TSTP Solution File: SET616+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 00:20:50 EDT 2022
% Result : Theorem 13.47s 4.27s
% Output : Proof 16.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jul 11 04:39:03 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.61 ____ _
% 0.22/0.61 ___ / __ \_____(_)___ ________ __________
% 0.22/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.22/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.22/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.22/0.61
% 0.22/0.61 A Theorem Prover for First-Order Logic
% 0.22/0.61 (ePrincess v.1.0)
% 0.22/0.61
% 0.22/0.61 (c) Philipp Rümmer, 2009-2015
% 0.22/0.61 (c) Peter Backeman, 2014-2015
% 0.22/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.22/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.22/0.61 Bug reports to peter@backeman.se
% 0.22/0.61
% 0.22/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.22/0.61
% 0.22/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.91 Prover 0: Preprocessing ...
% 1.67/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.81/1.07 Prover 0: Constructing countermodel ...
% 2.14/1.20 Prover 0: gave up
% 2.14/1.20 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.23/1.23 Prover 1: Preprocessing ...
% 2.40/1.32 Prover 1: Warning: ignoring some quantifiers
% 2.40/1.33 Prover 1: Constructing countermodel ...
% 2.62/1.35 Prover 1: gave up
% 2.62/1.35 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.62/1.37 Prover 2: Preprocessing ...
% 3.07/1.45 Prover 2: Warning: ignoring some quantifiers
% 3.07/1.46 Prover 2: Constructing countermodel ...
% 3.13/1.49 Prover 2: gave up
% 3.13/1.49 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.13/1.50 Prover 3: Preprocessing ...
% 3.37/1.53 Prover 3: Warning: ignoring some quantifiers
% 3.37/1.53 Prover 3: Constructing countermodel ...
% 3.56/1.56 Prover 3: gave up
% 3.56/1.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.56/1.57 Prover 4: Preprocessing ...
% 3.94/1.64 Prover 4: Warning: ignoring some quantifiers
% 3.94/1.64 Prover 4: Constructing countermodel ...
% 4.95/1.91 Prover 4: gave up
% 4.95/1.91 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.95/1.92 Prover 5: Preprocessing ...
% 5.24/1.95 Prover 5: Warning: ignoring some quantifiers
% 5.24/1.96 Prover 5: Constructing countermodel ...
% 5.46/1.97 Prover 5: gave up
% 5.46/1.97 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.46/1.98 Prover 6: Preprocessing ...
% 5.46/2.01 Prover 6: Warning: ignoring some quantifiers
% 5.46/2.01 Prover 6: Constructing countermodel ...
% 5.46/2.03 Prover 6: gave up
% 5.46/2.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.46/2.03 Prover 7: Preprocessing ...
% 5.83/2.05 Prover 7: Proving ...
% 13.47/4.27 Prover 7: proved (2240ms)
% 13.47/4.27
% 13.47/4.27 % SZS status Theorem for theBenchmark
% 13.47/4.27
% 13.47/4.27 Generating proof ... found it (size 55)
% 16.04/5.04
% 16.04/5.04 % SZS output start Proof for theBenchmark
% 16.04/5.04 Assumed formulas after preprocessing and simplification:
% 16.04/5.04 | (0) ! [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] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ! [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] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & difference(v1, v0) = v2 & difference(v0, v1) = v2)
% 16.41/5.06 | Applying alpha-rule on (0) yields:
% 16.41/5.06 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | (member(v2, v0) & ~ member(v2, v1)))
% 16.41/5.06 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 16.41/5.06 | (3) ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & difference(v1, v0) = v2 & difference(v0, v1) = v2)
% 16.41/5.06 | (4) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ member(v2, v0) | member(v2, v1)))
% 16.41/5.06 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 16.41/5.06 | (6) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 16.41/5.06 | (7) ! [v0] : subset(v0, v0)
% 16.41/5.06 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 16.41/5.06 | (9) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 16.41/5.06 |
% 16.41/5.06 | Instantiating (3) with all_1_0_0, all_1_1_1, all_1_2_2 yields:
% 16.41/5.06 | (10) ~ (all_1_1_1 = all_1_2_2) & difference(all_1_1_1, all_1_2_2) = all_1_0_0 & difference(all_1_2_2, all_1_1_1) = all_1_0_0
% 16.41/5.06 |
% 16.41/5.06 | Applying alpha-rule on (10) yields:
% 16.41/5.06 | (11) ~ (all_1_1_1 = all_1_2_2)
% 16.41/5.06 | (12) difference(all_1_1_1, all_1_2_2) = all_1_0_0
% 16.41/5.06 | (13) difference(all_1_2_2, all_1_1_1) = all_1_0_0
% 16.41/5.06 |
% 16.41/5.06 | Introducing new symbol ex_17_1_5 defined by:
% 16.41/5.06 | (14) ex_17_1_5 = all_1_2_2
% 16.41/5.06 |
% 16.41/5.06 | Introducing new symbol ex_17_0_4 defined by:
% 16.41/5.06 | (15) ex_17_0_4 = all_1_1_1
% 16.41/5.06 |
% 16.41/5.06 | Instantiating formula (6) with ex_17_0_4, ex_17_1_5 yields:
% 16.41/5.06 | (16) ex_17_0_4 = ex_17_1_5 | ? [v0] : (( ~ member(v0, ex_17_0_4) | ~ member(v0, ex_17_1_5)) & (member(v0, ex_17_0_4) | member(v0, ex_17_1_5)))
% 16.41/5.06 |
% 16.41/5.06 +-Applying beta-rule and splitting (16), into two cases.
% 16.41/5.06 |-Branch one:
% 16.41/5.06 | (17) ex_17_0_4 = ex_17_1_5
% 16.41/5.06 |
% 16.41/5.06 | Combining equations (17,15) yields a new equation:
% 16.41/5.06 | (18) ex_17_1_5 = all_1_1_1
% 16.41/5.06 |
% 16.41/5.06 | Simplifying 18 yields:
% 16.41/5.06 | (19) ex_17_1_5 = all_1_1_1
% 16.41/5.06 |
% 16.41/5.06 | Combining equations (19,14) yields a new equation:
% 16.41/5.06 | (20) all_1_1_1 = all_1_2_2
% 16.41/5.06 |
% 16.41/5.06 | Simplifying 20 yields:
% 16.41/5.06 | (21) all_1_1_1 = all_1_2_2
% 16.41/5.06 |
% 16.41/5.06 | Equations (21) can reduce 11 to:
% 16.41/5.06 | (22) $false
% 16.41/5.06 |
% 16.41/5.06 |-The branch is then unsatisfiable
% 16.41/5.06 |-Branch two:
% 16.41/5.06 | (23) ? [v0] : (( ~ member(v0, ex_17_0_4) | ~ member(v0, ex_17_1_5)) & (member(v0, ex_17_0_4) | member(v0, ex_17_1_5)))
% 16.41/5.06 |
% 16.41/5.06 | Instantiating (23) with all_20_0_6 yields:
% 16.41/5.06 | (24) ( ~ member(all_20_0_6, ex_17_0_4) | ~ member(all_20_0_6, ex_17_1_5)) & (member(all_20_0_6, ex_17_0_4) | member(all_20_0_6, ex_17_1_5))
% 16.41/5.06 |
% 16.41/5.06 | Applying alpha-rule on (24) yields:
% 16.41/5.06 | (25) ~ member(all_20_0_6, ex_17_0_4) | ~ member(all_20_0_6, ex_17_1_5)
% 16.41/5.06 | (26) member(all_20_0_6, ex_17_0_4) | member(all_20_0_6, ex_17_1_5)
% 16.41/5.06 |
% 16.41/5.06 +-Applying beta-rule and splitting (26), into two cases.
% 16.41/5.06 |-Branch one:
% 16.41/5.06 | (27) member(all_20_0_6, ex_17_0_4)
% 16.41/5.06 |
% 16.41/5.06 +-Applying beta-rule and splitting (25), into two cases.
% 16.41/5.06 |-Branch one:
% 16.41/5.06 | (28) ~ member(all_20_0_6, ex_17_0_4)
% 16.41/5.06 |
% 16.41/5.06 | Using (27) and (28) yields:
% 16.41/5.06 | (29) $false
% 16.41/5.06 |
% 16.41/5.06 |-The branch is then unsatisfiable
% 16.41/5.06 |-Branch two:
% 16.41/5.06 | (30) ~ member(all_20_0_6, ex_17_1_5)
% 16.41/5.06 |
% 16.41/5.06 | Instantiating formula (2) with all_1_0_0, all_20_0_6, all_1_2_2, all_1_1_1 and discharging atoms difference(all_1_1_1, all_1_2_2) = all_1_0_0, yields:
% 16.41/5.06 | (31) ~ member(all_20_0_6, all_1_1_1) | member(all_20_0_6, all_1_0_0) | member(all_20_0_6, all_1_2_2)
% 16.41/5.06 |
% 16.41/5.06 | Instantiating formula (1) with all_1_0_0, all_20_0_6, all_1_1_1, all_1_2_2 and discharging atoms difference(all_1_2_2, all_1_1_1) = all_1_0_0, yields:
% 16.41/5.06 | (32) ~ member(all_20_0_6, all_1_0_0) | (member(all_20_0_6, all_1_2_2) & ~ member(all_20_0_6, all_1_1_1))
% 16.41/5.07 |
% 16.41/5.07 | Instantiating formula (2) with all_1_0_0, all_20_0_6, all_1_1_1, all_1_2_2 and discharging atoms difference(all_1_2_2, all_1_1_1) = all_1_0_0, yields:
% 16.41/5.07 | (33) ~ member(all_20_0_6, all_1_2_2) | member(all_20_0_6, all_1_0_0) | member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 +-Applying beta-rule and splitting (33), into two cases.
% 16.41/5.07 |-Branch one:
% 16.41/5.07 | (34) ~ member(all_20_0_6, all_1_2_2)
% 16.41/5.07 |
% 16.41/5.07 +-Applying beta-rule and splitting (32), into two cases.
% 16.41/5.07 |-Branch one:
% 16.41/5.07 | (35) ~ member(all_20_0_6, all_1_0_0)
% 16.41/5.07 |
% 16.41/5.07 +-Applying beta-rule and splitting (31), into two cases.
% 16.41/5.07 |-Branch one:
% 16.41/5.07 | (36) ~ member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 | From (15) and (27) follows:
% 16.41/5.07 | (37) member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 | Using (37) and (36) yields:
% 16.41/5.07 | (29) $false
% 16.41/5.07 |
% 16.41/5.07 |-The branch is then unsatisfiable
% 16.41/5.07 |-Branch two:
% 16.41/5.07 | (39) member(all_20_0_6, all_1_0_0) | member(all_20_0_6, all_1_2_2)
% 16.41/5.07 |
% 16.41/5.07 +-Applying beta-rule and splitting (39), into two cases.
% 16.41/5.07 |-Branch one:
% 16.41/5.07 | (40) member(all_20_0_6, all_1_0_0)
% 16.41/5.07 |
% 16.41/5.07 | Using (40) and (35) yields:
% 16.41/5.07 | (29) $false
% 16.41/5.07 |
% 16.41/5.07 |-The branch is then unsatisfiable
% 16.41/5.07 |-Branch two:
% 16.41/5.07 | (42) member(all_20_0_6, all_1_2_2)
% 16.41/5.07 |
% 16.41/5.07 | Using (42) and (34) yields:
% 16.41/5.07 | (29) $false
% 16.41/5.07 |
% 16.41/5.07 |-The branch is then unsatisfiable
% 16.41/5.07 |-Branch two:
% 16.41/5.07 | (44) member(all_20_0_6, all_1_2_2) & ~ member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 | Applying alpha-rule on (44) yields:
% 16.41/5.07 | (42) member(all_20_0_6, all_1_2_2)
% 16.41/5.07 | (36) ~ member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 | Using (42) and (34) yields:
% 16.41/5.07 | (29) $false
% 16.41/5.07 |
% 16.41/5.07 |-The branch is then unsatisfiable
% 16.41/5.07 |-Branch two:
% 16.41/5.07 | (42) member(all_20_0_6, all_1_2_2)
% 16.41/5.07 | (49) member(all_20_0_6, all_1_0_0) | member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 | From (14) and (30) follows:
% 16.41/5.07 | (34) ~ member(all_20_0_6, all_1_2_2)
% 16.41/5.07 |
% 16.41/5.07 | Using (42) and (34) yields:
% 16.41/5.07 | (29) $false
% 16.41/5.07 |
% 16.41/5.07 |-The branch is then unsatisfiable
% 16.41/5.07 |-Branch two:
% 16.41/5.07 | (28) ~ member(all_20_0_6, ex_17_0_4)
% 16.41/5.07 | (53) member(all_20_0_6, ex_17_1_5)
% 16.41/5.07 |
% 16.41/5.07 | Instantiating formula (1) with all_1_0_0, all_20_0_6, all_1_2_2, all_1_1_1 and discharging atoms difference(all_1_1_1, all_1_2_2) = all_1_0_0, yields:
% 16.41/5.07 | (54) ~ member(all_20_0_6, all_1_0_0) | (member(all_20_0_6, all_1_1_1) & ~ member(all_20_0_6, all_1_2_2))
% 16.41/5.07 |
% 16.41/5.07 | Instantiating formula (2) with all_1_0_0, all_20_0_6, all_1_1_1, all_1_2_2 and discharging atoms difference(all_1_2_2, all_1_1_1) = all_1_0_0, yields:
% 16.41/5.07 | (33) ~ member(all_20_0_6, all_1_2_2) | member(all_20_0_6, all_1_0_0) | member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 +-Applying beta-rule and splitting (33), into two cases.
% 16.41/5.07 |-Branch one:
% 16.41/5.07 | (34) ~ member(all_20_0_6, all_1_2_2)
% 16.41/5.07 |
% 16.41/5.07 | From (14) and (53) follows:
% 16.41/5.07 | (42) member(all_20_0_6, all_1_2_2)
% 16.41/5.07 |
% 16.41/5.07 | Using (42) and (34) yields:
% 16.41/5.07 | (29) $false
% 16.41/5.07 |
% 16.41/5.07 |-The branch is then unsatisfiable
% 16.41/5.07 |-Branch two:
% 16.41/5.07 | (42) member(all_20_0_6, all_1_2_2)
% 16.41/5.07 | (49) member(all_20_0_6, all_1_0_0) | member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 +-Applying beta-rule and splitting (49), into two cases.
% 16.41/5.07 |-Branch one:
% 16.41/5.07 | (40) member(all_20_0_6, all_1_0_0)
% 16.41/5.07 |
% 16.41/5.07 +-Applying beta-rule and splitting (54), into two cases.
% 16.41/5.07 |-Branch one:
% 16.41/5.07 | (35) ~ member(all_20_0_6, all_1_0_0)
% 16.41/5.07 |
% 16.41/5.07 | Using (40) and (35) yields:
% 16.41/5.07 | (29) $false
% 16.41/5.07 |
% 16.41/5.07 |-The branch is then unsatisfiable
% 16.41/5.07 |-Branch two:
% 16.41/5.07 | (64) member(all_20_0_6, all_1_1_1) & ~ member(all_20_0_6, all_1_2_2)
% 16.41/5.07 |
% 16.41/5.07 | Applying alpha-rule on (64) yields:
% 16.41/5.07 | (37) member(all_20_0_6, all_1_1_1)
% 16.41/5.07 | (34) ~ member(all_20_0_6, all_1_2_2)
% 16.41/5.07 |
% 16.41/5.07 | Using (42) and (34) yields:
% 16.41/5.07 | (29) $false
% 16.41/5.07 |
% 16.41/5.07 |-The branch is then unsatisfiable
% 16.41/5.07 |-Branch two:
% 16.41/5.07 | (37) member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 | From (15) and (28) follows:
% 16.41/5.07 | (36) ~ member(all_20_0_6, all_1_1_1)
% 16.41/5.07 |
% 16.41/5.07 | Using (37) and (36) yields:
% 16.41/5.07 | (29) $false
% 16.41/5.07 |
% 16.41/5.07 |-The branch is then unsatisfiable
% 16.41/5.07 % SZS output end Proof for theBenchmark
% 16.41/5.07
% 16.41/5.07 4453ms
%------------------------------------------------------------------------------