TSTP Solution File: SEU284+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0.
% 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 08:48:28 EDT 2022
% Result : Theorem 66.31s 30.97s
% Output : Proof 75.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.08/0.31 % Computer : n011.cluster.edu
% 0.08/0.31 % Model : x86_64 x86_64
% 0.08/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.31 % Memory : 8042.1875MB
% 0.08/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.31 % CPULimit : 300
% 0.08/0.31 % WCLimit : 600
% 0.08/0.31 % DateTime : Mon Jun 20 02:31:09 EDT 2022
% 0.08/0.31 % CPUTime :
% 0.13/0.56 ____ _
% 0.13/0.56 ___ / __ \_____(_)___ ________ __________
% 0.13/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.13/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.13/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.13/0.56
% 0.13/0.56 A Theorem Prover for First-Order Logic
% 0.13/0.57 (ePrincess v.1.0)
% 0.13/0.57
% 0.13/0.57 (c) Philipp Rümmer, 2009-2015
% 0.13/0.57 (c) Peter Backeman, 2014-2015
% 0.13/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.13/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.13/0.57 Bug reports to peter@backeman.se
% 0.13/0.57
% 0.13/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.13/0.57
% 0.13/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.57/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.45/1.09 Prover 0: Preprocessing ...
% 1.94/1.49 Prover 0: Warning: ignoring some quantifiers
% 2.00/1.53 Prover 0: Constructing countermodel ...
% 3.50/2.39 Prover 0: gave up
% 3.50/2.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.50/2.44 Prover 1: Preprocessing ...
% 3.85/2.56 Prover 1: Warning: ignoring some quantifiers
% 3.85/2.57 Prover 1: Constructing countermodel ...
% 4.98/2.93 Prover 1: gave up
% 4.98/2.93 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.98/2.97 Prover 2: Preprocessing ...
% 5.57/3.13 Prover 2: Warning: ignoring some quantifiers
% 5.57/3.13 Prover 2: Constructing countermodel ...
% 11.03/4.97 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 11.15/5.01 Prover 3: Preprocessing ...
% 11.23/5.04 Prover 3: Warning: ignoring some quantifiers
% 11.23/5.04 Prover 3: Constructing countermodel ...
% 11.49/5.18 Prover 3: gave up
% 11.49/5.18 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 11.71/5.22 Prover 4: Preprocessing ...
% 12.08/5.32 Prover 4: Warning: ignoring some quantifiers
% 12.08/5.33 Prover 4: Constructing countermodel ...
% 14.70/6.16 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.70/6.19 Prover 5: Preprocessing ...
% 15.05/6.25 Prover 5: Warning: ignoring some quantifiers
% 15.05/6.25 Prover 5: Constructing countermodel ...
% 18.59/7.08 Prover 5: gave up
% 18.59/7.08 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.59/7.10 Prover 6: Preprocessing ...
% 18.93/7.16 Prover 6: Warning: ignoring some quantifiers
% 18.93/7.17 Prover 6: Constructing countermodel ...
% 61.48/29.85 Prover 4: gave up
% 61.48/29.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 61.48/29.86 Prover 7: Preprocessing ...
% 61.48/29.87 Prover 7: Proving ...
% 66.31/30.97 Prover 7: proved (1123ms)
% 66.31/30.97 Prover 2: stopped
% 66.31/30.97 Prover 6: stopped
% 66.31/30.97
% 66.31/30.97 % SZS status Theorem for theBenchmark
% 66.31/30.97
% 66.31/30.97 Generating proof ... found it (size 26)
% 75.14/33.51
% 75.14/33.51 % SZS output start Proof for theBenchmark
% 75.14/33.51 Assumed formulas after preprocessing and simplification:
% 75.14/33.51 | (0) ? [v0] : (relation_empty_yielding(v0) & empty(v0) & relation(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (apply(v4, v3) = v2) | ~ (apply(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (relation_dom(v3) = v2) | ~ (relation_dom(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v3) = v2) | ~ (singleton(v3) = v1)) & ! [v1] : ! [v2] : (v2 = v1 | ~ empty(v2) | ~ empty(v1)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ empty(v2) | ~ relation(v1) | empty(v1)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ empty(v1) | (empty(v2) & relation(v2))) & ! [v1] : ! [v2] : ( ~ element(v1, v2) | empty(v2) | in(v1, v2)) & ! [v1] : ! [v2] : ( ~ empty(v2) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ in(v1, v2) | element(v1, v2)) & ? [v1] : ! [v2] : ( ~ (relation_dom(v2) = v1) | ~ function(v2) | ~ relation(v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & apply(v2, v3) = v4 & singleton(v3) = v5 & in(v3, v1))) & ! [v1] : (v1 = v0 | ~ empty(v1)) & ! [v1] : ( ~ empty(v1) | function(v1)) & ! [v1] : ( ~ empty(v1) | relation(v1)) & ! [v1] : ? [v2] : element(v2, v1) & ! [v1] : ? [v2] : (relation_dom(v2) = v1 & function(v2) & relation(v2) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v2, v3) = v4 & singleton(v3) = v4))) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1) & ? [v1] : (relation_empty_yielding(v1) & relation(v1)) & ? [v1] : (empty(v1) & relation(v1)) & ? [v1] : (function(v1) & relation(v1)) & ? [v1] : (relation(v1) & ~ empty(v1)))
% 75.14/33.53 | Instantiating (0) with all_0_0_0 yields:
% 75.14/33.53 | (1) relation_empty_yielding(all_0_0_0) & empty(all_0_0_0) & relation(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v1) | ~ relation(v0) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | (empty(v1) & relation(v1))) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ? [v0] : ! [v1] : ( ~ (relation_dom(v1) = v0) | ~ function(v1) | ~ relation(v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v2) = v3 & singleton(v2) = v4 & in(v2, v0))) & ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ? [v1] : element(v1, v0) & ! [v0] : ? [v1] : (relation_dom(v1) = v0 & function(v1) & relation(v1) & ! [v2] : ( ~ in(v2, v0) | ? [v3] : (apply(v1, v2) = v3 & singleton(v2) = v3))) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) & ? [v0] : (relation_empty_yielding(v0) & relation(v0)) & ? [v0] : (empty(v0) & relation(v0)) & ? [v0] : (function(v0) & relation(v0)) & ? [v0] : (relation(v0) & ~ empty(v0))
% 75.14/33.53 |
% 75.14/33.53 | Applying alpha-rule on (1) yields:
% 75.14/33.53 | (2) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v1) | ~ relation(v0) | empty(v0))
% 75.14/33.54 | (3) ? [v0] : (relation_empty_yielding(v0) & relation(v0))
% 75.14/33.54 | (4) ? [v0] : ! [v1] : ( ~ (relation_dom(v1) = v0) | ~ function(v1) | ~ relation(v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v2) = v3 & singleton(v2) = v4 & in(v2, v0)))
% 75.14/33.54 | (5) ! [v0] : ( ~ empty(v0) | relation(v0))
% 75.14/33.54 | (6) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0))
% 75.14/33.54 | (7) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | (empty(v1) & relation(v1)))
% 75.14/33.54 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 75.14/33.54 | (9) ! [v0] : ( ~ empty(v0) | function(v0))
% 75.14/33.54 | (10) ? [v0] : (function(v0) & relation(v0))
% 75.14/33.54 | (11) ? [v0] : ~ empty(v0)
% 75.14/33.54 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 75.14/33.54 | (13) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 75.14/33.54 | (14) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 75.14/33.54 | (15) ! [v0] : ? [v1] : (relation_dom(v1) = v0 & function(v1) & relation(v1) & ! [v2] : ( ~ in(v2, v0) | ? [v3] : (apply(v1, v2) = v3 & singleton(v2) = v3)))
% 75.14/33.54 | (16) ! [v0] : ? [v1] : element(v1, v0)
% 75.14/33.54 | (17) ? [v0] : empty(v0)
% 75.14/33.54 | (18) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 75.14/33.54 | (19) empty(all_0_0_0)
% 75.14/33.54 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 75.14/33.54 | (21) ? [v0] : (empty(v0) & relation(v0))
% 75.14/33.54 | (22) relation_empty_yielding(all_0_0_0)
% 75.14/33.54 | (23) relation(all_0_0_0)
% 75.14/33.54 | (24) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 75.14/33.54 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 75.14/33.54 | (26) ? [v0] : (relation(v0) & ~ empty(v0))
% 75.14/33.54 |
% 75.14/33.54 | Instantiating (4) with all_15_0_7 yields:
% 75.14/33.54 | (27) ! [v0] : ( ~ (relation_dom(v0) = all_15_0_7) | ~ function(v0) | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & apply(v0, v1) = v2 & singleton(v1) = v3 & in(v1, all_15_0_7)))
% 75.14/33.54 |
% 75.14/33.54 | Introducing new symbol ex_33_0_8 defined by:
% 75.14/33.54 | (28) ex_33_0_8 = all_15_0_7
% 75.14/33.54 |
% 75.14/33.54 | Instantiating formula (15) with ex_33_0_8 yields:
% 75.14/33.54 | (29) ? [v0] : (relation_dom(v0) = ex_33_0_8 & function(v0) & relation(v0) & ! [v1] : ( ~ in(v1, ex_33_0_8) | ? [v2] : (apply(v0, v1) = v2 & singleton(v1) = v2)))
% 75.14/33.54 |
% 75.14/33.54 | Instantiating (29) with all_34_0_9 yields:
% 75.14/33.54 | (30) relation_dom(all_34_0_9) = ex_33_0_8 & function(all_34_0_9) & relation(all_34_0_9) & ! [v0] : ( ~ in(v0, ex_33_0_8) | ? [v1] : (apply(all_34_0_9, v0) = v1 & singleton(v0) = v1))
% 75.14/33.54 |
% 75.14/33.54 | Applying alpha-rule on (30) yields:
% 75.14/33.54 | (31) relation_dom(all_34_0_9) = ex_33_0_8
% 75.14/33.54 | (32) function(all_34_0_9)
% 75.14/33.54 | (33) relation(all_34_0_9)
% 75.14/33.54 | (34) ! [v0] : ( ~ in(v0, ex_33_0_8) | ? [v1] : (apply(all_34_0_9, v0) = v1 & singleton(v0) = v1))
% 75.14/33.54 |
% 75.14/33.54 | Instantiating formula (27) with all_34_0_9 and discharging atoms function(all_34_0_9), relation(all_34_0_9), yields:
% 75.14/33.54 | (35) ~ (relation_dom(all_34_0_9) = all_15_0_7) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_34_0_9, v0) = v1 & singleton(v0) = v2 & in(v0, all_15_0_7))
% 75.14/33.54 |
% 75.14/33.54 +-Applying beta-rule and splitting (35), into two cases.
% 75.14/33.54 |-Branch one:
% 75.14/33.54 | (36) ~ (relation_dom(all_34_0_9) = all_15_0_7)
% 75.14/33.54 |
% 75.14/33.54 | From (28) and (31) follows:
% 75.14/33.54 | (37) relation_dom(all_34_0_9) = all_15_0_7
% 75.14/33.54 |
% 75.14/33.54 | Using (37) and (36) yields:
% 75.14/33.54 | (38) $false
% 75.14/33.54 |
% 75.14/33.54 |-The branch is then unsatisfiable
% 75.14/33.54 |-Branch two:
% 75.14/33.54 | (39) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_34_0_9, v0) = v1 & singleton(v0) = v2 & in(v0, all_15_0_7))
% 75.14/33.54 |
% 75.14/33.54 | Instantiating (39) with all_85_0_13, all_85_1_14, all_85_2_15 yields:
% 75.14/33.54 | (40) ~ (all_85_0_13 = all_85_1_14) & apply(all_34_0_9, all_85_2_15) = all_85_1_14 & singleton(all_85_2_15) = all_85_0_13 & in(all_85_2_15, all_15_0_7)
% 75.14/33.54 |
% 75.14/33.54 | Applying alpha-rule on (40) yields:
% 75.14/33.54 | (41) ~ (all_85_0_13 = all_85_1_14)
% 75.14/33.54 | (42) apply(all_34_0_9, all_85_2_15) = all_85_1_14
% 75.14/33.54 | (43) singleton(all_85_2_15) = all_85_0_13
% 75.14/33.54 | (44) in(all_85_2_15, all_15_0_7)
% 75.14/33.54 |
% 75.14/33.54 | Instantiating formula (34) with all_85_2_15 yields:
% 75.14/33.55 | (45) ~ in(all_85_2_15, ex_33_0_8) | ? [v0] : (apply(all_34_0_9, all_85_2_15) = v0 & singleton(all_85_2_15) = v0)
% 75.14/33.55 |
% 75.14/33.55 +-Applying beta-rule and splitting (45), into two cases.
% 75.14/33.55 |-Branch one:
% 75.14/33.55 | (46) ~ in(all_85_2_15, ex_33_0_8)
% 75.14/33.55 |
% 75.14/33.55 | From (28) and (46) follows:
% 75.14/33.55 | (47) ~ in(all_85_2_15, all_15_0_7)
% 75.14/33.55 |
% 75.14/33.55 | Using (44) and (47) yields:
% 75.14/33.55 | (38) $false
% 75.14/33.55 |
% 75.14/33.55 |-The branch is then unsatisfiable
% 75.14/33.55 |-Branch two:
% 75.14/33.55 | (49) ? [v0] : (apply(all_34_0_9, all_85_2_15) = v0 & singleton(all_85_2_15) = v0)
% 75.14/33.55 |
% 75.14/33.55 | Instantiating (49) with all_100_0_18 yields:
% 75.14/33.55 | (50) apply(all_34_0_9, all_85_2_15) = all_100_0_18 & singleton(all_85_2_15) = all_100_0_18
% 75.14/33.55 |
% 75.14/33.55 | Applying alpha-rule on (50) yields:
% 75.14/33.55 | (51) apply(all_34_0_9, all_85_2_15) = all_100_0_18
% 75.14/33.55 | (52) singleton(all_85_2_15) = all_100_0_18
% 75.14/33.55 |
% 75.14/33.55 | Instantiating formula (12) with all_34_0_9, all_85_2_15, all_100_0_18, all_85_1_14 and discharging atoms apply(all_34_0_9, all_85_2_15) = all_100_0_18, apply(all_34_0_9, all_85_2_15) = all_85_1_14, yields:
% 75.14/33.55 | (53) all_100_0_18 = all_85_1_14
% 75.14/33.55 |
% 75.14/33.55 | Instantiating formula (8) with all_85_2_15, all_100_0_18, all_85_0_13 and discharging atoms singleton(all_85_2_15) = all_100_0_18, singleton(all_85_2_15) = all_85_0_13, yields:
% 75.14/33.55 | (54) all_100_0_18 = all_85_0_13
% 75.14/33.55 |
% 75.14/33.55 | Combining equations (53,54) yields a new equation:
% 75.14/33.55 | (55) all_85_0_13 = all_85_1_14
% 75.14/33.55 |
% 75.14/33.55 | Equations (55) can reduce 41 to:
% 75.14/33.55 | (56) $false
% 75.14/33.55 |
% 75.14/33.55 |-The branch is then unsatisfiable
% 75.14/33.55 % SZS output end Proof for theBenchmark
% 75.14/33.55
% 75.14/33.55 32968ms
%------------------------------------------------------------------------------