TSTP Solution File: KLE002+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 01:50:46 EDT 2022
% Result : Theorem 3.14s 1.43s
% Output : Proof 4.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % 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 : Thu Jun 16 13:20:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.48/0.60 ____ _
% 0.48/0.60 ___ / __ \_____(_)___ ________ __________
% 0.48/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.60
% 0.48/0.60 A Theorem Prover for First-Order Logic
% 0.48/0.60 (ePrincess v.1.0)
% 0.48/0.60
% 0.48/0.60 (c) Philipp Rümmer, 2009-2015
% 0.48/0.60 (c) Peter Backeman, 2014-2015
% 0.48/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.60 Bug reports to peter@backeman.se
% 0.48/0.60
% 0.48/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.60
% 0.48/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.89 Prover 0: Preprocessing ...
% 1.97/1.08 Prover 0: Constructing countermodel ...
% 2.69/1.29 Prover 0: gave up
% 2.69/1.29 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.69/1.31 Prover 1: Preprocessing ...
% 2.94/1.37 Prover 1: Constructing countermodel ...
% 3.14/1.43 Prover 1: proved (142ms)
% 3.14/1.43
% 3.14/1.43 No countermodel exists, formula is valid
% 3.14/1.43 % SZS status Theorem for theBenchmark
% 3.14/1.43
% 3.14/1.43 Generating proof ... found it (size 20)
% 3.81/1.62
% 3.81/1.62 % SZS output start Proof for theBenchmark
% 3.81/1.62 Assumed formulas after preprocessing and simplification:
% 3.81/1.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & leq(v3, v4) = v5 & leq(v0, v1) = 0 & multiplication(v1, v2) = v4 & multiplication(v0, v2) = v3 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (multiplication(v7, v8) = v10) | ~ (multiplication(v6, v8) = v9) | ~ (addition(v9, v10) = v11) | ? [v12] : (multiplication(v12, v8) = v11 & addition(v6, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (multiplication(v6, v8) = v10) | ~ (multiplication(v6, v7) = v9) | ~ (addition(v9, v10) = v11) | ? [v12] : (multiplication(v6, v12) = v11 & addition(v7, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v9, v8) = v10) | ~ (multiplication(v6, v7) = v9) | ? [v11] : (multiplication(v7, v8) = v11 & multiplication(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v9, v6) = v10) | ~ (addition(v8, v7) = v9) | ? [v11] : (addition(v8, v11) = v10 & addition(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (leq(v9, v8) = v7) | ~ (leq(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (multiplication(v9, v8) = v7) | ~ (multiplication(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (addition(v9, v8) = v7) | ~ (addition(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (leq(v6, v7) = v8) | ? [v9] : ( ~ (v9 = v7) & addition(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | addition(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = v6 | ~ (multiplication(v6, one) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (multiplication(one, v6) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v6, v6) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v6, zero) = v7)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(v6, zero) = v7)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(zero, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (leq(v6, v7) = 0) | addition(v6, v7) = v7))
% 4.09/1.65 | 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:
% 4.09/1.65 | (1) ~ (all_0_0_0 = 0) & leq(all_0_2_2, all_0_1_1) = all_0_0_0 & leq(all_0_5_5, all_0_4_4) = 0 & multiplication(all_0_4_4, all_0_3_3) = all_0_1_1 & multiplication(all_0_5_5, all_0_3_3) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 4.09/1.66 |
% 4.09/1.66 | Applying alpha-rule on (1) yields:
% 4.09/1.66 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 4.09/1.66 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 4.09/1.66 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 4.09/1.66 | (5) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 4.09/1.66 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 4.09/1.66 | (7) multiplication(all_0_4_4, all_0_3_3) = all_0_1_1
% 4.09/1.66 | (8) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 4.09/1.66 | (9) multiplication(all_0_5_5, all_0_3_3) = all_0_2_2
% 4.09/1.66 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 4.09/1.66 | (11) leq(all_0_2_2, all_0_1_1) = all_0_0_0
% 4.15/1.66 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 4.15/1.66 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 4.15/1.66 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 4.15/1.66 | (15) leq(all_0_5_5, all_0_4_4) = 0
% 4.15/1.66 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6))
% 4.15/1.66 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 4.15/1.66 | (18) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 4.15/1.66 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 4.15/1.66 | (20) ~ (all_0_0_0 = 0)
% 4.15/1.66 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 4.15/1.66 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 4.15/1.66 |
% 4.15/1.67 | Instantiating formula (3) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms leq(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 4.15/1.67 | (23) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_2_2, all_0_1_1) = v0)
% 4.15/1.67 |
% 4.15/1.67 | Instantiating formula (18) with all_0_4_4, all_0_5_5 and discharging atoms leq(all_0_5_5, all_0_4_4) = 0, yields:
% 4.15/1.67 | (24) addition(all_0_5_5, all_0_4_4) = all_0_4_4
% 4.15/1.67 |
% 4.15/1.67 +-Applying beta-rule and splitting (23), into two cases.
% 4.15/1.67 |-Branch one:
% 4.15/1.67 | (25) all_0_0_0 = 0
% 4.15/1.67 |
% 4.15/1.67 | Equations (25) can reduce 20 to:
% 4.15/1.67 | (26) $false
% 4.15/1.67 |
% 4.15/1.67 |-The branch is then unsatisfiable
% 4.15/1.67 |-Branch two:
% 4.15/1.67 | (20) ~ (all_0_0_0 = 0)
% 4.15/1.67 | (28) ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_2_2, all_0_1_1) = v0)
% 4.15/1.67 |
% 4.15/1.67 | Instantiating (28) with all_13_0_6 yields:
% 4.15/1.67 | (29) ~ (all_13_0_6 = all_0_1_1) & addition(all_0_2_2, all_0_1_1) = all_13_0_6
% 4.15/1.67 |
% 4.15/1.67 | Applying alpha-rule on (29) yields:
% 4.15/1.67 | (30) ~ (all_13_0_6 = all_0_1_1)
% 4.15/1.67 | (31) addition(all_0_2_2, all_0_1_1) = all_13_0_6
% 4.15/1.67 |
% 4.15/1.67 | Instantiating formula (10) with all_13_0_6, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms multiplication(all_0_4_4, all_0_3_3) = all_0_1_1, multiplication(all_0_5_5, all_0_3_3) = all_0_2_2, addition(all_0_2_2, all_0_1_1) = all_13_0_6, yields:
% 4.15/1.67 | (32) ? [v0] : (multiplication(v0, all_0_3_3) = all_13_0_6 & addition(all_0_5_5, all_0_4_4) = v0)
% 4.15/1.67 |
% 4.15/1.67 | Instantiating (32) with all_21_0_7 yields:
% 4.15/1.67 | (33) multiplication(all_21_0_7, all_0_3_3) = all_13_0_6 & addition(all_0_5_5, all_0_4_4) = all_21_0_7
% 4.15/1.67 |
% 4.15/1.67 | Applying alpha-rule on (33) yields:
% 4.15/1.67 | (34) multiplication(all_21_0_7, all_0_3_3) = all_13_0_6
% 4.15/1.67 | (35) addition(all_0_5_5, all_0_4_4) = all_21_0_7
% 4.15/1.67 |
% 4.15/1.67 | Instantiating formula (14) with all_0_4_4, all_0_3_3, all_13_0_6, all_0_1_1 and discharging atoms multiplication(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 4.15/1.67 | (36) all_13_0_6 = all_0_1_1 | ~ (multiplication(all_0_4_4, all_0_3_3) = all_13_0_6)
% 4.15/1.67 |
% 4.15/1.67 | Instantiating formula (13) with all_0_5_5, all_0_4_4, all_21_0_7, all_0_4_4 and discharging atoms addition(all_0_5_5, all_0_4_4) = all_21_0_7, addition(all_0_5_5, all_0_4_4) = all_0_4_4, yields:
% 4.15/1.67 | (37) all_21_0_7 = all_0_4_4
% 4.15/1.67 |
% 4.15/1.67 | From (37) and (34) follows:
% 4.15/1.67 | (38) multiplication(all_0_4_4, all_0_3_3) = all_13_0_6
% 4.15/1.67 |
% 4.15/1.67 +-Applying beta-rule and splitting (36), into two cases.
% 4.15/1.67 |-Branch one:
% 4.15/1.67 | (39) ~ (multiplication(all_0_4_4, all_0_3_3) = all_13_0_6)
% 4.15/1.67 |
% 4.15/1.67 | Using (38) and (39) yields:
% 4.15/1.67 | (40) $false
% 4.15/1.67 |
% 4.15/1.67 |-The branch is then unsatisfiable
% 4.15/1.67 |-Branch two:
% 4.15/1.67 | (38) multiplication(all_0_4_4, all_0_3_3) = all_13_0_6
% 4.15/1.67 | (42) all_13_0_6 = all_0_1_1
% 4.15/1.67 |
% 4.15/1.67 | Equations (42) can reduce 30 to:
% 4.15/1.67 | (26) $false
% 4.15/1.67 |
% 4.15/1.67 |-The branch is then unsatisfiable
% 4.15/1.67 % SZS output end Proof for theBenchmark
% 4.15/1.67
% 4.15/1.67 1063ms
%------------------------------------------------------------------------------