TSTP Solution File: SET882+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 00:22:54 EDT 2022
% Result : Theorem 1.93s 1.15s
% Output : Proof 2.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n011.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 : Mon Jul 11 08:48:27 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.57 ____ _
% 0.19/0.57 ___ / __ \_____(_)___ ________ __________
% 0.19/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.57
% 0.19/0.57 A Theorem Prover for First-Order Logic
% 0.19/0.57 (ePrincess v.1.0)
% 0.19/0.57
% 0.19/0.57 (c) Philipp Rümmer, 2009-2015
% 0.19/0.57 (c) Peter Backeman, 2014-2015
% 0.19/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.57 Bug reports to peter@backeman.se
% 0.19/0.57
% 0.19/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.57
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.21/0.85 Prover 0: Preprocessing ...
% 1.53/1.01 Prover 0: Warning: ignoring some quantifiers
% 1.72/1.03 Prover 0: Constructing countermodel ...
% 1.93/1.14 Prover 0: proved (523ms)
% 1.93/1.15
% 1.93/1.15 No countermodel exists, formula is valid
% 1.93/1.15 % SZS status Theorem for theBenchmark
% 1.93/1.15
% 1.93/1.15 Generating proof ... Warning: ignoring some quantifiers
% 2.64/1.36 found it (size 11)
% 2.64/1.36
% 2.64/1.36 % SZS output start Proof for theBenchmark
% 2.64/1.36 Assumed formulas after preprocessing and simplification:
% 2.64/1.36 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v5 = v4) & ~ (v1 = v0) & set_difference(v2, v3) = v4 & singleton(v1) = v3 & singleton(v0) = v5 & unordered_pair(v0, v1) = v2 & empty(v7) & ~ empty(v6) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (set_difference(v11, v10) = v12) | ~ (unordered_pair(v8, v9) = v11) | in(v9, v10) | ? [v13] : ( ~ (v13 = v12) & singleton(v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v11, v10) = v12) | ~ (unordered_pair(v8, v9) = v11) | ~ in(v9, v10) | singleton(v8) = v12 | in(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v11, v10) = v12) | ~ (unordered_pair(v8, v9) = v11) | ~ in(v8, v10) | ? [v13] : ( ~ (v13 = v12) & singleton(v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_difference(v11, v10) = v9) | ~ (set_difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v10, v9) = v11) | ~ (unordered_pair(v8, v8) = v10) | singleton(v8) = v11 | in(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v8) = v9) | ~ in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v8) = v10) | unordered_pair(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v9) = v10) | ? [v11] : (( ~ (v11 = v9) | ~ in(v9, v8)) & (v11 = v9 | in(v11, v8)))) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | in(v8, v9)) & ! [v8] : ! [v9] : ( ~ in(v9, v8) | ~ in(v8, v9)))
% 2.84/1.40 | 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 yields:
% 2.84/1.40 | (1) ~ (all_0_2_2 = all_0_3_3) & ~ (all_0_6_6 = all_0_7_7) & set_difference(all_0_5_5, all_0_4_4) = all_0_3_3 & singleton(all_0_6_6) = all_0_4_4 & singleton(all_0_7_7) = all_0_2_2 & unordered_pair(all_0_7_7, all_0_6_6) = all_0_5_5 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | singleton(v0) = v4 | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v0, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (unordered_pair(v0, v0) = v2) | singleton(v0) = v3 | in(v0, v1)) & ! [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] : ( ~ (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))
% 2.84/1.41 |
% 2.84/1.41 | Applying alpha-rule on (1) yields:
% 2.84/1.41 | (2) ~ (all_0_6_6 = all_0_7_7)
% 2.84/1.41 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 2.84/1.41 | (4) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 2.84/1.41 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | singleton(v0) = v4 | in(v0, v2))
% 2.84/1.41 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 2.84/1.41 | (7) empty(all_0_0_0)
% 2.84/1.41 | (8) set_difference(all_0_5_5, all_0_4_4) = all_0_3_3
% 2.84/1.41 | (9) singleton(all_0_6_6) = all_0_4_4
% 2.84/1.41 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.84/1.41 | (11) ~ empty(all_0_1_1)
% 2.84/1.41 | (12) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 2.84/1.41 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 2.84/1.41 | (14) ~ (all_0_2_2 = all_0_3_3)
% 2.84/1.41 | (15) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.84/1.41 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | in(v1, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5))
% 2.84/1.41 | (17) singleton(all_0_7_7) = all_0_2_2
% 2.84/1.41 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ in(v0, v2) | ? [v5] : ( ~ (v5 = v4) & singleton(v0) = v5))
% 2.84/1.42 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (unordered_pair(v0, v0) = v2) | singleton(v0) = v3 | in(v0, v1))
% 2.84/1.42 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 2.84/1.42 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 2.84/1.42 | (22) unordered_pair(all_0_7_7, all_0_6_6) = all_0_5_5
% 2.84/1.42 |
% 2.84/1.42 | Instantiating formula (12) with all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_4_4, yields:
% 2.84/1.42 | (23) in(all_0_6_6, all_0_4_4)
% 2.84/1.42 |
% 2.84/1.42 | Instantiating formula (5) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms set_difference(all_0_5_5, all_0_4_4) = all_0_3_3, unordered_pair(all_0_7_7, all_0_6_6) = all_0_5_5, in(all_0_6_6, all_0_4_4), yields:
% 2.84/1.42 | (24) singleton(all_0_7_7) = all_0_3_3 | in(all_0_7_7, all_0_4_4)
% 2.84/1.42 |
% 2.84/1.42 +-Applying beta-rule and splitting (24), into two cases.
% 2.84/1.42 |-Branch one:
% 2.84/1.42 | (25) singleton(all_0_7_7) = all_0_3_3
% 2.84/1.42 |
% 2.84/1.42 | Instantiating formula (10) with all_0_7_7, all_0_3_3, all_0_2_2 and discharging atoms singleton(all_0_7_7) = all_0_2_2, singleton(all_0_7_7) = all_0_3_3, yields:
% 2.84/1.42 | (26) all_0_2_2 = all_0_3_3
% 2.84/1.42 |
% 2.84/1.42 | Equations (26) can reduce 14 to:
% 2.84/1.42 | (27) $false
% 2.84/1.42 |
% 2.84/1.42 |-The branch is then unsatisfiable
% 2.84/1.42 |-Branch two:
% 2.84/1.42 | (28) ~ (singleton(all_0_7_7) = all_0_3_3)
% 2.84/1.42 | (29) in(all_0_7_7, all_0_4_4)
% 2.84/1.42 |
% 2.84/1.42 | Instantiating formula (3) with all_0_7_7, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_4_4, in(all_0_7_7, all_0_4_4), yields:
% 2.84/1.42 | (30) all_0_6_6 = all_0_7_7
% 2.84/1.42 |
% 2.84/1.42 | Equations (30) can reduce 2 to:
% 2.84/1.42 | (27) $false
% 2.84/1.42 |
% 2.84/1.42 |-The branch is then unsatisfiable
% 2.84/1.42 % SZS output end Proof for theBenchmark
% 2.84/1.42
% 2.84/1.42 838ms
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