TSTP Solution File: SET893+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 00:22:58 EDT 2022
% Result : Theorem 2.39s 1.26s
% Output : Proof 3.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.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 : Mon Jul 11 03:08:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.51/0.58 ____ _
% 0.51/0.58 ___ / __ \_____(_)___ ________ __________
% 0.51/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.58
% 0.51/0.58 A Theorem Prover for First-Order Logic
% 0.51/0.58 (ePrincess v.1.0)
% 0.51/0.58
% 0.51/0.58 (c) Philipp Rümmer, 2009-2015
% 0.51/0.58 (c) Peter Backeman, 2014-2015
% 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.58 Bug reports to peter@backeman.se
% 0.51/0.58
% 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.58
% 0.51/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.26/0.90 Prover 0: Preprocessing ...
% 1.76/1.07 Prover 0: Warning: ignoring some quantifiers
% 1.82/1.09 Prover 0: Constructing countermodel ...
% 2.39/1.26 Prover 0: proved (632ms)
% 2.39/1.26
% 2.39/1.26 No countermodel exists, formula is valid
% 2.39/1.26 % SZS status Theorem for theBenchmark
% 2.39/1.26
% 2.39/1.26 Generating proof ... Warning: ignoring some quantifiers
% 3.11/1.50 found it (size 25)
% 3.11/1.50
% 3.11/1.50 % SZS output start Proof for theBenchmark
% 3.11/1.50 Assumed formulas after preprocessing and simplification:
% 3.11/1.50 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v5, v6) = v7 & ordered_pair(v0, v1) = v4 & singleton(v3) = v6 & singleton(v2) = v5 & empty(v9) & ~ empty(v8) & ! [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] : (v12 = v10 | ~ (singleton(v10) = v11) | ~ in(v12, v11)) & ! [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] : ! [v12] : (v12 = v10 | ~ (singleton(v11) = v12) | ? [v13] : (( ~ (v13 = v11) | ~ in(v11, v10)) & (v13 = v11 | in(v13, v10)))) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | ~ in(v10, v11)) & ((v3 = v1 & v2 = v0 & ~ in(v4, v7)) | (in(v4, v7) & ( ~ (v3 = v1) | ~ (v2 = v0)))))
% 3.32/1.54 | 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:
% 3.32/1.54 | (1) cartesian_product2(all_0_4_4, all_0_3_3) = all_0_2_2 & ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5 & singleton(all_0_6_6) = all_0_3_3 & singleton(all_0_7_7) = all_0_4_4 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [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] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, 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] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ((all_0_6_6 = all_0_8_8 & all_0_7_7 = all_0_9_9 & ~ in(all_0_5_5, all_0_2_2)) | (in(all_0_5_5, all_0_2_2) & ( ~ (all_0_6_6 = all_0_8_8) | ~ (all_0_7_7 = all_0_9_9))))
% 3.32/1.55 |
% 3.32/1.55 | Applying alpha-rule on (1) yields:
% 3.32/1.55 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 3.32/1.55 | (3) cartesian_product2(all_0_4_4, all_0_3_3) = all_0_2_2
% 3.32/1.55 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 3.32/1.55 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 3.32/1.55 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2))
% 3.32/1.55 | (7) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 3.32/1.55 | (8) singleton(all_0_7_7) = all_0_4_4
% 3.32/1.55 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 3.32/1.55 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 3.32/1.55 | (11) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.32/1.55 | (12) singleton(all_0_6_6) = all_0_3_3
% 3.32/1.55 | (13) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 3.32/1.55 | (14) ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5
% 3.32/1.55 | (15) ~ empty(all_0_1_1)
% 3.32/1.55 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.32/1.55 | (17) ! [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))
% 3.32/1.55 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 3.32/1.55 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.32/1.55 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 3.32/1.55 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3))
% 3.32/1.55 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 3.32/1.55 | (23) (all_0_6_6 = all_0_8_8 & all_0_7_7 = all_0_9_9 & ~ in(all_0_5_5, all_0_2_2)) | (in(all_0_5_5, all_0_2_2) & ( ~ (all_0_6_6 = all_0_8_8) | ~ (all_0_7_7 = all_0_9_9)))
% 3.32/1.55 | (24) empty(all_0_0_0)
% 3.32/1.55 |
% 3.32/1.55 | Instantiating formula (9) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5, yields:
% 3.32/1.55 | (25) ? [v0] : ? [v1] : (singleton(all_0_9_9) = v1 & unordered_pair(v0, v1) = all_0_5_5 & unordered_pair(all_0_9_9, all_0_8_8) = v0)
% 3.32/1.56 |
% 3.32/1.56 | Instantiating formula (13) with all_0_3_3, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_3_3, yields:
% 3.32/1.56 | (26) in(all_0_6_6, all_0_3_3)
% 3.32/1.56 |
% 3.32/1.56 | Instantiating (25) with all_11_0_11, all_11_1_12 yields:
% 3.32/1.56 | (27) singleton(all_0_9_9) = all_11_0_11 & unordered_pair(all_11_1_12, all_11_0_11) = all_0_5_5 & unordered_pair(all_0_9_9, all_0_8_8) = all_11_1_12
% 3.32/1.56 |
% 3.32/1.56 | Applying alpha-rule on (27) yields:
% 3.32/1.56 | (28) singleton(all_0_9_9) = all_11_0_11
% 3.32/1.56 | (29) unordered_pair(all_11_1_12, all_11_0_11) = all_0_5_5
% 3.32/1.56 | (30) unordered_pair(all_0_9_9, all_0_8_8) = all_11_1_12
% 3.32/1.56 |
% 3.32/1.56 | Instantiating formula (13) with all_11_0_11, all_0_9_9 and discharging atoms singleton(all_0_9_9) = all_11_0_11, yields:
% 3.32/1.56 | (31) in(all_0_9_9, all_11_0_11)
% 3.32/1.56 |
% 3.32/1.56 +-Applying beta-rule and splitting (23), into two cases.
% 3.32/1.56 |-Branch one:
% 3.32/1.56 | (32) all_0_6_6 = all_0_8_8 & all_0_7_7 = all_0_9_9 & ~ in(all_0_5_5, all_0_2_2)
% 3.32/1.56 |
% 3.32/1.56 | Applying alpha-rule on (32) yields:
% 3.32/1.56 | (33) all_0_6_6 = all_0_8_8
% 3.32/1.56 | (34) all_0_7_7 = all_0_9_9
% 3.32/1.56 | (35) ~ in(all_0_5_5, all_0_2_2)
% 3.32/1.56 |
% 3.32/1.56 | From (34) and (8) follows:
% 3.32/1.56 | (36) singleton(all_0_9_9) = all_0_4_4
% 3.32/1.56 |
% 3.32/1.56 | From (33) and (26) follows:
% 3.32/1.56 | (37) in(all_0_8_8, all_0_3_3)
% 3.32/1.56 |
% 3.32/1.56 | Instantiating formula (4) with all_0_9_9, all_0_4_4, all_11_0_11 and discharging atoms singleton(all_0_9_9) = all_11_0_11, singleton(all_0_9_9) = all_0_4_4, yields:
% 3.32/1.56 | (38) all_11_0_11 = all_0_4_4
% 3.32/1.56 |
% 3.32/1.56 | From (38) and (31) follows:
% 3.32/1.56 | (39) in(all_0_9_9, all_0_4_4)
% 3.32/1.56 |
% 3.32/1.56 | Instantiating formula (17) with all_0_2_2, all_0_5_5, all_0_3_3, all_0_4_4, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_4_4, all_0_3_3) = all_0_2_2, ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5, in(all_0_8_8, all_0_3_3), in(all_0_9_9, all_0_4_4), ~ in(all_0_5_5, all_0_2_2), yields:
% 3.32/1.56 | (40) $false
% 3.32/1.56 |
% 3.32/1.56 |-The branch is then unsatisfiable
% 3.32/1.56 |-Branch two:
% 3.32/1.56 | (41) in(all_0_5_5, all_0_2_2) & ( ~ (all_0_6_6 = all_0_8_8) | ~ (all_0_7_7 = all_0_9_9))
% 3.32/1.56 |
% 3.32/1.56 | Applying alpha-rule on (41) yields:
% 3.32/1.56 | (42) in(all_0_5_5, all_0_2_2)
% 3.32/1.56 | (43) ~ (all_0_6_6 = all_0_8_8) | ~ (all_0_7_7 = all_0_9_9)
% 3.32/1.56 |
% 3.32/1.56 | Instantiating formula (21) with all_0_2_2, all_0_5_5, all_0_3_3, all_0_4_4, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_4_4, all_0_3_3) = all_0_2_2, ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5, in(all_0_5_5, all_0_2_2), yields:
% 3.32/1.56 | (37) in(all_0_8_8, all_0_3_3)
% 3.32/1.56 |
% 3.32/1.56 | Instantiating formula (6) with all_0_2_2, all_0_5_5, all_0_3_3, all_0_4_4, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_4_4, all_0_3_3) = all_0_2_2, ordered_pair(all_0_9_9, all_0_8_8) = all_0_5_5, in(all_0_5_5, all_0_2_2), yields:
% 3.32/1.56 | (39) in(all_0_9_9, all_0_4_4)
% 3.32/1.56 |
% 3.32/1.56 | Instantiating formula (22) with all_0_8_8, all_0_3_3, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_3_3, in(all_0_8_8, all_0_3_3), yields:
% 3.32/1.56 | (33) all_0_6_6 = all_0_8_8
% 3.32/1.56 |
% 3.32/1.56 | Instantiating formula (22) with all_0_9_9, all_0_4_4, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_4_4, in(all_0_9_9, all_0_4_4), yields:
% 3.32/1.56 | (34) all_0_7_7 = all_0_9_9
% 3.32/1.56 |
% 3.32/1.56 +-Applying beta-rule and splitting (43), into two cases.
% 3.32/1.56 |-Branch one:
% 3.32/1.56 | (48) ~ (all_0_6_6 = all_0_8_8)
% 3.32/1.56 |
% 3.32/1.56 | Equations (33) can reduce 48 to:
% 3.32/1.56 | (49) $false
% 3.32/1.56 |
% 3.32/1.56 |-The branch is then unsatisfiable
% 3.32/1.56 |-Branch two:
% 3.32/1.56 | (33) all_0_6_6 = all_0_8_8
% 3.32/1.57 | (51) ~ (all_0_7_7 = all_0_9_9)
% 3.32/1.57 |
% 3.32/1.57 | Equations (34) can reduce 51 to:
% 3.32/1.57 | (49) $false
% 3.32/1.57 |
% 3.32/1.57 |-The branch is then unsatisfiable
% 3.32/1.57 % SZS output end Proof for theBenchmark
% 3.32/1.57
% 3.32/1.57 975ms
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