TSTP Solution File: KLE001+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 3.02s 1.38s
% Output : Proof 3.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n026.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 : Thu Jun 16 14:57:23 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58 Bug reports to peter@backeman.se
% 0.55/0.58
% 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58
% 0.55/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.55/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.50/0.89 Prover 0: Preprocessing ...
% 2.03/1.09 Prover 0: Constructing countermodel ...
% 2.62/1.27 Prover 0: gave up
% 2.62/1.27 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.62/1.29 Prover 1: Preprocessing ...
% 2.86/1.34 Prover 1: Constructing countermodel ...
% 3.02/1.38 Prover 1: proved (110ms)
% 3.02/1.38
% 3.02/1.38 No countermodel exists, formula is valid
% 3.02/1.38 % SZS status Theorem for theBenchmark
% 3.02/1.38
% 3.02/1.38 Generating proof ... found it (size 11)
% 3.71/1.56
% 3.71/1.56 % SZS output start Proof for theBenchmark
% 3.71/1.56 Assumed formulas after preprocessing and simplification:
% 3.71/1.56 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & leq(v3, v3) = v4 & leq(v0, v1) = 0 & addition(v0, v2) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v6, v7) = v9) | ~ (multiplication(v5, v7) = v8) | ~ (addition(v8, v9) = v10) | ? [v11] : (multiplication(v11, v7) = v10 & addition(v5, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v5, v7) = v9) | ~ (multiplication(v5, v6) = v8) | ~ (addition(v8, v9) = v10) | ? [v11] : (multiplication(v5, v11) = v10 & addition(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v8, v7) = v9) | ~ (multiplication(v5, v6) = v8) | ? [v10] : (multiplication(v6, v7) = v10 & multiplication(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (addition(v8, v5) = v9) | ~ (addition(v7, v6) = v8) | ? [v10] : (addition(v7, v10) = v9 & addition(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (leq(v8, v7) = v6) | ~ (leq(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (multiplication(v8, v7) = v6) | ~ (multiplication(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (addition(v8, v7) = v6) | ~ (addition(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (leq(v5, v6) = v7) | ? [v8] : ( ~ (v8 = v6) & addition(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v5, v6) = v7) | addition(v6, v5) = v7) & ! [v5] : ! [v6] : (v6 = v5 | ~ (multiplication(v5, one) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (multiplication(one, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v5, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v5, zero) = v6)) & ! [v5] : ! [v6] : (v6 = zero | ~ (multiplication(v5, zero) = v6)) & ! [v5] : ! [v6] : (v6 = zero | ~ (multiplication(zero, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (leq(v5, v6) = 0) | addition(v5, v6) = v6))
% 3.71/1.59 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.71/1.59 | (1) ~ (all_0_0_0 = 0) & leq(all_0_1_1, all_0_1_1) = all_0_0_0 & leq(all_0_4_4, all_0_3_3) = 0 & addition(all_0_4_4, all_0_2_2) = all_0_1_1 & ! [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)
% 3.71/1.60 |
% 3.71/1.60 | Applying alpha-rule on (1) yields:
% 3.71/1.60 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 3.71/1.60 | (3) leq(all_0_4_4, all_0_3_3) = 0
% 3.71/1.60 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 3.71/1.60 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 3.71/1.60 | (6) ! [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))
% 3.71/1.60 | (7) ! [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))
% 3.71/1.60 | (8) ~ (all_0_0_0 = 0)
% 3.71/1.60 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 3.71/1.60 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 3.71/1.60 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 3.71/1.60 | (12) leq(all_0_1_1, all_0_1_1) = all_0_0_0
% 3.71/1.60 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 3.71/1.60 | (14) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 3.71/1.60 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 3.71/1.60 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 3.71/1.60 | (17) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 3.71/1.60 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 3.71/1.60 | (19) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 3.71/1.60 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 3.71/1.60 | (21) addition(all_0_4_4, all_0_2_2) = all_0_1_1
% 3.71/1.60 |
% 3.71/1.60 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms leq(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 3.71/1.60 | (22) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_1_1, all_0_1_1) = v0)
% 3.71/1.60 |
% 3.71/1.60 +-Applying beta-rule and splitting (22), into two cases.
% 3.71/1.60 |-Branch one:
% 3.71/1.60 | (23) all_0_0_0 = 0
% 3.71/1.60 |
% 3.71/1.60 | Equations (23) can reduce 8 to:
% 3.71/1.60 | (24) $false
% 3.71/1.60 |
% 3.71/1.61 |-The branch is then unsatisfiable
% 3.71/1.61 |-Branch two:
% 3.71/1.61 | (8) ~ (all_0_0_0 = 0)
% 3.71/1.61 | (26) ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_1_1, all_0_1_1) = v0)
% 3.71/1.61 |
% 3.71/1.61 | Instantiating (26) with all_13_0_5 yields:
% 3.71/1.61 | (27) ~ (all_13_0_5 = all_0_1_1) & addition(all_0_1_1, all_0_1_1) = all_13_0_5
% 3.71/1.61 |
% 3.71/1.61 | Applying alpha-rule on (27) yields:
% 3.71/1.61 | (28) ~ (all_13_0_5 = all_0_1_1)
% 3.71/1.61 | (29) addition(all_0_1_1, all_0_1_1) = all_13_0_5
% 3.71/1.61 |
% 3.71/1.61 | Instantiating formula (2) with all_13_0_5, all_0_1_1 and discharging atoms addition(all_0_1_1, all_0_1_1) = all_13_0_5, yields:
% 3.71/1.61 | (30) all_13_0_5 = all_0_1_1
% 3.71/1.61 |
% 3.71/1.61 | Equations (30) can reduce 28 to:
% 3.71/1.61 | (24) $false
% 3.71/1.61 |
% 3.71/1.61 |-The branch is then unsatisfiable
% 3.71/1.61 % SZS output end Proof for theBenchmark
% 3.71/1.61
% 3.71/1.61 1018ms
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