TSTP Solution File: SET930+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.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 00:23:16 EDT 2022
% Result : Theorem 2.23s 1.30s
% Output : Proof 3.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 21:15:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.62/0.60 ____ _
% 0.62/0.60 ___ / __ \_____(_)___ ________ __________
% 0.62/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.62/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.62/0.60
% 0.62/0.60 A Theorem Prover for First-Order Logic
% 0.62/0.61 (ePrincess v.1.0)
% 0.62/0.61
% 0.62/0.61 (c) Philipp Rümmer, 2009-2015
% 0.62/0.61 (c) Peter Backeman, 2014-2015
% 0.62/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.61 Bug reports to peter@backeman.se
% 0.62/0.61
% 0.62/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.61
% 0.62/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.38/0.96 Prover 0: Preprocessing ...
% 1.73/1.16 Prover 0: Constructing countermodel ...
% 2.23/1.30 Prover 0: proved (616ms)
% 2.23/1.30
% 2.23/1.30 No countermodel exists, formula is valid
% 2.23/1.30 % SZS status Theorem for theBenchmark
% 2.23/1.30
% 2.23/1.30 Generating proof ... found it (size 20)
% 3.13/1.48
% 3.13/1.48 % SZS output start Proof for theBenchmark
% 3.13/1.48 Assumed formulas after preprocessing and simplification:
% 3.13/1.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v6 = v4) & ~ (v5 = v4) & ~ (v4 = v3) & ~ (v4 = empty_set) & set_difference(v3, v2) = v4 & singleton(v1) = v6 & singleton(v0) = v5 & unordered_pair(v0, v1) = v3 & empty(v8) & empty(empty_set) & ~ empty(v7) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (set_difference(v12, v11) = v13) | ~ (unordered_pair(v9, v10) = v12) | in(v10, v11) | in(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_difference(v12, v11) = v13) | ~ (unordered_pair(v9, v10) = v12) | ~ in(v10, v11) | ~ in(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (set_difference(v12, v11) = v13) | ~ (unordered_pair(v9, v10) = v12) | in(v10, v11) | ? [v14] : ( ~ (v14 = v13) & singleton(v9) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v12, v11) = v13) | ~ (unordered_pair(v9, v10) = v12) | ~ in(v10, v11) | singleton(v9) = v13 | in(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v12, v11) = v13) | ~ (unordered_pair(v9, v10) = v12) | ~ in(v9, v11) | ? [v14] : ( ~ (v14 = v13) & singleton(v9) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_difference(v12, v11) = v10) | ~ (set_difference(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v12, v11) = v12) | ~ (unordered_pair(v9, v10) = v12) | ~ in(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v12, v11) = v12) | ~ (unordered_pair(v9, v10) = v12) | ~ in(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v12, v11) = empty_set) | ~ (unordered_pair(v9, v10) = v12) | in(v10, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v12, v11) = empty_set) | ~ (unordered_pair(v9, v10) = v12) | in(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v11, v10) = v12) | ~ (unordered_pair(v9, v9) = v11) | singleton(v9) = v12 | in(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v9) = v11) | unordered_pair(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | unordered_pair(v10, v9) = v11) & ! [v9] : ! [v10] : ( ~ in(v10, v9) | ~ in(v9, v10)))
% 3.21/1.52 | 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, all_0_8_8 yields:
% 3.21/1.52 | (1) ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_4_4 = all_0_5_5) & ~ (all_0_4_4 = empty_set) & set_difference(all_0_5_5, all_0_6_6) = all_0_4_4 & singleton(all_0_7_7) = all_0_2_2 & singleton(all_0_8_8) = all_0_3_3 & unordered_pair(all_0_8_8, all_0_7_7) = all_0_5_5 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = empty_set | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | singleton(v0) = v4 | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v0, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v3, v2) = v3) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v3, v2) = v3) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v3, v2) = empty_set) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v3, v2) = empty_set) | ~ (unordered_pair(v0, v1) = v3) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (unordered_pair(v0, v0) = v2) | singleton(v0) = v3 | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [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))
% 3.21/1.53 |
% 3.21/1.53 | Applying alpha-rule on (1) yields:
% 3.21/1.53 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.21/1.53 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 3.21/1.53 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v3, v2) = empty_set) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2))
% 3.21/1.53 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = empty_set | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2))
% 3.21/1.53 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (unordered_pair(v0, v0) = v2) | singleton(v0) = v3 | in(v0, v1))
% 3.21/1.53 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v0, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5))
% 3.21/1.53 | (8) empty(all_0_0_0)
% 3.21/1.53 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v3, v2) = v3) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v0, v2))
% 3.21/1.53 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 3.21/1.54 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | singleton(v0) = v4 | in(v0, v2))
% 3.21/1.54 | (12) empty(empty_set)
% 3.21/1.54 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.21/1.54 | (14) unordered_pair(all_0_8_8, all_0_7_7) = all_0_5_5
% 3.21/1.54 | (15) ~ (all_0_4_4 = all_0_5_5)
% 3.21/1.54 | (16) ~ empty(all_0_1_1)
% 3.21/1.54 | (17) ~ (all_0_2_2 = all_0_4_4)
% 3.21/1.54 | (18) set_difference(all_0_5_5, all_0_6_6) = all_0_4_4
% 3.31/1.54 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5))
% 3.31/1.54 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v3, v2) = v3) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2))
% 3.31/1.54 | (21) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.31/1.54 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v3, v2) = empty_set) | ~ (unordered_pair(v0, v1) = v3) | in(v0, v2))
% 3.31/1.54 | (23) singleton(all_0_8_8) = all_0_3_3
% 3.31/1.54 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 3.31/1.54 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2) | in(v0, v2))
% 3.31/1.54 | (26) singleton(all_0_7_7) = all_0_2_2
% 3.31/1.54 | (27) ~ (all_0_4_4 = empty_set)
% 3.31/1.54 | (28) ~ (all_0_3_3 = all_0_4_4)
% 3.31/1.54 |
% 3.31/1.54 | Instantiating formula (3) with all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms unordered_pair(all_0_8_8, all_0_7_7) = all_0_5_5, yields:
% 3.31/1.54 | (29) unordered_pair(all_0_7_7, all_0_8_8) = all_0_5_5
% 3.31/1.54 |
% 3.31/1.54 | Instantiating formula (25) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms set_difference(all_0_5_5, all_0_6_6) = all_0_4_4, unordered_pair(all_0_7_7, all_0_8_8) = all_0_5_5, yields:
% 3.31/1.54 | (30) all_0_4_4 = all_0_5_5 | in(all_0_7_7, all_0_6_6) | in(all_0_8_8, all_0_6_6)
% 3.31/1.54 |
% 3.31/1.54 +-Applying beta-rule and splitting (30), into two cases.
% 3.31/1.54 |-Branch one:
% 3.31/1.54 | (31) in(all_0_7_7, all_0_6_6)
% 3.31/1.54 |
% 3.31/1.54 | Instantiating formula (11) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms set_difference(all_0_5_5, all_0_6_6) = all_0_4_4, unordered_pair(all_0_8_8, all_0_7_7) = all_0_5_5, in(all_0_7_7, all_0_6_6), yields:
% 3.31/1.54 | (32) singleton(all_0_8_8) = all_0_4_4 | in(all_0_8_8, all_0_6_6)
% 3.31/1.54 |
% 3.31/1.54 +-Applying beta-rule and splitting (32), into two cases.
% 3.31/1.54 |-Branch one:
% 3.31/1.54 | (33) in(all_0_8_8, all_0_6_6)
% 3.31/1.54 |
% 3.31/1.54 | Instantiating formula (5) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms set_difference(all_0_5_5, all_0_6_6) = all_0_4_4, unordered_pair(all_0_8_8, all_0_7_7) = all_0_5_5, in(all_0_7_7, all_0_6_6), in(all_0_8_8, all_0_6_6), yields:
% 3.31/1.54 | (34) all_0_4_4 = empty_set
% 3.31/1.55 |
% 3.31/1.55 | Equations (34) can reduce 27 to:
% 3.31/1.55 | (35) $false
% 3.31/1.55 |
% 3.31/1.55 |-The branch is then unsatisfiable
% 3.31/1.55 |-Branch two:
% 3.31/1.55 | (36) ~ in(all_0_8_8, all_0_6_6)
% 3.31/1.55 | (37) singleton(all_0_8_8) = all_0_4_4
% 3.31/1.55 |
% 3.31/1.55 | Instantiating formula (10) with all_0_8_8, all_0_4_4, all_0_3_3 and discharging atoms singleton(all_0_8_8) = all_0_3_3, singleton(all_0_8_8) = all_0_4_4, yields:
% 3.31/1.55 | (38) all_0_3_3 = all_0_4_4
% 3.31/1.55 |
% 3.31/1.55 | Equations (38) can reduce 28 to:
% 3.31/1.55 | (35) $false
% 3.31/1.55 |
% 3.31/1.55 |-The branch is then unsatisfiable
% 3.31/1.55 |-Branch two:
% 3.31/1.55 | (40) ~ in(all_0_7_7, all_0_6_6)
% 3.31/1.55 | (41) all_0_4_4 = all_0_5_5 | in(all_0_8_8, all_0_6_6)
% 3.31/1.55 |
% 3.31/1.55 +-Applying beta-rule and splitting (41), into two cases.
% 3.31/1.55 |-Branch one:
% 3.31/1.55 | (33) in(all_0_8_8, all_0_6_6)
% 3.31/1.55 |
% 3.31/1.55 | Instantiating formula (11) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms set_difference(all_0_5_5, all_0_6_6) = all_0_4_4, unordered_pair(all_0_7_7, all_0_8_8) = all_0_5_5, in(all_0_8_8, all_0_6_6), ~ in(all_0_7_7, all_0_6_6), yields:
% 3.31/1.55 | (43) singleton(all_0_7_7) = all_0_4_4
% 3.31/1.55 |
% 3.31/1.55 | Instantiating formula (10) with all_0_7_7, all_0_4_4, all_0_2_2 and discharging atoms singleton(all_0_7_7) = all_0_2_2, singleton(all_0_7_7) = all_0_4_4, yields:
% 3.31/1.55 | (44) all_0_2_2 = all_0_4_4
% 3.31/1.55 |
% 3.31/1.55 | Equations (44) can reduce 17 to:
% 3.31/1.55 | (35) $false
% 3.31/1.55 |
% 3.31/1.55 |-The branch is then unsatisfiable
% 3.31/1.55 |-Branch two:
% 3.31/1.55 | (36) ~ in(all_0_8_8, all_0_6_6)
% 3.31/1.55 | (47) all_0_4_4 = all_0_5_5
% 3.31/1.55 |
% 3.31/1.55 | Equations (47) can reduce 15 to:
% 3.31/1.55 | (35) $false
% 3.31/1.55 |
% 3.31/1.55 |-The branch is then unsatisfiable
% 3.31/1.55 % SZS output end Proof for theBenchmark
% 3.31/1.55
% 3.31/1.55 927ms
%------------------------------------------------------------------------------