TSTP Solution File: LCL897+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL897+1 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 09:40:03 EDT 2022
% Result : Theorem 2.82s 1.34s
% Output : Proof 4.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL897+1 : TPTP v8.1.0. Released v5.5.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n005.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 : Sat Jul 2 22:06:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.31/0.87 Prover 0: Preprocessing ...
% 1.68/1.04 Prover 0: Constructing countermodel ...
% 2.82/1.34 Prover 0: proved (699ms)
% 2.82/1.34
% 2.82/1.34 No countermodel exists, formula is valid
% 2.82/1.34 % SZS status Theorem for theBenchmark
% 2.82/1.34
% 2.82/1.34 Generating proof ... found it (size 36)
% 4.43/1.72
% 4.43/1.72 % SZS output start Proof for theBenchmark
% 4.43/1.72 Assumed formulas after preprocessing and simplification:
% 4.43/1.72 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v3) & ==>(v1, c) = v2 & ==>(b, c) = v4 & ==>(a, v5) = v6 & ==>(a, b) = v0 & +(v1, v2) = v3 & +(b, v4) = v5 & +(a, v6) = v7 & +(a, v0) = v1 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (==>(v11, v10) = v12) | ~ (+(v8, v9) = v11) | ? [v13] : (==>(v9, v10) = v13 & ==>(v8, v13) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (==>(v9, v10) = v11) | ~ (==>(v8, v11) = v12) | ? [v13] : (==>(v13, v10) = v12 & +(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (+(v11, v10) = v12) | ~ (+(v8, v9) = v11) | ? [v13] : (+(v9, v10) = v13 & +(v8, v13) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (+(v9, v10) = v11) | ~ (+(v8, v11) = v12) | ? [v13] : (+(v13, v10) = v12 & +(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (==>(v11, v10) = v9) | ~ (==>(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (+(v11, v10) = v9) | ~ (+(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (==>(v9, v8) = v10) | ~ (+(v9, v10) = v11) | ? [v12] : (==>(v8, v9) = v12 & +(v8, v12) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (==>(v8, v9) = v10) | ~ (+(v8, v10) = v11) | ? [v12] : (==>(v9, v8) = v12 & +(v9, v12) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (+(v9, v8) = v10) | +(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (+(v8, v9) = v10) | +(v9, v8) = v10) & ! [v8] : ! [v9] : (v9 = v8 | ~ (==>(0, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (+(v8, 0) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (==>(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (==>(v8, 0) = v9)))
% 4.43/1.78 | 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:
% 4.43/1.78 | (1) ~ (all_0_0_0 = all_0_4_4) & ==>(all_0_6_6, c) = all_0_5_5 & ==>(b, c) = all_0_3_3 & ==>(a, all_0_2_2) = all_0_1_1 & ==>(a, b) = all_0_7_7 & +(all_0_6_6, all_0_5_5) = all_0_4_4 & +(b, all_0_3_3) = all_0_2_2 & +(a, all_0_1_1) = all_0_0_0 & +(a, all_0_7_7) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (==>(v3, v2) = v4) | ~ (+(v0, v1) = v3) | ? [v5] : (==>(v1, v2) = v5 & ==>(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (==>(v1, v2) = v3) | ~ (==>(v0, v3) = v4) | ? [v5] : (==>(v5, v2) = v4 & +(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (+(v3, v2) = v4) | ~ (+(v0, v1) = v3) | ? [v5] : (+(v1, v2) = v5 & +(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (+(v1, v2) = v3) | ~ (+(v0, v3) = v4) | ? [v5] : (+(v5, v2) = v4 & +(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (==>(v3, v2) = v1) | ~ (==>(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (+(v3, v2) = v1) | ~ (+(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (==>(v1, v0) = v2) | ~ (+(v1, v2) = v3) | ? [v4] : (==>(v0, v1) = v4 & +(v0, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (==>(v0, v1) = v2) | ~ (+(v0, v2) = v3) | ? [v4] : (==>(v1, v0) = v4 & +(v1, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (+(v1, v0) = v2) | +(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (+(v0, v1) = v2) | +(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (==>(0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (+(v0, 0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (==>(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (==>(v0, 0) = v1))
% 4.72/1.79 |
% 4.72/1.79 | Applying alpha-rule on (1) yields:
% 4.72/1.79 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (+(v3, v2) = v1) | ~ (+(v3, v2) = v0))
% 4.72/1.79 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (==>(v0, v1) = v2) | ~ (+(v0, v2) = v3) | ? [v4] : (==>(v1, v0) = v4 & +(v1, v4) = v3))
% 4.72/1.79 | (4) +(all_0_6_6, all_0_5_5) = all_0_4_4
% 4.72/1.79 | (5) +(a, all_0_1_1) = all_0_0_0
% 4.72/1.79 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (==>(v3, v2) = v4) | ~ (+(v0, v1) = v3) | ? [v5] : (==>(v1, v2) = v5 & ==>(v0, v5) = v4))
% 4.72/1.79 | (7) ==>(all_0_6_6, c) = all_0_5_5
% 4.72/1.79 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (+(v3, v2) = v4) | ~ (+(v0, v1) = v3) | ? [v5] : (+(v1, v2) = v5 & +(v0, v5) = v4))
% 4.72/1.79 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (+(v1, v2) = v3) | ~ (+(v0, v3) = v4) | ? [v5] : (+(v5, v2) = v4 & +(v0, v1) = v5))
% 4.72/1.79 | (10) +(b, all_0_3_3) = all_0_2_2
% 4.72/1.79 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (==>(v0, 0) = v1))
% 4.72/1.79 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (==>(v1, v2) = v3) | ~ (==>(v0, v3) = v4) | ? [v5] : (==>(v5, v2) = v4 & +(v0, v1) = v5))
% 4.72/1.79 | (13) ==>(b, c) = all_0_3_3
% 4.72/1.79 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (==>(v3, v2) = v1) | ~ (==>(v3, v2) = v0))
% 4.72/1.79 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (==>(v0, v0) = v1))
% 4.72/1.79 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (+(v0, v1) = v2) | +(v1, v0) = v2)
% 4.72/1.79 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (+(v1, v0) = v2) | +(v0, v1) = v2)
% 4.72/1.79 | (18) +(a, all_0_7_7) = all_0_6_6
% 4.72/1.79 | (19) ==>(a, b) = all_0_7_7
% 4.72/1.79 | (20) ~ (all_0_0_0 = all_0_4_4)
% 4.72/1.79 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (==>(v1, v0) = v2) | ~ (+(v1, v2) = v3) | ? [v4] : (==>(v0, v1) = v4 & +(v0, v4) = v3))
% 4.72/1.79 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (==>(0, v0) = v1))
% 4.72/1.79 | (23) ==>(a, all_0_2_2) = all_0_1_1
% 4.72/1.79 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ (+(v0, 0) = v1))
% 4.72/1.79 |
% 4.72/1.79 | Instantiating formula (17) with all_0_2_2, b, all_0_3_3 and discharging atoms +(b, all_0_3_3) = all_0_2_2, yields:
% 4.72/1.79 | (25) +(all_0_3_3, b) = all_0_2_2
% 4.72/1.79 |
% 4.72/1.79 | Instantiating formula (21) with all_0_0_0, all_0_1_1, a, all_0_2_2 and discharging atoms ==>(a, all_0_2_2) = all_0_1_1, +(a, all_0_1_1) = all_0_0_0, yields:
% 4.72/1.79 | (26) ? [v0] : (==>(all_0_2_2, a) = v0 & +(all_0_2_2, v0) = all_0_0_0)
% 4.72/1.79 |
% 4.72/1.79 | Instantiating formula (21) with all_0_6_6, all_0_7_7, a, b and discharging atoms ==>(a, b) = all_0_7_7, +(a, all_0_7_7) = all_0_6_6, yields:
% 4.72/1.80 | (27) ? [v0] : (==>(b, a) = v0 & +(b, v0) = all_0_6_6)
% 4.72/1.80 |
% 4.72/1.80 | Instantiating (27) with all_9_0_8 yields:
% 4.72/1.80 | (28) ==>(b, a) = all_9_0_8 & +(b, all_9_0_8) = all_0_6_6
% 4.72/1.80 |
% 4.72/1.80 | Applying alpha-rule on (28) yields:
% 4.72/1.80 | (29) ==>(b, a) = all_9_0_8
% 4.72/1.80 | (30) +(b, all_9_0_8) = all_0_6_6
% 4.72/1.80 |
% 4.72/1.80 | Instantiating (26) with all_17_0_12 yields:
% 4.72/1.80 | (31) ==>(all_0_2_2, a) = all_17_0_12 & +(all_0_2_2, all_17_0_12) = all_0_0_0
% 4.72/1.80 |
% 4.72/1.80 | Applying alpha-rule on (31) yields:
% 4.72/1.80 | (32) ==>(all_0_2_2, a) = all_17_0_12
% 4.72/1.80 | (33) +(all_0_2_2, all_17_0_12) = all_0_0_0
% 4.72/1.80 |
% 4.72/1.80 | Instantiating formula (8) with all_0_0_0, all_0_2_2, all_17_0_12, all_0_3_3, b and discharging atoms +(all_0_2_2, all_17_0_12) = all_0_0_0, +(b, all_0_3_3) = all_0_2_2, yields:
% 4.72/1.80 | (34) ? [v0] : (+(all_0_3_3, all_17_0_12) = v0 & +(b, v0) = all_0_0_0)
% 4.72/1.80 |
% 4.72/1.80 | Instantiating formula (6) with all_17_0_12, all_0_2_2, a, b, all_0_3_3 and discharging atoms ==>(all_0_2_2, a) = all_17_0_12, +(all_0_3_3, b) = all_0_2_2, yields:
% 4.72/1.80 | (35) ? [v0] : (==>(all_0_3_3, v0) = all_17_0_12 & ==>(b, a) = v0)
% 4.72/1.80 |
% 4.72/1.80 | Instantiating formula (8) with all_0_4_4, all_0_6_6, all_0_5_5, all_9_0_8, b and discharging atoms +(all_0_6_6, all_0_5_5) = all_0_4_4, +(b, all_9_0_8) = all_0_6_6, yields:
% 4.72/1.80 | (36) ? [v0] : (+(all_9_0_8, all_0_5_5) = v0 & +(b, v0) = all_0_4_4)
% 4.72/1.80 |
% 4.72/1.80 | Instantiating formula (17) with all_0_6_6, b, all_9_0_8 and discharging atoms +(b, all_9_0_8) = all_0_6_6, yields:
% 4.72/1.80 | (37) +(all_9_0_8, b) = all_0_6_6
% 4.72/1.80 |
% 4.72/1.80 | Instantiating (34) with all_35_0_18 yields:
% 4.72/1.80 | (38) +(all_0_3_3, all_17_0_12) = all_35_0_18 & +(b, all_35_0_18) = all_0_0_0
% 4.72/1.80 |
% 4.72/1.80 | Applying alpha-rule on (38) yields:
% 4.72/1.80 | (39) +(all_0_3_3, all_17_0_12) = all_35_0_18
% 4.72/1.80 | (40) +(b, all_35_0_18) = all_0_0_0
% 4.72/1.80 |
% 4.72/1.80 | Instantiating (36) with all_41_0_21 yields:
% 4.72/1.80 | (41) +(all_9_0_8, all_0_5_5) = all_41_0_21 & +(b, all_41_0_21) = all_0_4_4
% 4.72/1.80 |
% 4.72/1.80 | Applying alpha-rule on (41) yields:
% 4.72/1.80 | (42) +(all_9_0_8, all_0_5_5) = all_41_0_21
% 4.72/1.80 | (43) +(b, all_41_0_21) = all_0_4_4
% 4.72/1.80 |
% 4.72/1.80 | Instantiating (35) with all_47_0_24 yields:
% 4.72/1.80 | (44) ==>(all_0_3_3, all_47_0_24) = all_17_0_12 & ==>(b, a) = all_47_0_24
% 4.72/1.80 |
% 4.72/1.80 | Applying alpha-rule on (44) yields:
% 4.72/1.80 | (45) ==>(all_0_3_3, all_47_0_24) = all_17_0_12
% 4.72/1.80 | (46) ==>(b, a) = all_47_0_24
% 4.72/1.80 |
% 4.72/1.80 | Instantiating formula (14) with b, a, all_47_0_24, all_9_0_8 and discharging atoms ==>(b, a) = all_47_0_24, ==>(b, a) = all_9_0_8, yields:
% 4.72/1.80 | (47) all_47_0_24 = all_9_0_8
% 4.72/1.80 |
% 4.72/1.80 | From (47) and (45) follows:
% 4.72/1.80 | (48) ==>(all_0_3_3, all_9_0_8) = all_17_0_12
% 4.72/1.80 |
% 4.72/1.80 | Instantiating formula (6) with all_0_5_5, all_0_6_6, c, b, all_9_0_8 and discharging atoms ==>(all_0_6_6, c) = all_0_5_5, +(all_9_0_8, b) = all_0_6_6, yields:
% 4.72/1.80 | (49) ? [v0] : (==>(all_9_0_8, v0) = all_0_5_5 & ==>(b, c) = v0)
% 4.72/1.80 |
% 4.72/1.80 | Instantiating formula (21) with all_35_0_18, all_17_0_12, all_0_3_3, all_9_0_8 and discharging atoms ==>(all_0_3_3, all_9_0_8) = all_17_0_12, +(all_0_3_3, all_17_0_12) = all_35_0_18, yields:
% 4.72/1.80 | (50) ? [v0] : (==>(all_9_0_8, all_0_3_3) = v0 & +(all_9_0_8, v0) = all_35_0_18)
% 4.79/1.80 |
% 4.79/1.80 | Instantiating (49) with all_75_0_33 yields:
% 4.79/1.80 | (51) ==>(all_9_0_8, all_75_0_33) = all_0_5_5 & ==>(b, c) = all_75_0_33
% 4.79/1.80 |
% 4.79/1.80 | Applying alpha-rule on (51) yields:
% 4.79/1.80 | (52) ==>(all_9_0_8, all_75_0_33) = all_0_5_5
% 4.79/1.80 | (53) ==>(b, c) = all_75_0_33
% 4.79/1.80 |
% 4.79/1.80 | Instantiating (50) with all_83_0_37 yields:
% 4.79/1.80 | (54) ==>(all_9_0_8, all_0_3_3) = all_83_0_37 & +(all_9_0_8, all_83_0_37) = all_35_0_18
% 4.79/1.80 |
% 4.79/1.80 | Applying alpha-rule on (54) yields:
% 4.79/1.80 | (55) ==>(all_9_0_8, all_0_3_3) = all_83_0_37
% 4.79/1.80 | (56) +(all_9_0_8, all_83_0_37) = all_35_0_18
% 4.79/1.80 |
% 4.79/1.80 | Instantiating formula (14) with b, c, all_75_0_33, all_0_3_3 and discharging atoms ==>(b, c) = all_75_0_33, ==>(b, c) = all_0_3_3, yields:
% 4.79/1.80 | (57) all_75_0_33 = all_0_3_3
% 4.79/1.80 |
% 4.79/1.80 | From (57) and (52) follows:
% 4.79/1.80 | (58) ==>(all_9_0_8, all_0_3_3) = all_0_5_5
% 4.79/1.80 |
% 4.79/1.80 | Instantiating formula (14) with all_9_0_8, all_0_3_3, all_0_5_5, all_83_0_37 and discharging atoms ==>(all_9_0_8, all_0_3_3) = all_83_0_37, ==>(all_9_0_8, all_0_3_3) = all_0_5_5, yields:
% 4.79/1.80 | (59) all_83_0_37 = all_0_5_5
% 4.79/1.80 |
% 4.79/1.80 | From (59) and (56) follows:
% 4.79/1.80 | (60) +(all_9_0_8, all_0_5_5) = all_35_0_18
% 4.79/1.80 |
% 4.79/1.80 | Instantiating formula (2) with all_9_0_8, all_0_5_5, all_35_0_18, all_41_0_21 and discharging atoms +(all_9_0_8, all_0_5_5) = all_41_0_21, +(all_9_0_8, all_0_5_5) = all_35_0_18, yields:
% 4.79/1.81 | (61) all_41_0_21 = all_35_0_18
% 4.79/1.81 |
% 4.79/1.81 | From (61) and (43) follows:
% 4.79/1.81 | (62) +(b, all_35_0_18) = all_0_4_4
% 4.79/1.81 |
% 4.79/1.81 | Instantiating formula (2) with b, all_35_0_18, all_0_4_4, all_0_0_0 and discharging atoms +(b, all_35_0_18) = all_0_0_0, +(b, all_35_0_18) = all_0_4_4, yields:
% 4.79/1.81 | (63) all_0_0_0 = all_0_4_4
% 4.79/1.81 |
% 4.79/1.81 | Equations (63) can reduce 20 to:
% 4.79/1.81 | (64) $false
% 4.79/1.81 |
% 4.79/1.81 |-The branch is then unsatisfiable
% 4.79/1.81 % SZS output end Proof for theBenchmark
% 4.79/1.81
% 4.79/1.81 1208ms
%------------------------------------------------------------------------------