TSTP Solution File: SET906+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 00:23:03 EDT 2022
% Result : Theorem 2.47s 1.19s
% Output : Proof 3.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.10/0.30 % Computer : n020.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Sun Jul 10 22:44:43 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.55 ____ _
% 0.15/0.55 ___ / __ \_____(_)___ ________ __________
% 0.15/0.55 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.15/0.55 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.15/0.55 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.15/0.55
% 0.15/0.55 A Theorem Prover for First-Order Logic
% 0.15/0.56 (ePrincess v.1.0)
% 0.15/0.56
% 0.15/0.56 (c) Philipp Rümmer, 2009-2015
% 0.15/0.56 (c) Peter Backeman, 2014-2015
% 0.15/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.15/0.56 Free software under GNU Lesser General Public License (LGPL).
% 0.15/0.56 Bug reports to peter@backeman.se
% 0.15/0.56
% 0.15/0.56 For more information, visit http://user.uu.se/~petba168/breu/
% 0.15/0.56
% 0.15/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.60 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.45/0.87 Prover 0: Preprocessing ...
% 1.82/1.04 Prover 0: Warning: ignoring some quantifiers
% 1.82/1.06 Prover 0: Constructing countermodel ...
% 2.47/1.18 Prover 0: proved (580ms)
% 2.47/1.19
% 2.47/1.19 No countermodel exists, formula is valid
% 2.47/1.19 % SZS status Theorem for theBenchmark
% 2.47/1.19
% 2.47/1.19 Generating proof ... Warning: ignoring some quantifiers
% 2.97/1.39 found it (size 7)
% 2.97/1.39
% 2.97/1.39 % SZS output start Proof for theBenchmark
% 2.97/1.39 Assumed formulas after preprocessing and simplification:
% 2.97/1.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_union2(v3, v2) = v4 & unordered_pair(v0, v1) = v3 & empty(v6) & subset(v4, v2) & ~ empty(v5) & ~ in(v0, v2) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v10 = v7 | ~ (unordered_pair(v7, v8) = v9) | ~ in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v8) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v8) | in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v7) | in(v10, v9)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_union2(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v7) | ( ~ in(v11, v9) & ~ in(v11, v8))) & (in(v11, v9) | in(v11, v8) | in(v11, v7)))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (unordered_pair(v8, v9) = v10) | ? [v11] : ((v11 = v9 | v11 = v8 | in(v11, v7)) & ( ~ in(v11, v7) | ( ~ (v11 = v9) & ~ (v11 = v8))))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | set_union2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [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] : ( ~ (unordered_pair(v7, v8) = v9) | in(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ subset(v7, v8) | ~ in(v9, v7) | in(v9, v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ? [v7] : ? [v8] : (subset(v7, v8) | ? [v9] : (in(v9, v7) & ~ in(v9, v8))) & ? [v7] : subset(v7, v7))
% 3.17/1.43 | 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:
% 3.17/1.43 | (1) set_union2(all_0_3_3, all_0_4_4) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3 & empty(all_0_0_0) & subset(all_0_2_2, all_0_4_4) & ~ empty(all_0_1_1) & ~ in(all_0_6_6, all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [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] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : subset(v0, v0)
% 3.17/1.44 |
% 3.17/1.44 | Applying alpha-rule on (1) yields:
% 3.17/1.44 | (2) ~ empty(all_0_1_1)
% 3.17/1.44 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 3.17/1.44 | (4) ~ in(all_0_6_6, all_0_4_4)
% 3.17/1.44 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 3.17/1.44 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 3.17/1.44 | (7) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1)))))
% 3.17/1.45 | (8) empty(all_0_0_0)
% 3.17/1.45 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 3.17/1.45 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 3.17/1.45 | (11) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 3.17/1.45 | (12) unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3
% 3.17/1.45 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 3.17/1.45 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 3.17/1.45 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 3.17/1.45 | (16) set_union2(all_0_3_3, all_0_4_4) = all_0_2_2
% 3.17/1.45 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 3.17/1.45 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.17/1.45 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 3.17/1.45 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 3.17/1.45 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 3.17/1.45 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 3.17/1.45 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 3.17/1.45 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 3.17/1.45 | (25) ? [v0] : subset(v0, v0)
% 3.17/1.45 | (26) subset(all_0_2_2, all_0_4_4)
% 3.17/1.45 | (27) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 3.17/1.45 | (28) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0))))
% 3.17/1.46 |
% 3.17/1.46 | Instantiating formula (6) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms set_union2(all_0_3_3, all_0_4_4) = all_0_2_2, yields:
% 3.17/1.46 | (29) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2
% 3.17/1.46 |
% 3.17/1.46 | Instantiating formula (19) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 3.17/1.46 | (30) in(all_0_6_6, all_0_3_3)
% 3.17/1.46 |
% 3.17/1.46 | Instantiating formula (15) with all_0_6_6, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, in(all_0_6_6, all_0_3_3), yields:
% 3.17/1.46 | (31) in(all_0_6_6, all_0_2_2)
% 3.17/1.46 |
% 3.17/1.46 | Instantiating formula (20) with all_0_6_6, all_0_4_4, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_4_4), in(all_0_6_6, all_0_2_2), ~ in(all_0_6_6, all_0_4_4), yields:
% 3.17/1.46 | (32) $false
% 3.17/1.46 |
% 3.17/1.46 |-The branch is then unsatisfiable
% 3.17/1.46 % SZS output end Proof for theBenchmark
% 3.17/1.46
% 3.17/1.46 894ms
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