TSTP Solution File: SET591+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 00:20:31 EDT 2022
% Result : Theorem 15.00s 4.19s
% Output : Proof 23.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jul 10 13:03:40 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.51/0.57 ____ _
% 0.51/0.57 ___ / __ \_____(_)___ ________ __________
% 0.51/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.57
% 0.51/0.57 A Theorem Prover for First-Order Logic
% 0.51/0.57 (ePrincess v.1.0)
% 0.51/0.57
% 0.51/0.57 (c) Philipp Rümmer, 2009-2015
% 0.51/0.57 (c) Peter Backeman, 2014-2015
% 0.51/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.57 Bug reports to peter@backeman.se
% 0.51/0.57
% 0.51/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.57
% 0.51/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.33/0.86 Prover 0: Preprocessing ...
% 1.54/0.97 Prover 0: Warning: ignoring some quantifiers
% 1.65/0.99 Prover 0: Constructing countermodel ...
% 1.98/1.11 Prover 0: gave up
% 1.98/1.11 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.19/1.13 Prover 1: Preprocessing ...
% 2.35/1.21 Prover 1: Constructing countermodel ...
% 2.55/1.25 Prover 1: gave up
% 2.55/1.25 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.55/1.26 Prover 2: Preprocessing ...
% 2.70/1.32 Prover 2: Warning: ignoring some quantifiers
% 2.70/1.33 Prover 2: Constructing countermodel ...
% 3.02/1.37 Prover 2: gave up
% 3.02/1.37 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.02/1.38 Prover 3: Preprocessing ...
% 3.02/1.40 Prover 3: Warning: ignoring some quantifiers
% 3.02/1.40 Prover 3: Constructing countermodel ...
% 3.27/1.43 Prover 3: gave up
% 3.27/1.43 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.27/1.44 Prover 4: Preprocessing ...
% 3.42/1.51 Prover 4: Warning: ignoring some quantifiers
% 3.42/1.51 Prover 4: Constructing countermodel ...
% 5.82/2.02 Prover 4: gave up
% 5.82/2.03 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.82/2.03 Prover 5: Preprocessing ...
% 6.22/2.07 Prover 5: Constructing countermodel ...
% 6.22/2.09 Prover 5: gave up
% 6.22/2.09 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.22/2.10 Prover 6: Preprocessing ...
% 6.51/2.12 Prover 6: Warning: ignoring some quantifiers
% 6.51/2.13 Prover 6: Constructing countermodel ...
% 6.51/2.15 Prover 6: gave up
% 6.51/2.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 6.51/2.15 Prover 7: Preprocessing ...
% 6.51/2.16 Prover 7: Proving ...
% 15.00/4.19 Prover 7: proved (2042ms)
% 15.00/4.19
% 15.00/4.19 % SZS status Theorem for theBenchmark
% 15.00/4.19
% 15.00/4.19 Generating proof ... found it (size 45)
% 23.63/7.48
% 23.63/7.48 % SZS output start Proof for theBenchmark
% 23.63/7.48 Assumed formulas after preprocessing and simplification:
% 23.63/7.48 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (difference(v4, v3) = v2) | ~ (difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v2) = v4) | ~ member(v3, v4) | (member(v3, v1) & ~ member(v3, v2))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v2) = v4) | ~ member(v3, v1) | member(v3, v4) | member(v3, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v2, v1) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ member(v3, v1) | member(v3, v2))) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (member(v3, v1) & ~ member(v3, v2))) & ! [v1] : ( ~ empty(v1) | ! [v2] : ~ member(v2, v1)) & ! [v1] : ~ member(v1, v0) & ! [v1] : (empty(v1) | ? [v2] : member(v2, v1)) & ! [v1] : subset(v1, v1) & ? [v1] : ? [v2] : ? [v3] : ( ~ (v1 = v0) & difference(v2, v1) = v3 & subset(v1, v3)))
% 23.75/7.50 | Instantiating (0) with all_0_0_0 yields:
% 23.75/7.50 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v0) & ~ member(v2, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1))) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0)) & ! [v0] : ~ member(v0, all_0_0_0) & ! [v0] : (empty(v0) | ? [v1] : member(v1, v0)) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : ( ~ (v0 = all_0_0_0) & difference(v1, v0) = v2 & subset(v0, v2))
% 23.75/7.50 |
% 23.75/7.50 | Applying alpha-rule on (1) yields:
% 23.75/7.50 | (2) ! [v0] : ~ member(v0, all_0_0_0)
% 23.75/7.50 | (3) ! [v0] : ( ~ empty(v0) | ! [v1] : ~ member(v1, v0))
% 23.75/7.50 | (4) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 23.75/7.50 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 23.75/7.50 | (6) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1)))
% 23.75/7.50 | (7) ! [v0] : (empty(v0) | ? [v1] : member(v1, v0))
% 23.75/7.50 | (8) ? [v0] : ? [v1] : ? [v2] : ( ~ (v0 = all_0_0_0) & difference(v1, v0) = v2 & subset(v0, v2))
% 23.75/7.50 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v0) & ~ member(v2, v1)))
% 23.75/7.50 | (10) ! [v0] : subset(v0, v0)
% 23.75/7.50 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 23.75/7.50 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 23.75/7.50 |
% 23.75/7.50 | Instantiating (8) with all_2_0_1, all_2_1_2, all_2_2_3 yields:
% 23.75/7.50 | (13) ~ (all_2_2_3 = all_0_0_0) & difference(all_2_1_2, all_2_2_3) = all_2_0_1 & subset(all_2_2_3, all_2_0_1)
% 23.75/7.50 |
% 23.75/7.50 | Applying alpha-rule on (13) yields:
% 23.75/7.50 | (14) ~ (all_2_2_3 = all_0_0_0)
% 23.75/7.50 | (15) difference(all_2_1_2, all_2_2_3) = all_2_0_1
% 23.75/7.50 | (16) subset(all_2_2_3, all_2_0_1)
% 23.75/7.50 |
% 23.75/7.51 | Instantiating formula (6) with all_2_0_1, all_2_2_3 and discharging atoms subset(all_2_2_3, all_2_0_1), yields:
% 23.75/7.51 | (17) ! [v0] : ( ~ member(v0, all_2_2_3) | member(v0, all_2_0_1))
% 23.75/7.51 |
% 23.75/7.51 | Introducing new symbol ex_20_1_6 defined by:
% 23.75/7.51 | (18) ex_20_1_6 = all_0_0_0
% 23.75/7.51 |
% 23.75/7.51 | Introducing new symbol ex_20_0_5 defined by:
% 23.75/7.51 | (19) ex_20_0_5 = all_2_2_3
% 23.75/7.51 |
% 23.75/7.51 | Instantiating formula (4) with ex_20_0_5, ex_20_1_6 yields:
% 23.75/7.51 | (20) subset(ex_20_1_6, ex_20_0_5) | ? [v0] : (member(v0, ex_20_1_6) & ~ member(v0, ex_20_0_5))
% 23.75/7.51 |
% 23.75/7.51 +-Applying beta-rule and splitting (20), into two cases.
% 23.75/7.51 |-Branch one:
% 23.75/7.51 | (21) subset(ex_20_1_6, ex_20_0_5)
% 23.75/7.51 |
% 23.75/7.51 | Introducing new symbol ex_58_1_23 defined by:
% 23.75/7.51 | (22) ex_58_1_23 = all_2_2_3
% 23.75/7.51 |
% 23.75/7.51 | Introducing new symbol ex_58_0_22 defined by:
% 23.75/7.51 | (23) ex_58_0_22 = all_0_0_0
% 23.75/7.51 |
% 23.75/7.51 | Instantiating formula (4) with ex_58_0_22, ex_58_1_23 yields:
% 23.75/7.51 | (24) subset(ex_58_1_23, ex_58_0_22) | ? [v0] : (member(v0, ex_58_1_23) & ~ member(v0, ex_58_0_22))
% 23.75/7.51 |
% 23.75/7.51 +-Applying beta-rule and splitting (24), into two cases.
% 23.75/7.51 |-Branch one:
% 23.75/7.51 | (25) subset(ex_58_1_23, ex_58_0_22)
% 23.75/7.51 |
% 23.75/7.51 | Instantiating formula (5) with ex_20_0_5, ex_20_1_6 and discharging atoms subset(ex_20_1_6, ex_20_0_5), yields:
% 23.75/7.51 | (26) ex_20_0_5 = ex_20_1_6 | ~ subset(ex_20_0_5, ex_20_1_6)
% 23.75/7.51 |
% 23.75/7.51 +-Applying beta-rule and splitting (26), into two cases.
% 23.75/7.51 |-Branch one:
% 23.75/7.51 | (27) ~ subset(ex_20_0_5, ex_20_1_6)
% 23.75/7.51 |
% 23.75/7.51 | From (22)(23) and (25) follows:
% 23.75/7.51 | (28) subset(all_2_2_3, all_0_0_0)
% 23.75/7.51 |
% 23.75/7.51 | From (19)(18) and (27) follows:
% 23.75/7.51 | (29) ~ subset(all_2_2_3, all_0_0_0)
% 23.75/7.51 |
% 23.75/7.51 | Using (28) and (29) yields:
% 23.75/7.51 | (30) $false
% 23.75/7.51 |
% 23.75/7.51 |-The branch is then unsatisfiable
% 23.75/7.51 |-Branch two:
% 23.75/7.51 | (31) ex_20_0_5 = ex_20_1_6
% 23.75/7.51 |
% 23.75/7.51 | Combining equations (31,19) yields a new equation:
% 23.75/7.51 | (32) ex_20_1_6 = all_2_2_3
% 23.75/7.51 |
% 23.75/7.51 | Simplifying 32 yields:
% 23.75/7.51 | (33) ex_20_1_6 = all_2_2_3
% 23.75/7.51 |
% 23.75/7.51 | Combining equations (33,18) yields a new equation:
% 23.75/7.51 | (34) all_2_2_3 = all_0_0_0
% 23.75/7.51 |
% 23.75/7.51 | Simplifying 34 yields:
% 23.75/7.51 | (35) all_2_2_3 = all_0_0_0
% 23.75/7.51 |
% 23.75/7.51 | Equations (35) can reduce 14 to:
% 23.75/7.51 | (36) $false
% 23.75/7.51 |
% 23.75/7.51 |-The branch is then unsatisfiable
% 23.75/7.51 |-Branch two:
% 23.75/7.51 | (37) ? [v0] : (member(v0, ex_58_1_23) & ~ member(v0, ex_58_0_22))
% 23.75/7.51 |
% 23.75/7.51 | Instantiating (37) with all_60_0_26 yields:
% 23.75/7.51 | (38) member(all_60_0_26, ex_58_1_23) & ~ member(all_60_0_26, ex_58_0_22)
% 23.75/7.51 |
% 23.75/7.51 | Applying alpha-rule on (38) yields:
% 23.75/7.51 | (39) member(all_60_0_26, ex_58_1_23)
% 23.75/7.51 | (40) ~ member(all_60_0_26, ex_58_0_22)
% 23.75/7.51 |
% 23.75/7.51 | Instantiating formula (9) with all_2_0_1, all_60_0_26, all_2_2_3, all_2_1_2 and discharging atoms difference(all_2_1_2, all_2_2_3) = all_2_0_1, yields:
% 23.75/7.51 | (41) ~ member(all_60_0_26, all_2_0_1) | (member(all_60_0_26, all_2_1_2) & ~ member(all_60_0_26, all_2_2_3))
% 23.75/7.51 |
% 23.75/7.51 | Instantiating formula (17) with all_60_0_26 yields:
% 23.75/7.51 | (42) ~ member(all_60_0_26, all_2_2_3) | member(all_60_0_26, all_2_0_1)
% 23.75/7.51 |
% 23.75/7.51 +-Applying beta-rule and splitting (42), into two cases.
% 23.75/7.51 |-Branch one:
% 23.75/7.51 | (43) ~ member(all_60_0_26, all_2_2_3)
% 23.75/7.51 |
% 23.75/7.51 | From (22) and (39) follows:
% 23.75/7.51 | (44) member(all_60_0_26, all_2_2_3)
% 23.75/7.51 |
% 23.75/7.51 | Using (44) and (43) yields:
% 23.75/7.51 | (30) $false
% 23.75/7.51 |
% 23.75/7.51 |-The branch is then unsatisfiable
% 23.75/7.51 |-Branch two:
% 23.75/7.51 | (44) member(all_60_0_26, all_2_2_3)
% 23.75/7.51 | (47) member(all_60_0_26, all_2_0_1)
% 23.75/7.51 |
% 23.75/7.51 +-Applying beta-rule and splitting (41), into two cases.
% 23.75/7.51 |-Branch one:
% 23.75/7.51 | (48) ~ member(all_60_0_26, all_2_0_1)
% 23.75/7.51 |
% 23.75/7.51 | Using (47) and (48) yields:
% 23.75/7.51 | (30) $false
% 23.75/7.51 |
% 23.75/7.51 |-The branch is then unsatisfiable
% 23.75/7.51 |-Branch two:
% 23.75/7.51 | (50) member(all_60_0_26, all_2_1_2) & ~ member(all_60_0_26, all_2_2_3)
% 23.75/7.51 |
% 23.75/7.51 | Applying alpha-rule on (50) yields:
% 23.75/7.51 | (51) member(all_60_0_26, all_2_1_2)
% 23.75/7.51 | (43) ~ member(all_60_0_26, all_2_2_3)
% 23.75/7.51 |
% 23.75/7.51 | Using (44) and (43) yields:
% 23.75/7.51 | (30) $false
% 23.75/7.51 |
% 23.75/7.51 |-The branch is then unsatisfiable
% 23.75/7.51 |-Branch two:
% 23.75/7.51 | (54) ? [v0] : (member(v0, ex_20_1_6) & ~ member(v0, ex_20_0_5))
% 23.75/7.51 |
% 23.75/7.51 | Instantiating (54) with all_22_0_7 yields:
% 23.75/7.52 | (55) member(all_22_0_7, ex_20_1_6) & ~ member(all_22_0_7, ex_20_0_5)
% 23.75/7.52 |
% 23.75/7.52 | Applying alpha-rule on (55) yields:
% 23.75/7.52 | (56) member(all_22_0_7, ex_20_1_6)
% 23.75/7.52 | (57) ~ member(all_22_0_7, ex_20_0_5)
% 23.75/7.52 |
% 23.75/7.52 | Instantiating formula (2) with all_22_0_7 yields:
% 23.75/7.52 | (58) ~ member(all_22_0_7, all_0_0_0)
% 23.75/7.52 |
% 23.75/7.52 | From (18) and (56) follows:
% 23.75/7.52 | (59) member(all_22_0_7, all_0_0_0)
% 23.75/7.52 |
% 23.75/7.52 | Using (59) and (58) yields:
% 23.75/7.52 | (30) $false
% 23.75/7.52 |
% 23.75/7.52 |-The branch is then unsatisfiable
% 23.75/7.52 % SZS output end Proof for theBenchmark
% 23.75/7.52
% 23.75/7.52 6933ms
%------------------------------------------------------------------------------