TSTP Solution File: SET950+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% 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 00:23:23 EDT 2022
% Result : Theorem 2.30s 1.25s
% Output : Proof 3.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % 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 : Sun Jul 10 03:10:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.38/0.92 Prover 0: Preprocessing ...
% 1.79/1.11 Prover 0: Warning: ignoring some quantifiers
% 1.79/1.13 Prover 0: Constructing countermodel ...
% 2.30/1.24 Prover 0: proved (600ms)
% 2.30/1.25
% 2.30/1.25 No countermodel exists, formula is valid
% 2.30/1.25 % SZS status Theorem for theBenchmark
% 2.30/1.25
% 2.30/1.25 Generating proof ... Warning: ignoring some quantifiers
% 3.07/1.46 found it (size 12)
% 3.07/1.46
% 3.07/1.46 % SZS output start Proof for theBenchmark
% 3.07/1.46 Assumed formulas after preprocessing and simplification:
% 3.07/1.46 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v4 & empty(v6) & subset(v0, v4) & in(v3, v0) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v7, v8) = v9) | ~ (ordered_pair(v11, v12) = v10) | ~ in(v12, v8) | ~ in(v11, v7) | in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v7) = v10) | ~ (unordered_pair(v9, v10) = v11) | ~ (unordered_pair(v7, v8) = v9) | ordered_pair(v7, v8) = v11) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (cartesian_product2(v10, v9) = v8) | ~ (cartesian_product2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (ordered_pair(v10, v9) = v8) | ~ (ordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cartesian_product2(v7, v8) = v9) | ~ in(v10, v9) | ? [v11] : ? [v12] : (ordered_pair(v11, v12) = v10 & in(v12, v8) & in(v11, v7))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (cartesian_product2(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (( ~ in(v11, v7) | ! [v15] : ! [v16] : ( ~ (ordered_pair(v15, v16) = v11) | ~ in(v16, v9) | ~ in(v15, v8))) & (in(v11, v7) | (v14 = v11 & ordered_pair(v12, v13) = v11 & in(v13, v9) & in(v12, v8))))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ empty(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ? [v11] : (singleton(v7) = v11 & unordered_pair(v10, v11) = v9 & unordered_pair(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ subset(v7, v8) | ~ in(v9, v7) | in(v9, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v2) | ~ in(v7, v1) | ? [v9] : ( ~ (v9 = v3) & ordered_pair(v7, v8) = v9)) & ? [v7] : ? [v8] : (subset(v7, v8) | ? [v9] : (in(v9, v7) & ~ in(v9, v8))) & ? [v7] : subset(v7, v7))
% 3.07/1.50 | 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 yields:
% 3.07/1.50 | (1) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2 & empty(all_0_0_0) & subset(all_0_6_6, all_0_2_2) & in(all_0_3_3, all_0_6_6) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [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] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) & ! [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] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, all_0_4_4) | ~ in(v0, all_0_5_5) | ? [v2] : ( ~ (v2 = all_0_3_3) & ordered_pair(v0, v1) = v2)) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : subset(v0, v0)
% 3.07/1.51 |
% 3.07/1.51 | Applying alpha-rule on (1) yields:
% 3.07/1.51 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 3.07/1.51 | (3) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.07/1.51 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0)))
% 3.07/1.51 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 3.07/1.51 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 3.07/1.51 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 3.07/1.51 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.07/1.51 | (9) ! [v0] : ! [v1] : ( ~ in(v1, all_0_4_4) | ~ in(v0, all_0_5_5) | ? [v2] : ( ~ (v2 = all_0_3_3) & ordered_pair(v0, v1) = v2))
% 3.07/1.51 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 3.07/1.51 | (11) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 3.07/1.51 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2))
% 3.07/1.51 | (13) empty(all_0_0_0)
% 3.07/1.51 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.07/1.51 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 3.07/1.51 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 3.07/1.51 | (17) subset(all_0_6_6, all_0_2_2)
% 3.07/1.51 | (18) in(all_0_3_3, all_0_6_6)
% 3.07/1.51 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 3.07/1.52 | (20) ~ empty(all_0_1_1)
% 3.07/1.52 | (21) ? [v0] : subset(v0, v0)
% 3.07/1.52 | (22) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1)))))
% 3.07/1.52 | (23) cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2
% 3.07/1.52 |
% 3.07/1.52 | Instantiating formula (2) with all_0_3_3, all_0_2_2, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_2_2), in(all_0_3_3, all_0_6_6), yields:
% 3.07/1.52 | (24) in(all_0_3_3, all_0_2_2)
% 3.07/1.52 |
% 3.07/1.52 | Instantiating formula (4) with all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms cartesian_product2(all_0_5_5, all_0_4_4) = all_0_2_2, in(all_0_3_3, all_0_2_2), yields:
% 3.07/1.52 | (25) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_0_3_3 & in(v1, all_0_4_4) & in(v0, all_0_5_5))
% 3.07/1.52 |
% 3.07/1.52 | Instantiating (25) with all_19_0_11, all_19_1_12 yields:
% 3.07/1.52 | (26) ordered_pair(all_19_1_12, all_19_0_11) = all_0_3_3 & in(all_19_0_11, all_0_4_4) & in(all_19_1_12, all_0_5_5)
% 3.07/1.52 |
% 3.07/1.52 | Applying alpha-rule on (26) yields:
% 3.07/1.52 | (27) ordered_pair(all_19_1_12, all_19_0_11) = all_0_3_3
% 3.07/1.52 | (28) in(all_19_0_11, all_0_4_4)
% 3.07/1.52 | (29) in(all_19_1_12, all_0_5_5)
% 3.07/1.52 |
% 3.07/1.52 | Instantiating formula (9) with all_19_0_11, all_19_1_12 and discharging atoms in(all_19_0_11, all_0_4_4), in(all_19_1_12, all_0_5_5), yields:
% 3.07/1.52 | (30) ? [v0] : ( ~ (v0 = all_0_3_3) & ordered_pair(all_19_1_12, all_19_0_11) = v0)
% 3.07/1.52 |
% 3.07/1.52 | Instantiating (30) with all_26_0_13 yields:
% 3.07/1.52 | (31) ~ (all_26_0_13 = all_0_3_3) & ordered_pair(all_19_1_12, all_19_0_11) = all_26_0_13
% 3.07/1.52 |
% 3.07/1.52 | Applying alpha-rule on (31) yields:
% 3.07/1.52 | (32) ~ (all_26_0_13 = all_0_3_3)
% 3.07/1.52 | (33) ordered_pair(all_19_1_12, all_19_0_11) = all_26_0_13
% 3.07/1.52 |
% 3.07/1.52 | Instantiating formula (6) with all_19_1_12, all_19_0_11, all_26_0_13, all_0_3_3 and discharging atoms ordered_pair(all_19_1_12, all_19_0_11) = all_26_0_13, ordered_pair(all_19_1_12, all_19_0_11) = all_0_3_3, yields:
% 3.07/1.52 | (34) all_26_0_13 = all_0_3_3
% 3.07/1.52 |
% 3.07/1.52 | Equations (34) can reduce 32 to:
% 3.07/1.52 | (35) $false
% 3.07/1.52 |
% 3.07/1.52 |-The branch is then unsatisfiable
% 3.07/1.52 % SZS output end Proof for theBenchmark
% 3.07/1.52
% 3.07/1.52 920ms
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