27_4_53, all_39_0_55, 0 and discharging atoms big_r(all_27_3_52, all_27_4_53) = all_39_0_55, big_r(all_27_3_52, all_27_4_53) = 0, yields:
% 4.14/1.89 | (98) all_39_0_55 = 0
% 4.14/1.89 |
% 4.14/1.89 | Equations (98) can reduce 96 to:
% 4.14/1.89 | (16) $false
% 4.14/1.89 |
% 4.14/1.89 |-The branch is then unsatisfiable
% 4.14/1.89 |-Branch two:
% 4.14/1.89 | (100) ~ (all_27_4_53 = 0) & big_p(all_0_2_2) = all_27_4_53
% 4.14/1.89 |
% 4.14/1.89 | Applying alpha-rule on (100) yields:
% 4.14/1.89 | (101) ~ (all_27_4_53 = 0)
% 4.14/1.89 | (102) big_p(all_0_2_2) = all_27_4_53
% 4.14/1.89 |
% 4.14/1.89 | Instantiating formula (4) with all_0_2_2, all_27_4_53, 0 and discharging atoms big_p(all_0_2_2) = all_27_4_53, big_p(all_0_2_2) = 0, yields:
% 4.14/1.89 | (103) all_27_4_53 = 0
% 4.14/1.89 |
% 4.14/1.89 | Equations (103) can reduce 101 to:
% 4.14/1.89 | (16) $false
% 4.14/1.89 |
% 4.14/1.89 |-The branch is then unsatisfiable
% 4.14/1.89 % SZS output end Proof for theBenchmark
% 4.14/1.89
% 4.14/1.89 1317ms
%------------------------------------------------------------------------------