TSTP Solution File: SEU165+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Jul 19 08:47:12 EDT 2022
% Result : Theorem 2.38s 1.21s
% Output : Proof 3.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Mon Jun 20 08:21:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.60 ____ _
% 0.21/0.60 ___ / __ \_____(_)___ ________ __________
% 0.21/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.21/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.21/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic
% 0.21/0.60 (ePrincess v.1.0)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2015
% 0.21/0.60 (c) Peter Backeman, 2014-2015
% 0.21/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.21/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.21/0.60 Bug reports to peter@backeman.se
% 0.21/0.60
% 0.21/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.42/0.90 Prover 0: Preprocessing ...
% 1.83/1.07 Prover 0: Constructing countermodel ...
% 2.38/1.21 Prover 0: proved (561ms)
% 2.38/1.21
% 2.38/1.21 No countermodel exists, formula is valid
% 2.38/1.21 % SZS status Theorem for theBenchmark
% 2.38/1.21
% 2.38/1.21 Generating proof ... found it (size 14)
% 3.01/1.39
% 3.01/1.39 % SZS output start Proof for theBenchmark
% 3.01/1.39 Assumed formulas after preprocessing and simplification:
% 3.01/1.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (cartesian_product2(v2, v3) = v5 & ordered_pair(v0, v1) = v4 & empty(v7) & ~ empty(v6) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ in(v12, v13) | in(v9, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ in(v12, v13) | in(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ in(v9, v11) | ~ in(v8, v10) | in(v12, v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v8) = v11) | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v10) | ordered_pair(v8, v9) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cartesian_product2(v11, v10) = v9) | ~ (cartesian_product2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (ordered_pair(v11, v10) = v9) | ~ (ordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ empty(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : (singleton(v8) = v12 & unordered_pair(v11, v12) = v10 & unordered_pair(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v8) = v10) | unordered_pair(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ! [v8] : ! [v9] : ( ~ in(v9, v8) | ~ in(v8, v9)) & ((in(v4, v5) & ( ~ in(v1, v3) | ~ in(v0, v2))) | (in(v1, v3) & in(v0, v2) & ~ in(v4, v5))))
% 3.01/1.43 | 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:
% 3.01/1.43 | (1) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2 & ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ((in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))) | (in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2)))
% 3.01/1.44 |
% 3.01/1.44 | Applying alpha-rule on (1) yields:
% 3.01/1.44 | (2) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2
% 3.01/1.44 | (3) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.01/1.44 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 3.01/1.44 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 3.01/1.44 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3))
% 3.01/1.44 | (7) ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3
% 3.01/1.44 | (8) empty(all_0_0_0)
% 3.01/1.44 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 3.01/1.44 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 3.01/1.44 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.01/1.44 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 3.01/1.44 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5))
% 3.01/1.44 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2))
% 3.01/1.44 | (15) ~ empty(all_0_1_1)
% 3.01/1.44 | (16) (in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))) | (in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2))
% 3.01/1.44 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.01/1.44 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 3.01/1.44 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 3.01/1.44 |
% 3.01/1.44 +-Applying beta-rule and splitting (16), into two cases.
% 3.01/1.44 |-Branch one:
% 3.01/1.44 | (20) in(all_0_3_3, all_0_2_2) & ( ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5))
% 3.01/1.45 |
% 3.01/1.45 | Applying alpha-rule on (20) yields:
% 3.01/1.45 | (21) in(all_0_3_3, all_0_2_2)
% 3.01/1.45 | (22) ~ in(all_0_6_6, all_0_4_4) | ~ in(all_0_7_7, all_0_5_5)
% 3.01/1.45 |
% 3.01/1.45 | Instantiating formula (6) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_3_3, all_0_2_2), yields:
% 3.01/1.45 | (23) in(all_0_6_6, all_0_4_4)
% 3.01/1.45 |
% 3.01/1.45 | Instantiating formula (14) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_3_3, all_0_2_2), yields:
% 3.01/1.45 | (24) in(all_0_7_7, all_0_5_5)
% 3.01/1.45 |
% 3.01/1.45 +-Applying beta-rule and splitting (22), into two cases.
% 3.01/1.45 |-Branch one:
% 3.01/1.45 | (25) ~ in(all_0_6_6, all_0_4_4)
% 3.01/1.45 |
% 3.01/1.45 | Using (23) and (25) yields:
% 3.01/1.45 | (26) $false
% 3.01/1.45 |
% 3.01/1.45 |-The branch is then unsatisfiable
% 3.01/1.45 |-Branch two:
% 3.01/1.45 | (23) in(all_0_6_6, all_0_4_4)
% 3.01/1.45 | (28) ~ in(all_0_7_7, all_0_5_5)
% 3.01/1.45 |
% 3.01/1.45 | Using (24) and (28) yields:
% 3.01/1.45 | (26) $false
% 3.01/1.45 |
% 3.01/1.45 |-The branch is then unsatisfiable
% 3.01/1.45 |-Branch two:
% 3.01/1.45 | (30) in(all_0_6_6, all_0_4_4) & in(all_0_7_7, all_0_5_5) & ~ in(all_0_3_3, all_0_2_2)
% 3.01/1.45 |
% 3.01/1.45 | Applying alpha-rule on (30) yields:
% 3.01/1.45 | (23) in(all_0_6_6, all_0_4_4)
% 3.01/1.45 | (24) in(all_0_7_7, all_0_5_5)
% 3.01/1.45 | (33) ~ in(all_0_3_3, all_0_2_2)
% 3.01/1.45 |
% 3.01/1.45 | Instantiating formula (13) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, ordered_pair(all_0_7_7, all_0_6_6) = all_0_3_3, in(all_0_6_6, all_0_4_4), in(all_0_7_7, all_0_5_5), ~ in(all_0_3_3, all_0_2_2), yields:
% 3.01/1.45 | (26) $false
% 3.01/1.45 |
% 3.01/1.45 |-The branch is then unsatisfiable
% 3.01/1.45 % SZS output end Proof for theBenchmark
% 3.01/1.45
% 3.01/1.45 843ms
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