TSTP Solution File: SET902+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 00:23:01 EDT 2022
% Result : Theorem 2.13s 1.19s
% Output : Proof 2.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n014.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 02:20:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.58 ____ _
% 0.57/0.58 ___ / __ \_____(_)___ ________ __________
% 0.57/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.58
% 0.57/0.58 A Theorem Prover for First-Order Logic
% 0.57/0.58 (ePrincess v.1.0)
% 0.57/0.58
% 0.57/0.58 (c) Philipp Rümmer, 2009-2015
% 0.57/0.58 (c) Peter Backeman, 2014-2015
% 0.57/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.58 Bug reports to peter@backeman.se
% 0.57/0.58
% 0.57/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.58
% 0.57/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.57/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.91 Prover 0: Preprocessing ...
% 1.66/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.66/1.07 Prover 0: Constructing countermodel ...
% 2.13/1.19 Prover 0: proved (562ms)
% 2.13/1.19
% 2.13/1.19 No countermodel exists, formula is valid
% 2.13/1.19 % SZS status Theorem for theBenchmark
% 2.13/1.19
% 2.13/1.19 Generating proof ... Warning: ignoring some quantifiers
% 2.63/1.39 found it (size 34)
% 2.63/1.39
% 2.63/1.39 % SZS output start Proof for theBenchmark
% 2.63/1.39 Assumed formulas after preprocessing and simplification:
% 2.63/1.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (singleton(v0) = v3 & set_union2(v1, v2) = v3 & empty(v5) & empty(empty_set) & ~ empty(v4) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_union2(v9, v8) = v7) | ~ (set_union2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | v6 = empty_set | ~ (singleton(v7) = v8) | ~ subset(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | set_union2(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | set_union2(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | subset(v6, v8)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (set_union2(v6, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (singleton(v7) = v6) | subset(v6, v6)) & ! [v6] : ! [v7] : ( ~ (singleton(v6) = v7) | subset(empty_set, v7)) & ! [v6] : ~ (singleton(v6) = empty_set) & ? [v6] : subset(v6, v6) & ( ~ (v3 = v2) | ~ (v1 = empty_set)) & ( ~ (v3 = v1) | ~ (v2 = v1)) & ( ~ (v3 = v1) | ~ (v2 = empty_set)))
% 2.63/1.43 | 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 yields:
% 2.63/1.43 | (1) singleton(all_0_5_5) = all_0_2_2 & set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [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] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ~ (singleton(v0) = empty_set) & ? [v0] : subset(v0, v0) & ( ~ (all_0_2_2 = all_0_3_3) | ~ (all_0_4_4 = empty_set)) & ( ~ (all_0_2_2 = all_0_4_4) | ~ (all_0_3_3 = all_0_4_4)) & ( ~ (all_0_2_2 = all_0_4_4) | ~ (all_0_3_3 = empty_set))
% 2.63/1.43 |
% 2.63/1.43 | Applying alpha-rule on (1) yields:
% 2.63/1.43 | (2) empty(all_0_0_0)
% 2.63/1.43 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 2.63/1.44 | (4) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 2.63/1.44 | (5) ~ empty(all_0_1_1)
% 2.63/1.44 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 2.63/1.44 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 2.63/1.44 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.63/1.44 | (9) ~ (all_0_2_2 = all_0_4_4) | ~ (all_0_3_3 = all_0_4_4)
% 2.63/1.44 | (10) singleton(all_0_5_5) = all_0_2_2
% 2.63/1.44 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 2.63/1.44 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 2.63/1.44 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 2.63/1.44 | (14) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 2.63/1.44 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 2.63/1.44 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 2.63/1.44 | (17) ! [v0] : ~ (singleton(v0) = empty_set)
% 2.63/1.44 | (18) ? [v0] : subset(v0, v0)
% 2.63/1.44 | (19) empty(empty_set)
% 2.63/1.44 | (20) ~ (all_0_2_2 = all_0_4_4) | ~ (all_0_3_3 = empty_set)
% 2.63/1.44 | (21) ~ (all_0_2_2 = all_0_3_3) | ~ (all_0_4_4 = empty_set)
% 2.63/1.44 | (22) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2
% 2.63/1.44 |
% 2.63/1.44 | Instantiating formula (13) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 2.63/1.44 | (23) set_union2(all_0_3_3, all_0_4_4) = all_0_2_2
% 2.63/1.44 |
% 2.63/1.44 | Instantiating formula (11) with 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, yields:
% 2.63/1.44 | (24) subset(all_0_4_4, all_0_2_2)
% 2.63/1.44 |
% 2.63/1.44 | Instantiating formula (15) with all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms singleton(all_0_5_5) = all_0_2_2, subset(all_0_4_4, all_0_2_2), yields:
% 2.63/1.44 | (25) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set
% 2.63/1.44 |
% 2.63/1.44 | Instantiating formula (11) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms set_union2(all_0_3_3, all_0_4_4) = all_0_2_2, yields:
% 2.63/1.44 | (26) subset(all_0_3_3, all_0_2_2)
% 2.63/1.44 |
% 2.63/1.44 | Instantiating formula (15) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms singleton(all_0_5_5) = all_0_2_2, subset(all_0_3_3, all_0_2_2), yields:
% 2.63/1.44 | (27) all_0_2_2 = all_0_3_3 | all_0_3_3 = empty_set
% 2.63/1.44 |
% 2.63/1.44 +-Applying beta-rule and splitting (20), into two cases.
% 2.63/1.44 |-Branch one:
% 2.63/1.44 | (28) ~ (all_0_3_3 = empty_set)
% 2.63/1.44 |
% 2.63/1.44 +-Applying beta-rule and splitting (27), into two cases.
% 2.63/1.44 |-Branch one:
% 2.63/1.44 | (29) all_0_3_3 = empty_set
% 2.63/1.44 |
% 2.63/1.44 | Equations (29) can reduce 28 to:
% 2.63/1.44 | (30) $false
% 2.63/1.44 |
% 2.63/1.45 |-The branch is then unsatisfiable
% 2.63/1.45 |-Branch two:
% 2.63/1.45 | (28) ~ (all_0_3_3 = empty_set)
% 2.63/1.45 | (32) all_0_2_2 = all_0_3_3
% 2.63/1.45 |
% 2.63/1.45 +-Applying beta-rule and splitting (9), into two cases.
% 2.63/1.45 |-Branch one:
% 2.63/1.45 | (33) ~ (all_0_2_2 = all_0_4_4)
% 2.63/1.45 |
% 2.63/1.45 | Equations (32) can reduce 33 to:
% 2.63/1.45 | (34) ~ (all_0_3_3 = all_0_4_4)
% 2.63/1.45 |
% 2.63/1.45 +-Applying beta-rule and splitting (21), into two cases.
% 2.63/1.45 |-Branch one:
% 2.63/1.45 | (35) ~ (all_0_4_4 = empty_set)
% 2.63/1.45 |
% 2.63/1.45 +-Applying beta-rule and splitting (25), into two cases.
% 2.63/1.45 |-Branch one:
% 2.63/1.45 | (36) all_0_4_4 = empty_set
% 2.63/1.45 |
% 2.63/1.45 | Equations (36) can reduce 35 to:
% 2.63/1.45 | (30) $false
% 2.63/1.45 |
% 2.63/1.45 |-The branch is then unsatisfiable
% 2.63/1.45 |-Branch two:
% 2.63/1.45 | (35) ~ (all_0_4_4 = empty_set)
% 2.63/1.45 | (39) all_0_2_2 = all_0_4_4
% 2.63/1.45 |
% 2.63/1.45 | Combining equations (39,32) yields a new equation:
% 2.63/1.45 | (40) all_0_3_3 = all_0_4_4
% 2.63/1.45 |
% 2.63/1.45 | Equations (40) can reduce 34 to:
% 2.63/1.45 | (30) $false
% 2.63/1.45 |
% 2.63/1.45 |-The branch is then unsatisfiable
% 2.63/1.45 |-Branch two:
% 2.63/1.45 | (36) all_0_4_4 = empty_set
% 2.63/1.45 | (43) ~ (all_0_2_2 = all_0_3_3)
% 2.63/1.45 |
% 2.63/1.45 | Equations (32) can reduce 43 to:
% 2.63/1.45 | (30) $false
% 2.63/1.45 |
% 2.63/1.45 |-The branch is then unsatisfiable
% 2.63/1.45 |-Branch two:
% 2.63/1.45 | (39) all_0_2_2 = all_0_4_4
% 2.63/1.45 | (34) ~ (all_0_3_3 = all_0_4_4)
% 2.63/1.45 |
% 2.63/1.45 | Combining equations (39,32) yields a new equation:
% 2.63/1.45 | (40) all_0_3_3 = all_0_4_4
% 2.63/1.45 |
% 2.63/1.45 | Equations (40) can reduce 34 to:
% 2.63/1.45 | (30) $false
% 2.63/1.45 |
% 2.63/1.45 |-The branch is then unsatisfiable
% 2.63/1.45 |-Branch two:
% 2.63/1.45 | (29) all_0_3_3 = empty_set
% 2.63/1.45 | (33) ~ (all_0_2_2 = all_0_4_4)
% 2.63/1.45 |
% 2.63/1.45 | From (29) and (23) follows:
% 2.63/1.45 | (51) set_union2(empty_set, all_0_4_4) = all_0_2_2
% 2.63/1.45 |
% 2.63/1.45 +-Applying beta-rule and splitting (25), into two cases.
% 2.63/1.45 |-Branch one:
% 2.63/1.45 | (36) all_0_4_4 = empty_set
% 2.63/1.45 |
% 2.63/1.45 | Equations (36) can reduce 33 to:
% 2.63/1.45 | (53) ~ (all_0_2_2 = empty_set)
% 2.63/1.45 |
% 2.63/1.45 | From (36) and (51) follows:
% 2.63/1.45 | (54) set_union2(empty_set, empty_set) = all_0_2_2
% 2.91/1.45 |
% 2.91/1.45 | Instantiating formula (16) with all_0_2_2, empty_set and discharging atoms set_union2(empty_set, empty_set) = all_0_2_2, yields:
% 2.91/1.45 | (55) all_0_2_2 = empty_set
% 2.91/1.45 |
% 2.91/1.45 | Equations (55) can reduce 53 to:
% 2.91/1.45 | (30) $false
% 2.91/1.45 |
% 2.91/1.45 |-The branch is then unsatisfiable
% 2.91/1.45 |-Branch two:
% 2.91/1.45 | (35) ~ (all_0_4_4 = empty_set)
% 2.91/1.45 | (39) all_0_2_2 = all_0_4_4
% 2.91/1.45 |
% 2.91/1.45 | Equations (39) can reduce 33 to:
% 2.91/1.45 | (30) $false
% 2.91/1.45 |
% 2.91/1.45 |-The branch is then unsatisfiable
% 2.91/1.45 % SZS output end Proof for theBenchmark
% 2.91/1.45
% 2.91/1.45 862ms
%------------------------------------------------------------------------------