TSTP Solution File: LCL658+1.001 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL658+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 09:37:53 EDT 2022
% Result : Theorem 4.24s 1.62s
% Output : Proof 6.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL658+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n004.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 : Sat Jul 2 15:56:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ____ _
% 0.19/0.60 ___ / __ \_____(_)___ ________ __________
% 0.19/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic
% 0.19/0.60 (ePrincess v.1.0)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2015
% 0.19/0.60 (c) Peter Backeman, 2014-2015
% 0.19/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.60 Bug reports to peter@backeman.se
% 0.19/0.60
% 0.19/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.70/0.93 Prover 0: Preprocessing ...
% 1.91/1.05 Prover 0: Warning: ignoring some quantifiers
% 2.08/1.07 Prover 0: Constructing countermodel ...
% 4.24/1.62 Prover 0: proved (975ms)
% 4.24/1.62
% 4.24/1.62 No countermodel exists, formula is valid
% 4.24/1.62 % SZS status Theorem for theBenchmark
% 4.24/1.62
% 4.24/1.62 Generating proof ... Warning: ignoring some quantifiers
% 5.86/1.97 found it (size 41)
% 5.86/1.97
% 5.86/1.97 % SZS output start Proof for theBenchmark
% 5.86/1.97 Assumed formulas after preprocessing and simplification:
% 5.86/1.97 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (r1(v1, v3) & r1(v1, v2) & r1(v0, v1) & ~ p1(v3) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v7) | ? [v8] : (r1(v5, v8) & ~ p1(v8))) & ! [v4] : ! [v5] : ! [v6] : ( ~ p1(v4) | ~ r1(v4, v6) | ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v6) | ? [v7] : ? [v8] : ((p1(v7) & r1(v7, v8) & r1(v5, v7) & ~ p1(v8)) | (p1(v7) & r1(v7, v8) & r1(v4, v7) & ~ p1(v8) & ! [v9] : ! [v10] : ! [v11] : ( ~ p1(v10) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v7, v9) | p1(v11) | p1(v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ p1(v10) | ~ r1(v10, v11) | ~ r1(v9, v10) | ~ r1(v7, v9) | p1(v11) | ? [v12] : (r1(v9, v12) & ~ p1(v12)))))) & ! [v4] : ! [v5] : ! [v6] : ( ~ r1(v5, v6) | ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v6) | ? [v7] : ? [v8] : ((p1(v7) & r1(v7, v8) & r1(v6, v7) & ~ p1(v8)) | (r1(v4, v7) & ~ p1(v7) & ! [v9] : ! [v10] : ( ~ p1(v9) | ~ r1(v9, v10) | ~ r1(v7, v9) | p1(v10))))) & ! [v4] : ! [v5] : ( ~ r1(v4, v5) | ~ r1(v0, v4) | p1(v4) | ? [v6] : ((r1(v5, v6) & ~ p1(v6)) | (r1(v4, v6) & ~ p1(v6) & ! [v7] : ! [v8] : ( ~ p1(v7) | ~ r1(v7, v8) | ~ r1(v6, v7) | p1(v8))))) & ! [v4] : ( ~ r1(v2, v4) | p1(v4)) & ! [v4] : ( ~ r1(v1, v4) | p1(v4) | ? [v5] : ? [v6] : (p1(v5) & r1(v5, v6) & r1(v4, v5) & ~ p1(v6))) & ? [v4] : r1(v4, v4))
% 6.12/1.99 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 6.12/1.99 | (1) r1(all_0_2_2, all_0_0_0) & r1(all_0_2_2, all_0_1_1) & r1(all_0_3_3, all_0_2_2) & ~ p1(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_3_3, v0) | p1(v3) | ? [v4] : (r1(v1, v4) & ~ p1(v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_0_3_3, v0) | p1(v2) | ? [v3] : ? [v4] : ((p1(v3) & r1(v3, v4) & r1(v1, v3) & ~ p1(v4)) | (p1(v3) & r1(v3, v4) & r1(v0, v3) & ~ p1(v4) & ! [v5] : ! [v6] : ! [v7] : ( ~ p1(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v7) | p1(v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ p1(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v7) | ? [v8] : (r1(v5, v8) & ~ p1(v8)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_3_3, v0) | p1(v2) | ? [v3] : ? [v4] : ((p1(v3) & r1(v3, v4) & r1(v2, v3) & ~ p1(v4)) | (r1(v0, v3) & ~ p1(v3) & ! [v5] : ! [v6] : ( ~ p1(v5) | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v6))))) & ! [v0] : ! [v1] : ( ~ r1(v0, v1) | ~ r1(all_0_3_3, v0) | p1(v0) | ? [v2] : ((r1(v1, v2) & ~ p1(v2)) | (r1(v0, v2) & ~ p1(v2) & ! [v3] : ! [v4] : ( ~ p1(v3) | ~ r1(v3, v4) | ~ r1(v2, v3) | p1(v4))))) & ! [v0] : ( ~ r1(all_0_1_1, v0) | p1(v0)) & ! [v0] : ( ~ r1(all_0_2_2, v0) | p1(v0) | ? [v1] : ? [v2] : (p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ p1(v2))) & ? [v0] : r1(v0, v0)
% 6.12/1.99 |
% 6.12/1.99 | Applying alpha-rule on (1) yields:
% 6.12/1.99 | (2) r1(all_0_3_3, all_0_2_2)
% 6.12/1.99 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v0) | ~ r1(v0, v2) | ~ r1(v0, v1) | ~ r1(all_0_3_3, v0) | p1(v2) | ? [v3] : ? [v4] : ((p1(v3) & r1(v3, v4) & r1(v1, v3) & ~ p1(v4)) | (p1(v3) & r1(v3, v4) & r1(v0, v3) & ~ p1(v4) & ! [v5] : ! [v6] : ! [v7] : ( ~ p1(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v7) | p1(v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ p1(v6) | ~ r1(v6, v7) | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v7) | ? [v8] : (r1(v5, v8) & ~ p1(v8))))))
% 6.12/2.00 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_3_3, v0) | p1(v2) | ? [v3] : ? [v4] : ((p1(v3) & r1(v3, v4) & r1(v2, v3) & ~ p1(v4)) | (r1(v0, v3) & ~ p1(v3) & ! [v5] : ! [v6] : ( ~ p1(v5) | ~ r1(v5, v6) | ~ r1(v3, v5) | p1(v6)))))
% 6.12/2.00 | (5) ! [v0] : ! [v1] : ( ~ r1(v0, v1) | ~ r1(all_0_3_3, v0) | p1(v0) | ? [v2] : ((r1(v1, v2) & ~ p1(v2)) | (r1(v0, v2) & ~ p1(v2) & ! [v3] : ! [v4] : ( ~ p1(v3) | ~ r1(v3, v4) | ~ r1(v2, v3) | p1(v4)))))
% 6.12/2.00 | (6) ! [v0] : ( ~ r1(all_0_2_2, v0) | p1(v0) | ? [v1] : ? [v2] : (p1(v1) & r1(v1, v2) & r1(v0, v1) & ~ p1(v2)))
% 6.12/2.00 | (7) ! [v0] : ( ~ r1(all_0_1_1, v0) | p1(v0))
% 6.12/2.00 | (8) r1(all_0_2_2, all_0_1_1)
% 6.12/2.00 | (9) ? [v0] : r1(v0, v0)
% 6.12/2.00 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ r1(v2, v3) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_0_3_3, v0) | p1(v3) | ? [v4] : (r1(v1, v4) & ~ p1(v4)))
% 6.12/2.00 | (11) ~ p1(all_0_0_0)
% 6.12/2.00 | (12) r1(all_0_2_2, all_0_0_0)
% 6.12/2.00 |
% 6.12/2.00 | Instantiating formula (5) with all_0_0_0, all_0_2_2 and discharging atoms r1(all_0_2_2, all_0_0_0), r1(all_0_3_3, all_0_2_2), yields:
% 6.12/2.00 | (13) p1(all_0_2_2) | ? [v0] : ((r1(all_0_0_0, v0) & ~ p1(v0)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | p1(v2))))
% 6.12/2.00 |
% 6.12/2.00 | Instantiating formula (5) with all_0_1_1, all_0_2_2 and discharging atoms r1(all_0_2_2, all_0_1_1), r1(all_0_3_3, all_0_2_2), yields:
% 6.12/2.00 | (14) p1(all_0_2_2) | ? [v0] : ((r1(all_0_1_1, v0) & ~ p1(v0)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | p1(v2))))
% 6.12/2.00 |
% 6.12/2.00 +-Applying beta-rule and splitting (13), into two cases.
% 6.12/2.00 |-Branch one:
% 6.12/2.00 | (15) p1(all_0_2_2)
% 6.12/2.00 |
% 6.12/2.00 | Instantiating formula (3) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms p1(all_0_2_2), r1(all_0_2_2, all_0_0_0), r1(all_0_2_2, all_0_1_1), r1(all_0_3_3, all_0_2_2), ~ p1(all_0_0_0), yields:
% 6.12/2.00 | (16) ? [v0] : ? [v1] : ((p1(v0) & r1(v0, v1) & r1(all_0_1_1, v0) & ~ p1(v1)) | (p1(v0) & r1(v0, v1) & r1(all_0_2_2, v0) & ~ p1(v1) & ! [v2] : ! [v3] : ! [v4] : ( ~ p1(v3) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | p1(v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ p1(v3) | ~ r1(v3, v4) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v4) | ? [v5] : (r1(v2, v5) & ~ p1(v5)))))
% 6.12/2.00 |
% 6.12/2.00 | Instantiating (16) with all_32_0_10, all_32_1_11 yields:
% 6.12/2.00 | (17) (p1(all_32_1_11) & r1(all_32_1_11, all_32_0_10) & r1(all_0_1_1, all_32_1_11) & ~ p1(all_32_0_10)) | (p1(all_32_1_11) & r1(all_32_1_11, all_32_0_10) & r1(all_0_2_2, all_32_1_11) & ~ p1(all_32_0_10) & ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_32_1_11, v0) | p1(v2) | p1(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_32_1_11, v0) | p1(v2) | ? [v3] : (r1(v0, v3) & ~ p1(v3))))
% 6.12/2.01 |
% 6.12/2.01 +-Applying beta-rule and splitting (17), into two cases.
% 6.12/2.01 |-Branch one:
% 6.12/2.01 | (18) p1(all_32_1_11) & r1(all_32_1_11, all_32_0_10) & r1(all_0_1_1, all_32_1_11) & ~ p1(all_32_0_10)
% 6.12/2.01 |
% 6.12/2.01 | Applying alpha-rule on (18) yields:
% 6.12/2.01 | (19) p1(all_32_1_11)
% 6.12/2.01 | (20) r1(all_32_1_11, all_32_0_10)
% 6.12/2.01 | (21) r1(all_0_1_1, all_32_1_11)
% 6.12/2.01 | (22) ~ p1(all_32_0_10)
% 6.12/2.01 |
% 6.12/2.01 | Instantiating formula (10) with all_32_0_10, all_32_1_11, all_0_1_1, all_0_2_2 and discharging atoms r1(all_32_1_11, all_32_0_10), r1(all_0_1_1, all_32_1_11), r1(all_0_2_2, all_0_1_1), r1(all_0_3_3, all_0_2_2), ~ p1(all_32_0_10), yields:
% 6.12/2.01 | (23) ? [v0] : (r1(all_0_1_1, v0) & ~ p1(v0))
% 6.12/2.01 |
% 6.12/2.01 | Instantiating (23) with all_55_0_14 yields:
% 6.12/2.01 | (24) r1(all_0_1_1, all_55_0_14) & ~ p1(all_55_0_14)
% 6.12/2.01 |
% 6.12/2.01 | Applying alpha-rule on (24) yields:
% 6.12/2.01 | (25) r1(all_0_1_1, all_55_0_14)
% 6.12/2.01 | (26) ~ p1(all_55_0_14)
% 6.12/2.01 |
% 6.12/2.01 | Instantiating formula (7) with all_55_0_14 and discharging atoms r1(all_0_1_1, all_55_0_14), ~ p1(all_55_0_14), yields:
% 6.12/2.01 | (27) $false
% 6.12/2.01 |
% 6.12/2.01 |-The branch is then unsatisfiable
% 6.12/2.01 |-Branch two:
% 6.12/2.01 | (28) p1(all_32_1_11) & r1(all_32_1_11, all_32_0_10) & r1(all_0_2_2, all_32_1_11) & ~ p1(all_32_0_10) & ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_32_1_11, v0) | p1(v2) | p1(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_32_1_11, v0) | p1(v2) | ? [v3] : (r1(v0, v3) & ~ p1(v3)))
% 6.12/2.01 |
% 6.12/2.01 | Applying alpha-rule on (28) yields:
% 6.12/2.01 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_32_1_11, v0) | p1(v2) | ? [v3] : (r1(v0, v3) & ~ p1(v3)))
% 6.12/2.01 | (20) r1(all_32_1_11, all_32_0_10)
% 6.12/2.01 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | ~ r1(all_32_1_11, v0) | p1(v2) | p1(v0))
% 6.12/2.01 | (22) ~ p1(all_32_0_10)
% 6.12/2.01 | (33) r1(all_0_2_2, all_32_1_11)
% 6.12/2.01 | (19) p1(all_32_1_11)
% 6.12/2.01 |
% 6.12/2.01 | Instantiating formula (4) with all_32_0_10, all_32_1_11, all_0_2_2 and discharging atoms r1(all_32_1_11, all_32_0_10), r1(all_0_2_2, all_32_1_11), r1(all_0_3_3, all_0_2_2), ~ p1(all_32_0_10), yields:
% 6.12/2.01 | (35) ? [v0] : ? [v1] : ((p1(v0) & r1(v0, v1) & r1(all_32_0_10, v0) & ~ p1(v1)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v2] : ! [v3] : ( ~ p1(v2) | ~ r1(v2, v3) | ~ r1(v0, v2) | p1(v3))))
% 6.12/2.01 |
% 6.12/2.01 | Instantiating (35) with all_57_0_17, all_57_1_18 yields:
% 6.12/2.01 | (36) (p1(all_57_1_18) & r1(all_57_1_18, all_57_0_17) & r1(all_32_0_10, all_57_1_18) & ~ p1(all_57_0_17)) | (r1(all_0_2_2, all_57_1_18) & ~ p1(all_57_1_18) & ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_57_1_18, v0) | p1(v1)))
% 6.12/2.01 |
% 6.12/2.01 +-Applying beta-rule and splitting (36), into two cases.
% 6.12/2.01 |-Branch one:
% 6.12/2.01 | (37) p1(all_57_1_18) & r1(all_57_1_18, all_57_0_17) & r1(all_32_0_10, all_57_1_18) & ~ p1(all_57_0_17)
% 6.12/2.01 |
% 6.12/2.01 | Applying alpha-rule on (37) yields:
% 6.12/2.01 | (38) p1(all_57_1_18)
% 6.12/2.01 | (39) r1(all_57_1_18, all_57_0_17)
% 6.12/2.01 | (40) r1(all_32_0_10, all_57_1_18)
% 6.12/2.01 | (41) ~ p1(all_57_0_17)
% 6.12/2.01 |
% 6.12/2.01 | Instantiating formula (31) with all_57_0_17, all_57_1_18, all_32_0_10 and discharging atoms p1(all_57_1_18), r1(all_57_1_18, all_57_0_17), r1(all_32_0_10, all_57_1_18), r1(all_32_1_11, all_32_0_10), ~ p1(all_57_0_17), ~ p1(all_32_0_10), yields:
% 6.12/2.01 | (27) $false
% 6.12/2.01 |
% 6.12/2.01 |-The branch is then unsatisfiable
% 6.12/2.01 |-Branch two:
% 6.12/2.01 | (43) r1(all_0_2_2, all_57_1_18) & ~ p1(all_57_1_18) & ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_57_1_18, v0) | p1(v1))
% 6.12/2.01 |
% 6.12/2.01 | Applying alpha-rule on (43) yields:
% 6.12/2.01 | (44) r1(all_0_2_2, all_57_1_18)
% 6.12/2.02 | (45) ~ p1(all_57_1_18)
% 6.12/2.02 | (46) ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_57_1_18, v0) | p1(v1))
% 6.12/2.02 |
% 6.12/2.02 | Instantiating formula (6) with all_57_1_18 and discharging atoms r1(all_0_2_2, all_57_1_18), ~ p1(all_57_1_18), yields:
% 6.12/2.02 | (47) ? [v0] : ? [v1] : (p1(v0) & r1(v0, v1) & r1(all_57_1_18, v0) & ~ p1(v1))
% 6.12/2.02 |
% 6.12/2.02 | Instantiating (47) with all_96_0_25, all_96_1_26 yields:
% 6.12/2.02 | (48) p1(all_96_1_26) & r1(all_96_1_26, all_96_0_25) & r1(all_57_1_18, all_96_1_26) & ~ p1(all_96_0_25)
% 6.12/2.02 |
% 6.12/2.02 | Applying alpha-rule on (48) yields:
% 6.12/2.02 | (49) p1(all_96_1_26)
% 6.12/2.02 | (50) r1(all_96_1_26, all_96_0_25)
% 6.12/2.02 | (51) r1(all_57_1_18, all_96_1_26)
% 6.12/2.02 | (52) ~ p1(all_96_0_25)
% 6.12/2.02 |
% 6.12/2.02 | Instantiating formula (46) with all_96_0_25, all_96_1_26 and discharging atoms p1(all_96_1_26), r1(all_96_1_26, all_96_0_25), r1(all_57_1_18, all_96_1_26), ~ p1(all_96_0_25), yields:
% 6.12/2.02 | (27) $false
% 6.12/2.02 |
% 6.12/2.02 |-The branch is then unsatisfiable
% 6.12/2.02 |-Branch two:
% 6.12/2.02 | (54) ~ p1(all_0_2_2)
% 6.12/2.02 | (55) ? [v0] : ((r1(all_0_0_0, v0) & ~ p1(v0)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | p1(v2))))
% 6.12/2.02 |
% 6.12/2.02 +-Applying beta-rule and splitting (14), into two cases.
% 6.12/2.02 |-Branch one:
% 6.12/2.02 | (15) p1(all_0_2_2)
% 6.12/2.02 |
% 6.12/2.02 | Using (15) and (54) yields:
% 6.12/2.02 | (27) $false
% 6.12/2.02 |
% 6.12/2.02 |-The branch is then unsatisfiable
% 6.12/2.02 |-Branch two:
% 6.12/2.02 | (54) ~ p1(all_0_2_2)
% 6.12/2.02 | (59) ? [v0] : ((r1(all_0_1_1, v0) & ~ p1(v0)) | (r1(all_0_2_2, v0) & ~ p1(v0) & ! [v1] : ! [v2] : ( ~ p1(v1) | ~ r1(v1, v2) | ~ r1(v0, v1) | p1(v2))))
% 6.12/2.02 |
% 6.12/2.02 | Instantiating (59) with all_32_0_36 yields:
% 6.12/2.02 | (60) (r1(all_0_1_1, all_32_0_36) & ~ p1(all_32_0_36)) | (r1(all_0_2_2, all_32_0_36) & ~ p1(all_32_0_36) & ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_32_0_36, v0) | p1(v1)))
% 6.12/2.02 |
% 6.12/2.02 +-Applying beta-rule and splitting (60), into two cases.
% 6.12/2.02 |-Branch one:
% 6.12/2.02 | (61) r1(all_0_1_1, all_32_0_36) & ~ p1(all_32_0_36)
% 6.12/2.02 |
% 6.12/2.02 | Applying alpha-rule on (61) yields:
% 6.12/2.02 | (62) r1(all_0_1_1, all_32_0_36)
% 6.12/2.02 | (63) ~ p1(all_32_0_36)
% 6.12/2.02 |
% 6.12/2.02 | Instantiating formula (7) with all_32_0_36 and discharging atoms r1(all_0_1_1, all_32_0_36), ~ p1(all_32_0_36), yields:
% 6.12/2.02 | (27) $false
% 6.12/2.02 |
% 6.12/2.02 |-The branch is then unsatisfiable
% 6.12/2.02 |-Branch two:
% 6.12/2.02 | (65) r1(all_0_2_2, all_32_0_36) & ~ p1(all_32_0_36) & ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_32_0_36, v0) | p1(v1))
% 6.12/2.02 |
% 6.12/2.02 | Applying alpha-rule on (65) yields:
% 6.12/2.02 | (66) r1(all_0_2_2, all_32_0_36)
% 6.12/2.02 | (63) ~ p1(all_32_0_36)
% 6.12/2.02 | (68) ! [v0] : ! [v1] : ( ~ p1(v0) | ~ r1(v0, v1) | ~ r1(all_32_0_36, v0) | p1(v1))
% 6.12/2.02 |
% 6.12/2.02 | Instantiating formula (6) with all_32_0_36 and discharging atoms r1(all_0_2_2, all_32_0_36), ~ p1(all_32_0_36), yields:
% 6.12/2.02 | (69) ? [v0] : ? [v1] : (p1(v0) & r1(v0, v1) & r1(all_32_0_36, v0) & ~ p1(v1))
% 6.12/2.02 |
% 6.12/2.02 | Instantiating (69) with all_68_0_39, all_68_1_40 yields:
% 6.12/2.02 | (70) p1(all_68_1_40) & r1(all_68_1_40, all_68_0_39) & r1(all_32_0_36, all_68_1_40) & ~ p1(all_68_0_39)
% 6.12/2.02 |
% 6.12/2.02 | Applying alpha-rule on (70) yields:
% 6.12/2.02 | (71) p1(all_68_1_40)
% 6.12/2.02 | (72) r1(all_68_1_40, all_68_0_39)
% 6.12/2.02 | (73) r1(all_32_0_36, all_68_1_40)
% 6.12/2.03 | (74) ~ p1(all_68_0_39)
% 6.12/2.03 |
% 6.12/2.03 | Instantiating formula (68) with all_68_0_39, all_68_1_40 and discharging atoms p1(all_68_1_40), r1(all_68_1_40, all_68_0_39), r1(all_32_0_36, all_68_1_40), ~ p1(all_68_0_39), yields:
% 6.12/2.03 | (27) $false
% 6.12/2.03 |
% 6.12/2.03 |-The branch is then unsatisfiable
% 6.12/2.03 % SZS output end Proof for theBenchmark
% 6.12/2.03
% 6.12/2.03 1418ms
%------------------------------------------------------------------------------