TSTP Solution File: SET954+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 00:23:25 EDT 2022
% Result : Theorem 2.24s 1.23s
% Output : Proof 2.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 17:00:32 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.49/0.62 ____ _
% 0.49/0.62 ___ / __ \_____(_)___ ________ __________
% 0.49/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.62
% 0.49/0.62 A Theorem Prover for First-Order Logic
% 0.49/0.62 (ePrincess v.1.0)
% 0.49/0.62
% 0.49/0.62 (c) Philipp Rümmer, 2009-2015
% 0.49/0.62 (c) Peter Backeman, 2014-2015
% 0.49/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.62 Bug reports to peter@backeman.se
% 0.49/0.62
% 0.49/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.62
% 0.66/0.62 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
% 1.38/0.95 Prover 0: Preprocessing ...
% 1.73/1.10 Prover 0: Constructing countermodel ...
% 2.24/1.23 Prover 0: proved (553ms)
% 2.24/1.23
% 2.24/1.23 No countermodel exists, formula is valid
% 2.24/1.23 % SZS status Theorem for theBenchmark
% 2.24/1.23
% 2.24/1.23 Generating proof ... found it (size 6)
% 2.86/1.43
% 2.86/1.43 % SZS output start Proof for theBenchmark
% 2.86/1.43 Assumed formulas after preprocessing and simplification:
% 2.86/1.43 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v3, v2) = v7 & cartesian_product2(v2, v3) = v5 & ordered_pair(v1, v0) = v6 & ordered_pair(v0, v1) = v4 & empty(v9) & in(v4, v5) & ~ empty(v8) & ~ in(v6, v7) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ in(v14, v15) | in(v11, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ in(v14, v15) | in(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ in(v11, v13) | ~ in(v10, v12) | in(v14, v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v10) = v13) | ~ (unordered_pair(v12, v13) = v14) | ~ (unordered_pair(v10, v11) = v12) | ordered_pair(v10, v11) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ~ empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & unordered_pair(v13, v14) = v12 & unordered_pair(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | ~ in(v10, v11)))
% 2.95/1.47 | 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, all_0_9_9 yields:
% 2.95/1.47 | (1) cartesian_product2(all_0_6_6, all_0_7_7) = all_0_2_2 & cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4 & ordered_pair(all_0_8_8, all_0_9_9) = all_0_3_3 & ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5 & empty(all_0_0_0) & in(all_0_5_5, all_0_4_4) & ~ empty(all_0_1_1) & ~ in(all_0_3_3, all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [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] : (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] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.95/1.48 |
% 2.95/1.48 | Applying alpha-rule on (1) yields:
% 2.95/1.48 | (2) ordered_pair(all_0_8_8, all_0_9_9) = all_0_3_3
% 2.95/1.48 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 2.95/1.48 | (4) ~ in(all_0_3_3, all_0_2_2)
% 2.95/1.48 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 2.95/1.48 | (6) in(all_0_5_5, all_0_4_4)
% 2.95/1.48 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2))
% 2.95/1.48 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 2.95/1.48 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.95/1.48 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 2.95/1.48 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 2.95/1.48 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 2.95/1.48 | (13) empty(all_0_0_0)
% 2.95/1.48 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3))
% 2.95/1.48 | (15) ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5
% 2.95/1.48 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 2.95/1.48 | (17) cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4
% 2.95/1.48 | (18) ~ empty(all_0_1_1)
% 2.95/1.48 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5))
% 2.95/1.48 | (20) cartesian_product2(all_0_6_6, all_0_7_7) = all_0_2_2
% 2.95/1.48 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 2.95/1.48 | (22) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.95/1.48 |
% 2.95/1.48 | Instantiating formula (14) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4, ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5, in(all_0_5_5, all_0_4_4), yields:
% 2.95/1.49 | (23) in(all_0_8_8, all_0_6_6)
% 2.95/1.49 |
% 2.95/1.49 | Instantiating formula (7) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_7_7, all_0_6_6) = all_0_4_4, ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5, in(all_0_5_5, all_0_4_4), yields:
% 2.95/1.49 | (24) in(all_0_9_9, all_0_7_7)
% 2.95/1.49 |
% 2.95/1.49 | Instantiating formula (19) with all_0_2_2, all_0_3_3, all_0_7_7, all_0_6_6, all_0_9_9, all_0_8_8 and discharging atoms cartesian_product2(all_0_6_6, all_0_7_7) = all_0_2_2, ordered_pair(all_0_8_8, all_0_9_9) = all_0_3_3, in(all_0_8_8, all_0_6_6), in(all_0_9_9, all_0_7_7), ~ in(all_0_3_3, all_0_2_2), yields:
% 2.95/1.49 | (25) $false
% 2.95/1.49 |
% 2.95/1.49 |-The branch is then unsatisfiable
% 2.95/1.49 % SZS output end Proof for theBenchmark
% 2.95/1.49
% 2.95/1.49 851ms
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