TSTP Solution File: SET956+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 00:23:26 EDT 2022
% Result : Theorem 3.44s 1.52s
% Output : Proof 4.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 02:02:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.59 (ePrincess v.1.0)
% 0.54/0.59
% 0.54/0.59 (c) Philipp Rümmer, 2009-2015
% 0.54/0.59 (c) Peter Backeman, 2014-2015
% 0.54/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.59 Bug reports to peter@backeman.se
% 0.54/0.59
% 0.54/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.59
% 0.54/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.38/0.88 Prover 0: Preprocessing ...
% 1.79/1.04 Prover 0: Warning: ignoring some quantifiers
% 1.79/1.05 Prover 0: Constructing countermodel ...
% 2.96/1.40 Prover 0: gave up
% 2.96/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.96/1.42 Prover 1: Preprocessing ...
% 3.32/1.48 Prover 1: Constructing countermodel ...
% 3.44/1.52 Prover 1: proved (116ms)
% 3.44/1.52
% 3.44/1.52 No countermodel exists, formula is valid
% 3.44/1.52 % SZS status Theorem for theBenchmark
% 3.44/1.52
% 3.44/1.52 Generating proof ... found it (size 18)
% 4.27/1.69
% 4.27/1.69 % SZS output start Proof for theBenchmark
% 4.27/1.69 Assumed formulas after preprocessing and simplification:
% 4.27/1.69 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v7 = 0) & ~ (v5 = 0) & cartesian_product2(v1, v2) = v4 & empty(v8) = 0 & empty(v6) = v7 & subset(v0, v4) = 0 & subset(v0, v3) = v5 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (subset(v9, v13) = 0) | ~ (in(v12, v9) = 0) | ? [v14] : ? [v15] : (ordered_pair(v14, v15) = v12 & in(v15, v11) = 0 & in(v14, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v9) = v12) | ~ (unordered_pair(v11, v12) = v13) | ~ (unordered_pair(v9, v10) = v11) | ordered_pair(v9, v10) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (cartesian_product2(v12, v11) = v10) | ~ (cartesian_product2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (ordered_pair(v12, v11) = v10) | ~ (ordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset(v12, v11) = v10) | ~ (subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (in(v12, v11) = v10) | ~ (in(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & in(v12, v10) = v13 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (empty(v11) = v10) | ~ (empty(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ (in(v11, v0) = 0) | in(v11, v3) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v9, v10) = 0) | ~ (in(v11, v9) = 0) | in(v11, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | unordered_pair(v10, v9) = v11) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v9, v9) = v10)) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)))
% 4.27/1.72 | 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, all_0_8_8 yields:
% 4.27/1.72 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & subset(all_0_8_8, all_0_4_4) = 0 & subset(all_0_8_8, all_0_5_5) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (subset(v0, v4) = 0) | ~ (in(v3, v0) = 0) | ? [v5] : ? [v6] : (ordered_pair(v5, v6) = v3 & in(v6, v2) = 0 & in(v5, v1) = 0)) & ! [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 | ~ (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] : (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 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_0_8_8) = 0) | in(v2, all_0_5_5) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [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] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.27/1.73 |
% 4.27/1.73 | Applying alpha-rule on (1) yields:
% 4.27/1.73 | (2) empty(all_0_0_0) = 0
% 4.27/1.73 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 4.27/1.73 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 4.27/1.73 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 4.27/1.73 | (6) cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4
% 4.27/1.73 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 4.27/1.74 | (8) subset(all_0_8_8, all_0_4_4) = 0
% 4.27/1.74 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 4.27/1.74 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 4.27/1.74 | (11) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.27/1.74 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 4.27/1.74 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 4.27/1.74 | (14) ~ (all_0_1_1 = 0)
% 4.27/1.74 | (15) subset(all_0_8_8, all_0_5_5) = all_0_3_3
% 4.27/1.74 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 4.27/1.74 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 4.27/1.74 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (subset(v0, v4) = 0) | ~ (in(v3, v0) = 0) | ? [v5] : ? [v6] : (ordered_pair(v5, v6) = v3 & in(v6, v2) = 0 & in(v5, v1) = 0))
% 4.27/1.74 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 4.27/1.74 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 4.27/1.74 | (21) empty(all_0_2_2) = all_0_1_1
% 4.27/1.74 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_0_8_8) = 0) | in(v2, all_0_5_5) = 0)
% 4.27/1.74 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.27/1.74 | (24) ~ (all_0_3_3 = 0)
% 4.27/1.74 |
% 4.27/1.74 | Instantiating formula (20) with all_0_3_3, all_0_5_5, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_5_5) = all_0_3_3, yields:
% 4.27/1.74 | (25) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = v1 & in(v0, all_0_8_8) = 0)
% 4.27/1.74 |
% 4.27/1.74 +-Applying beta-rule and splitting (25), into two cases.
% 4.27/1.74 |-Branch one:
% 4.27/1.74 | (26) all_0_3_3 = 0
% 4.27/1.74 |
% 4.27/1.74 | Equations (26) can reduce 24 to:
% 4.27/1.74 | (27) $false
% 4.27/1.74 |
% 4.27/1.74 |-The branch is then unsatisfiable
% 4.27/1.74 |-Branch two:
% 4.27/1.74 | (24) ~ (all_0_3_3 = 0)
% 4.27/1.74 | (29) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = v1 & in(v0, all_0_8_8) = 0)
% 4.27/1.74 |
% 4.27/1.74 | Instantiating (29) with all_14_0_9, all_14_1_10 yields:
% 4.27/1.74 | (30) ~ (all_14_0_9 = 0) & in(all_14_1_10, all_0_5_5) = all_14_0_9 & in(all_14_1_10, all_0_8_8) = 0
% 4.27/1.74 |
% 4.27/1.74 | Applying alpha-rule on (30) yields:
% 4.27/1.74 | (31) ~ (all_14_0_9 = 0)
% 4.27/1.74 | (32) in(all_14_1_10, all_0_5_5) = all_14_0_9
% 4.27/1.74 | (33) in(all_14_1_10, all_0_8_8) = 0
% 4.27/1.74 |
% 4.27/1.74 | Instantiating formula (18) with all_0_4_4, all_14_1_10, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4, subset(all_0_8_8, all_0_4_4) = 0, in(all_14_1_10, all_0_8_8) = 0, yields:
% 4.27/1.75 | (34) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_14_1_10 & in(v1, all_0_6_6) = 0 & in(v0, all_0_7_7) = 0)
% 4.27/1.75 |
% 4.27/1.75 | Instantiating (34) with all_26_0_11, all_26_1_12 yields:
% 4.27/1.75 | (35) ordered_pair(all_26_1_12, all_26_0_11) = all_14_1_10 & in(all_26_0_11, all_0_6_6) = 0 & in(all_26_1_12, all_0_7_7) = 0
% 4.27/1.75 |
% 4.27/1.75 | Applying alpha-rule on (35) yields:
% 4.27/1.75 | (36) ordered_pair(all_26_1_12, all_26_0_11) = all_14_1_10
% 4.27/1.75 | (37) in(all_26_0_11, all_0_6_6) = 0
% 4.27/1.75 | (38) in(all_26_1_12, all_0_7_7) = 0
% 4.27/1.75 |
% 4.27/1.75 | Instantiating formula (23) with all_14_1_10, all_0_5_5, 0, all_14_0_9 and discharging atoms in(all_14_1_10, all_0_5_5) = all_14_0_9, yields:
% 4.27/1.75 | (39) all_14_0_9 = 0 | ~ (in(all_14_1_10, all_0_5_5) = 0)
% 4.27/1.75 |
% 4.27/1.75 | Instantiating formula (22) with all_14_1_10, all_26_0_11, all_26_1_12 and discharging atoms ordered_pair(all_26_1_12, all_26_0_11) = all_14_1_10, in(all_14_1_10, all_0_8_8) = 0, yields:
% 4.27/1.75 | (40) in(all_14_1_10, all_0_5_5) = 0
% 4.27/1.75 |
% 4.27/1.75 +-Applying beta-rule and splitting (39), into two cases.
% 4.27/1.75 |-Branch one:
% 4.27/1.75 | (41) ~ (in(all_14_1_10, all_0_5_5) = 0)
% 4.27/1.75 |
% 4.27/1.75 | Using (40) and (41) yields:
% 4.27/1.75 | (42) $false
% 4.27/1.75 |
% 4.27/1.75 |-The branch is then unsatisfiable
% 4.27/1.75 |-Branch two:
% 4.27/1.75 | (40) in(all_14_1_10, all_0_5_5) = 0
% 4.27/1.75 | (44) all_14_0_9 = 0
% 4.27/1.75 |
% 4.27/1.75 | Equations (44) can reduce 31 to:
% 4.27/1.75 | (27) $false
% 4.27/1.75 |
% 4.27/1.75 |-The branch is then unsatisfiable
% 4.27/1.75 % SZS output end Proof for theBenchmark
% 4.27/1.75
% 4.27/1.75 1153ms
%------------------------------------------------------------------------------