TSTP Solution File: SET942+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET942+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 00:23:20 EDT 2022
% Result : Theorem 2.87s 1.46s
% Output : Proof 4.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET942+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 20:18:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.63/0.64 ____ _
% 0.63/0.64 ___ / __ \_____(_)___ ________ __________
% 0.63/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.64
% 0.63/0.64 A Theorem Prover for First-Order Logic
% 0.68/0.64 (ePrincess v.1.0)
% 0.68/0.64
% 0.68/0.64 (c) Philipp Rümmer, 2009-2015
% 0.68/0.64 (c) Peter Backeman, 2014-2015
% 0.68/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.68/0.65 Free software under GNU Lesser General Public License (LGPL).
% 0.68/0.65 Bug reports to peter@backeman.se
% 0.68/0.65
% 0.68/0.65 For more information, visit http://user.uu.se/~petba168/breu/
% 0.68/0.65
% 0.68/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.43/0.96 Prover 0: Preprocessing ...
% 1.76/1.09 Prover 0: Warning: ignoring some quantifiers
% 1.76/1.11 Prover 0: Constructing countermodel ...
% 2.28/1.27 Prover 0: gave up
% 2.28/1.27 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.28/1.29 Prover 1: Preprocessing ...
% 2.66/1.36 Prover 1: Warning: ignoring some quantifiers
% 2.66/1.36 Prover 1: Constructing countermodel ...
% 2.87/1.46 Prover 1: proved (186ms)
% 2.87/1.46
% 2.87/1.46 No countermodel exists, formula is valid
% 2.87/1.46 % SZS status Theorem for theBenchmark
% 2.87/1.46
% 2.87/1.46 Generating proof ... Warning: ignoring some quantifiers
% 3.71/1.68 found it (size 25)
% 3.71/1.68
% 3.71/1.68 % SZS output start Proof for theBenchmark
% 3.71/1.68 Assumed formulas after preprocessing and simplification:
% 3.71/1.68 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & ~ (v4 = 0) & empty(v7) = 0 & empty(v5) = v6 & union(v1) = v3 & union(v0) = v2 & subset(v2, v3) = v4 & subset(v0, v1) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (union(v8) = v9) | ~ (in(v10, v12) = 0) | ~ (in(v10, v9) = v11) | ? [v13] : ( ~ (v13 = 0) & in(v12, v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (union(v10) = v9) | ~ (union(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8) = v9) | ~ (in(v10, v9) = 0) | ? [v11] : (in(v11, v8) = 0 & in(v10, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (in(v10, v8) = 0) | in(v10, v9) = 0) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (union(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v11, v8) = v12 & ( ~ (v12 = 0) | ! [v16] : ( ~ (in(v11, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v16, v9) = v17))) & (v12 = 0 | (v15 = 0 & v14 = 0 & in(v13, v9) = 0 & in(v11, v13) = 0)))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)))
% 3.71/1.72 | 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:
% 3.71/1.72 | (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 & union(all_0_6_6) = all_0_4_4 & union(all_0_7_7) = all_0_5_5 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & subset(all_0_7_7, all_0_6_6) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.01/1.72 |
% 4.01/1.72 | Applying alpha-rule on (1) yields:
% 4.01/1.73 | (2) union(all_0_7_7) = all_0_5_5
% 4.01/1.73 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 4.01/1.73 | (4) subset(all_0_5_5, all_0_4_4) = all_0_3_3
% 4.01/1.73 | (5) empty(all_0_2_2) = all_0_1_1
% 4.01/1.73 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 4.01/1.73 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.01/1.73 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 4.01/1.73 | (9) ~ (all_0_3_3 = 0)
% 4.01/1.73 | (10) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.01/1.73 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 4.01/1.73 | (12) subset(all_0_7_7, all_0_6_6) = 0
% 4.01/1.73 | (13) union(all_0_6_6) = all_0_4_4
% 4.01/1.73 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 4.01/1.73 | (15) ~ (all_0_1_1 = 0)
% 4.01/1.73 | (16) empty(all_0_0_0) = 0
% 4.01/1.73 | (17) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 4.01/1.73 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 4.01/1.73 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.01/1.73 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.01/1.73 |
% 4.01/1.73 | Instantiating formula (14) 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:
% 4.01/1.73 | (21) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 4.01/1.73 |
% 4.01/1.73 +-Applying beta-rule and splitting (21), into two cases.
% 4.01/1.73 |-Branch one:
% 4.01/1.73 | (22) all_0_3_3 = 0
% 4.01/1.73 |
% 4.01/1.74 | Equations (22) can reduce 9 to:
% 4.01/1.74 | (23) $false
% 4.01/1.74 |
% 4.01/1.74 |-The branch is then unsatisfiable
% 4.01/1.74 |-Branch two:
% 4.01/1.74 | (9) ~ (all_0_3_3 = 0)
% 4.01/1.74 | (25) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 4.01/1.74 |
% 4.01/1.74 | Instantiating (25) with all_16_0_9, all_16_1_10 yields:
% 4.01/1.74 | (26) ~ (all_16_0_9 = 0) & in(all_16_1_10, all_0_4_4) = all_16_0_9 & in(all_16_1_10, all_0_5_5) = 0
% 4.01/1.74 |
% 4.01/1.74 | Applying alpha-rule on (26) yields:
% 4.01/1.74 | (27) ~ (all_16_0_9 = 0)
% 4.01/1.74 | (28) in(all_16_1_10, all_0_4_4) = all_16_0_9
% 4.01/1.74 | (29) in(all_16_1_10, all_0_5_5) = 0
% 4.01/1.74 |
% 4.01/1.74 | Instantiating formula (8) with all_0_5_5, all_16_0_9, all_16_1_10, all_0_4_4, all_0_6_6 and discharging atoms union(all_0_6_6) = all_0_4_4, in(all_16_1_10, all_0_4_4) = all_16_0_9, in(all_16_1_10, all_0_5_5) = 0, yields:
% 4.01/1.74 | (30) all_16_0_9 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_0_5_5, all_0_6_6) = v0)
% 4.01/1.74 |
% 4.01/1.74 | Instantiating formula (3) with all_16_1_10, all_0_5_5, all_0_7_7 and discharging atoms union(all_0_7_7) = all_0_5_5, in(all_16_1_10, all_0_5_5) = 0, yields:
% 4.01/1.74 | (31) ? [v0] : (in(v0, all_0_7_7) = 0 & in(all_16_1_10, v0) = 0)
% 4.01/1.74 |
% 4.01/1.74 | Instantiating (31) with all_29_0_12 yields:
% 4.01/1.74 | (32) in(all_29_0_12, all_0_7_7) = 0 & in(all_16_1_10, all_29_0_12) = 0
% 4.01/1.74 |
% 4.01/1.74 | Applying alpha-rule on (32) yields:
% 4.01/1.74 | (33) in(all_29_0_12, all_0_7_7) = 0
% 4.01/1.74 | (34) in(all_16_1_10, all_29_0_12) = 0
% 4.01/1.74 |
% 4.01/1.74 +-Applying beta-rule and splitting (30), into two cases.
% 4.01/1.74 |-Branch one:
% 4.01/1.74 | (35) all_16_0_9 = 0
% 4.01/1.74 |
% 4.01/1.74 | Equations (35) can reduce 27 to:
% 4.01/1.74 | (23) $false
% 4.01/1.74 |
% 4.01/1.74 |-The branch is then unsatisfiable
% 4.01/1.74 |-Branch two:
% 4.01/1.74 | (27) ~ (all_16_0_9 = 0)
% 4.01/1.74 | (38) ? [v0] : ( ~ (v0 = 0) & in(all_0_5_5, all_0_6_6) = v0)
% 4.01/1.74 |
% 4.01/1.74 | Instantiating formula (11) with all_29_0_12, all_0_6_6, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_6_6) = 0, in(all_29_0_12, all_0_7_7) = 0, yields:
% 4.01/1.74 | (39) in(all_29_0_12, all_0_6_6) = 0
% 4.01/1.74 |
% 4.01/1.74 | Instantiating formula (8) with all_29_0_12, all_16_0_9, all_16_1_10, all_0_4_4, all_0_6_6 and discharging atoms union(all_0_6_6) = all_0_4_4, in(all_16_1_10, all_29_0_12) = 0, in(all_16_1_10, all_0_4_4) = all_16_0_9, yields:
% 4.01/1.74 | (40) all_16_0_9 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_29_0_12, all_0_6_6) = v0)
% 4.01/1.74 |
% 4.01/1.74 +-Applying beta-rule and splitting (40), into two cases.
% 4.01/1.74 |-Branch one:
% 4.01/1.74 | (35) all_16_0_9 = 0
% 4.01/1.74 |
% 4.01/1.74 | Equations (35) can reduce 27 to:
% 4.01/1.74 | (23) $false
% 4.01/1.74 |
% 4.01/1.74 |-The branch is then unsatisfiable
% 4.01/1.74 |-Branch two:
% 4.01/1.74 | (27) ~ (all_16_0_9 = 0)
% 4.01/1.74 | (44) ? [v0] : ( ~ (v0 = 0) & in(all_29_0_12, all_0_6_6) = v0)
% 4.01/1.74 |
% 4.01/1.74 | Instantiating (44) with all_51_0_16 yields:
% 4.01/1.74 | (45) ~ (all_51_0_16 = 0) & in(all_29_0_12, all_0_6_6) = all_51_0_16
% 4.01/1.74 |
% 4.01/1.74 | Applying alpha-rule on (45) yields:
% 4.01/1.74 | (46) ~ (all_51_0_16 = 0)
% 4.01/1.74 | (47) in(all_29_0_12, all_0_6_6) = all_51_0_16
% 4.01/1.74 |
% 4.01/1.74 | Instantiating formula (19) with all_29_0_12, all_0_6_6, 0, all_51_0_16 and discharging atoms in(all_29_0_12, all_0_6_6) = all_51_0_16, in(all_29_0_12, all_0_6_6) = 0, yields:
% 4.01/1.74 | (48) all_51_0_16 = 0
% 4.01/1.74 |
% 4.01/1.74 | Equations (48) can reduce 46 to:
% 4.01/1.74 | (23) $false
% 4.01/1.74 |
% 4.01/1.74 |-The branch is then unsatisfiable
% 4.01/1.74 % SZS output end Proof for theBenchmark
% 4.01/1.74
% 4.01/1.74 1082ms
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