TSTP Solution File: SET983+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.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 00:23:36 EDT 2022
% Result : Theorem 2.30s 1.21s
% Output : Proof 3.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n018.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 15:14:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/0.59 ____ _
% 0.60/0.59 ___ / __ \_____(_)___ ________ __________
% 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.59
% 0.60/0.59 A Theorem Prover for First-Order Logic
% 0.60/0.59 (ePrincess v.1.0)
% 0.60/0.59
% 0.60/0.59 (c) Philipp Rümmer, 2009-2015
% 0.60/0.59 (c) Peter Backeman, 2014-2015
% 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.59 Bug reports to peter@backeman.se
% 0.60/0.59
% 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.59
% 0.60/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.37/0.90 Prover 0: Preprocessing ...
% 1.68/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.68/1.08 Prover 0: Constructing countermodel ...
% 2.30/1.21 Prover 0: proved (573ms)
% 2.30/1.21
% 2.30/1.21 No countermodel exists, formula is valid
% 2.30/1.21 % SZS status Theorem for theBenchmark
% 2.30/1.21
% 2.30/1.21 Generating proof ... Warning: ignoring some quantifiers
% 2.96/1.44 found it (size 10)
% 2.96/1.44
% 2.96/1.44 % SZS output start Proof for theBenchmark
% 2.96/1.44 Assumed formulas after preprocessing and simplification:
% 2.96/1.44 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (cartesian_product2(v7, v8) = v9 & cartesian_product2(v3, v4) = v6 & cartesian_product2(v1, v2) = v5 & set_intersection2(v2, v4) = v8 & set_intersection2(v1, v3) = v7 & empty(v11) & in(v0, v6) & in(v0, v5) & ~ empty(v10) & ~ in(v0, v9) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v16, v17) = v18) | ~ (set_intersection2(v14, v15) = v17) | ~ (set_intersection2(v12, v13) = v16) | ? [v19] : ? [v20] : (cartesian_product2(v13, v15) = v20 & cartesian_product2(v12, v14) = v19 & set_intersection2(v19, v20) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v13, v15) = v17) | ~ (cartesian_product2(v12, v14) = v16) | ~ (set_intersection2(v16, v17) = v18) | ? [v19] : ? [v20] : (cartesian_product2(v19, v20) = v18 & set_intersection2(v14, v15) = v20 & set_intersection2(v12, v13) = v19)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (cartesian_product2(v15, v14) = v13) | ~ (cartesian_product2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_intersection2(v15, v14) = v13) | ~ (set_intersection2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ in(v15, v14) | in(v15, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ in(v15, v14) | in(v15, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ in(v15, v13) | ~ in(v15, v12) | in(v15, v14)) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_intersection2(v13, v14) = v15) | ? [v16] : (( ~ in(v16, v14) | ~ in(v16, v13) | ~ in(v16, v12)) & (in(v16, v12) | (in(v16, v14) & in(v16, v13))))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v13, v12) = v14) | set_intersection2(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | set_intersection2(v13, v12) = v14) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_intersection2(v12, v12) = v13)) & ! [v12] : ! [v13] : ( ~ in(v13, v12) | ~ in(v12, v13)))
% 3.13/1.48 | 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, all_0_10_10, all_0_11_11 yields:
% 3.13/1.48 | (1) cartesian_product2(all_0_4_4, all_0_3_3) = all_0_2_2 & cartesian_product2(all_0_8_8, all_0_7_7) = all_0_5_5 & cartesian_product2(all_0_10_10, all_0_9_9) = all_0_6_6 & set_intersection2(all_0_9_9, all_0_7_7) = all_0_3_3 & set_intersection2(all_0_10_10, all_0_8_8) = all_0_4_4 & empty(all_0_0_0) & in(all_0_11_11, all_0_5_5) & in(all_0_11_11, all_0_6_6) & ~ empty(all_0_1_1) & ~ in(all_0_11_11, all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v4, v5) = v6) | ~ (set_intersection2(v2, v3) = v5) | ~ (set_intersection2(v0, v1) = v4) | ? [v7] : ? [v8] : (cartesian_product2(v1, v3) = v8 & cartesian_product2(v0, v2) = v7 & set_intersection2(v7, v8) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (set_intersection2(v4, v5) = v6) | ? [v7] : ? [v8] : (cartesian_product2(v7, v8) = v6 & set_intersection2(v2, v3) = v8 & set_intersection2(v0, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.13/1.48 |
% 3.13/1.48 | Applying alpha-rule on (1) yields:
% 3.13/1.48 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 3.13/1.49 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (set_intersection2(v4, v5) = v6) | ? [v7] : ? [v8] : (cartesian_product2(v7, v8) = v6 & set_intersection2(v2, v3) = v8 & set_intersection2(v0, v1) = v7))
% 3.13/1.49 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 3.13/1.49 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 3.13/1.49 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 3.13/1.49 | (7) in(all_0_11_11, all_0_5_5)
% 3.13/1.49 | (8) set_intersection2(all_0_9_9, all_0_7_7) = all_0_3_3
% 3.13/1.49 | (9) cartesian_product2(all_0_10_10, all_0_9_9) = all_0_6_6
% 3.13/1.49 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 3.13/1.49 | (11) cartesian_product2(all_0_8_8, all_0_7_7) = all_0_5_5
% 3.13/1.49 | (12) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.13/1.49 | (13) empty(all_0_0_0)
% 3.13/1.49 | (14) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1)))))
% 3.13/1.49 | (15) ~ in(all_0_11_11, all_0_2_2)
% 3.13/1.49 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 3.13/1.49 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1))
% 3.13/1.49 | (18) ~ empty(all_0_1_1)
% 3.13/1.49 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 3.13/1.49 | (20) cartesian_product2(all_0_4_4, all_0_3_3) = all_0_2_2
% 3.13/1.49 | (21) set_intersection2(all_0_10_10, all_0_8_8) = all_0_4_4
% 3.13/1.49 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v4, v5) = v6) | ~ (set_intersection2(v2, v3) = v5) | ~ (set_intersection2(v0, v1) = v4) | ? [v7] : ? [v8] : (cartesian_product2(v1, v3) = v8 & cartesian_product2(v0, v2) = v7 & set_intersection2(v7, v8) = v6))
% 3.13/1.49 | (23) in(all_0_11_11, all_0_6_6)
% 3.13/1.49 |
% 3.13/1.49 | Instantiating formula (22) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_7_7, all_0_9_9, all_0_8_8, all_0_10_10 and discharging atoms cartesian_product2(all_0_4_4, all_0_3_3) = all_0_2_2, set_intersection2(all_0_9_9, all_0_7_7) = all_0_3_3, set_intersection2(all_0_10_10, all_0_8_8) = all_0_4_4, yields:
% 3.13/1.49 | (24) ? [v0] : ? [v1] : (cartesian_product2(all_0_8_8, all_0_7_7) = v1 & cartesian_product2(all_0_10_10, all_0_9_9) = v0 & set_intersection2(v0, v1) = all_0_2_2)
% 3.13/1.49 |
% 3.13/1.49 | Instantiating (24) with all_11_0_13, all_11_1_14 yields:
% 3.13/1.49 | (25) cartesian_product2(all_0_8_8, all_0_7_7) = all_11_0_13 & cartesian_product2(all_0_10_10, all_0_9_9) = all_11_1_14 & set_intersection2(all_11_1_14, all_11_0_13) = all_0_2_2
% 3.13/1.49 |
% 3.13/1.49 | Applying alpha-rule on (25) yields:
% 3.13/1.49 | (26) cartesian_product2(all_0_8_8, all_0_7_7) = all_11_0_13
% 3.13/1.49 | (27) cartesian_product2(all_0_10_10, all_0_9_9) = all_11_1_14
% 3.13/1.50 | (28) set_intersection2(all_11_1_14, all_11_0_13) = all_0_2_2
% 3.13/1.50 |
% 3.13/1.50 | Instantiating formula (10) with all_0_8_8, all_0_7_7, all_11_0_13, all_0_5_5 and discharging atoms cartesian_product2(all_0_8_8, all_0_7_7) = all_11_0_13, cartesian_product2(all_0_8_8, all_0_7_7) = all_0_5_5, yields:
% 3.13/1.50 | (29) all_11_0_13 = all_0_5_5
% 3.13/1.50 |
% 3.13/1.50 | Instantiating formula (10) with all_0_10_10, all_0_9_9, all_11_1_14, all_0_6_6 and discharging atoms cartesian_product2(all_0_10_10, all_0_9_9) = all_11_1_14, cartesian_product2(all_0_10_10, all_0_9_9) = all_0_6_6, yields:
% 3.13/1.50 | (30) all_11_1_14 = all_0_6_6
% 3.13/1.50 |
% 3.13/1.50 | From (30)(29) and (28) follows:
% 3.13/1.50 | (31) set_intersection2(all_0_6_6, all_0_5_5) = all_0_2_2
% 3.13/1.50 |
% 3.13/1.50 | Instantiating formula (19) with all_0_11_11, all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_2_2, in(all_0_11_11, all_0_5_5), in(all_0_11_11, all_0_6_6), ~ in(all_0_11_11, all_0_2_2), yields:
% 3.13/1.50 | (32) $false
% 3.13/1.50 |
% 3.13/1.50 |-The branch is then unsatisfiable
% 3.13/1.50 % SZS output end Proof for theBenchmark
% 3.13/1.50
% 3.13/1.50 900ms
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