TSTP Solution File: SET872+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 00:22:50 EDT 2022
% Result : Theorem 3.26s 1.52s
% Output : Proof 3.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 14:00:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.61 ____ _
% 0.55/0.61 ___ / __ \_____(_)___ ________ __________
% 0.55/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.61
% 0.55/0.61 A Theorem Prover for First-Order Logic
% 0.55/0.61 (ePrincess v.1.0)
% 0.55/0.61
% 0.55/0.61 (c) Philipp Rümmer, 2009-2015
% 0.55/0.61 (c) Peter Backeman, 2014-2015
% 0.55/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.61 Bug reports to peter@backeman.se
% 0.55/0.61
% 0.55/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.61
% 0.55/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.95 Prover 0: Preprocessing ...
% 1.75/1.12 Prover 0: Warning: ignoring some quantifiers
% 1.75/1.14 Prover 0: Constructing countermodel ...
% 2.75/1.40 Prover 0: gave up
% 2.75/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.75/1.41 Prover 1: Preprocessing ...
% 3.18/1.48 Prover 1: Warning: ignoring some quantifiers
% 3.18/1.48 Prover 1: Constructing countermodel ...
% 3.26/1.52 Prover 1: proved (124ms)
% 3.26/1.52
% 3.26/1.52 No countermodel exists, formula is valid
% 3.26/1.52 % SZS status Theorem for theBenchmark
% 3.26/1.52
% 3.26/1.52 Generating proof ... Warning: ignoring some quantifiers
% 3.99/1.72 found it (size 17)
% 3.99/1.72
% 3.99/1.72 % SZS output start Proof for theBenchmark
% 3.99/1.72 Assumed formulas after preprocessing and simplification:
% 3.99/1.72 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & ~ (v4 = 0) & empty(v7) = 0 & empty(v5) = v6 & subset(v2, v3) = v4 & singleton(v0) = v2 & unordered_pair(v0, v1) = v3 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | v11 = v8 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v11, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (unordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : (in(v12, v8) = v13 & ( ~ (v13 = 0) | ( ~ (v12 = v10) & ~ (v12 = v9))) & (v13 = 0 | v12 = v10 | v12 = v9))) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v8) = v9) | ~ (in(v10, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (in(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (in(v10, v8) = 0) | in(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v9) = v10) | ? [v11] : ? [v12] : (in(v11, v8) = v12 & ( ~ (v12 = 0) | ~ (v11 = v9)) & (v12 = 0 | v11 = v9))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)))
% 3.99/1.75 | 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:
% 3.99/1.75 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & singleton(all_0_7_7) = all_0_5_5 & unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 3.99/1.76 |
% 3.99/1.76 | Applying alpha-rule on (1) yields:
% 3.99/1.76 | (2) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 3.99/1.76 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 3.99/1.76 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 3.99/1.76 | (5) singleton(all_0_7_7) = all_0_5_5
% 3.99/1.76 | (6) unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4
% 3.99/1.76 | (7) empty(all_0_0_0) = 0
% 3.99/1.76 | (8) empty(all_0_2_2) = all_0_1_1
% 3.99/1.76 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.99/1.76 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 3.99/1.76 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 3.99/1.76 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 3.99/1.76 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 3.99/1.76 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 3.99/1.76 | (15) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 3.99/1.76 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 3.99/1.76 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.99/1.76 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 3.99/1.76 | (19) ~ (all_0_3_3 = 0)
% 3.99/1.76 | (20) ~ (all_0_1_1 = 0)
% 3.99/1.76 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 3.99/1.76 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.99/1.76 | (23) subset(all_0_5_5, all_0_4_4) = all_0_3_3
% 3.99/1.76 | (24) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1)))
% 3.99/1.76 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 3.99/1.77 |
% 3.99/1.77 | Instantiating formula (16) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 3.99/1.77 | (26) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 3.99/1.77 |
% 3.99/1.77 | Instantiating formula (22) with all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, yields:
% 3.99/1.77 | (27) unordered_pair(all_0_6_6, all_0_7_7) = all_0_4_4
% 3.99/1.77 |
% 3.99/1.77 +-Applying beta-rule and splitting (26), into two cases.
% 3.99/1.77 |-Branch one:
% 3.99/1.77 | (28) all_0_3_3 = 0
% 3.99/1.77 |
% 3.99/1.77 | Equations (28) can reduce 19 to:
% 3.99/1.77 | (29) $false
% 3.99/1.77 |
% 3.99/1.77 |-The branch is then unsatisfiable
% 3.99/1.77 |-Branch two:
% 3.99/1.77 | (19) ~ (all_0_3_3 = 0)
% 3.99/1.77 | (31) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 3.99/1.77 |
% 3.99/1.77 | Instantiating (31) with all_21_0_10, all_21_1_11 yields:
% 3.99/1.77 | (32) ~ (all_21_0_10 = 0) & in(all_21_1_11, all_0_4_4) = all_21_0_10 & in(all_21_1_11, all_0_5_5) = 0
% 3.99/1.77 |
% 3.99/1.77 | Applying alpha-rule on (32) yields:
% 3.99/1.77 | (33) ~ (all_21_0_10 = 0)
% 3.99/1.77 | (34) in(all_21_1_11, all_0_4_4) = all_21_0_10
% 3.99/1.77 | (35) in(all_21_1_11, all_0_5_5) = 0
% 3.99/1.77 |
% 3.99/1.77 | Instantiating formula (12) with all_21_0_10, all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_7_7) = all_0_4_4, yields:
% 3.99/1.77 | (36) all_21_0_10 = 0 | ~ (in(all_0_7_7, all_0_4_4) = all_21_0_10)
% 3.99/1.77 |
% 3.99/1.77 | Instantiating formula (10) with all_21_1_11, all_0_5_5, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_5_5, in(all_21_1_11, all_0_5_5) = 0, yields:
% 3.99/1.77 | (37) all_21_1_11 = all_0_7_7
% 3.99/1.77 |
% 3.99/1.77 | From (37) and (34) follows:
% 3.99/1.77 | (38) in(all_0_7_7, all_0_4_4) = all_21_0_10
% 3.99/1.77 |
% 3.99/1.77 +-Applying beta-rule and splitting (36), into two cases.
% 3.99/1.77 |-Branch one:
% 3.99/1.77 | (39) ~ (in(all_0_7_7, all_0_4_4) = all_21_0_10)
% 3.99/1.77 |
% 3.99/1.77 | Using (38) and (39) yields:
% 3.99/1.77 | (40) $false
% 3.99/1.77 |
% 3.99/1.77 |-The branch is then unsatisfiable
% 3.99/1.77 |-Branch two:
% 3.99/1.77 | (38) in(all_0_7_7, all_0_4_4) = all_21_0_10
% 3.99/1.77 | (42) all_21_0_10 = 0
% 3.99/1.77 |
% 3.99/1.77 | Equations (42) can reduce 33 to:
% 3.99/1.77 | (29) $false
% 3.99/1.77 |
% 3.99/1.77 |-The branch is then unsatisfiable
% 3.99/1.77 % SZS output end Proof for theBenchmark
% 3.99/1.77
% 3.99/1.77 1144ms
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