TSTP Solution File: SET867+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 00:22:48 EDT 2022
% Result : Theorem 6.47s 2.27s
% Output : Proof 7.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 02:20:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.48/0.60 ____ _
% 0.48/0.60 ___ / __ \_____(_)___ ________ __________
% 0.48/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.60
% 0.48/0.60 A Theorem Prover for First-Order Logic
% 0.48/0.60 (ePrincess v.1.0)
% 0.48/0.60
% 0.48/0.60 (c) Philipp Rümmer, 2009-2015
% 0.48/0.60 (c) Peter Backeman, 2014-2015
% 0.48/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.60 Bug reports to peter@backeman.se
% 0.48/0.60
% 0.48/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.60
% 0.48/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.23/0.91 Prover 0: Preprocessing ...
% 1.50/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.50/1.04 Prover 0: Constructing countermodel ...
% 2.01/1.17 Prover 0: gave up
% 2.01/1.17 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.01/1.19 Prover 1: Preprocessing ...
% 2.26/1.25 Prover 1: Warning: ignoring some quantifiers
% 2.26/1.25 Prover 1: Constructing countermodel ...
% 2.34/1.31 Prover 1: gave up
% 2.34/1.31 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.34/1.32 Prover 2: Preprocessing ...
% 2.72/1.37 Prover 2: Warning: ignoring some quantifiers
% 2.72/1.38 Prover 2: Constructing countermodel ...
% 2.72/1.43 Prover 2: gave up
% 2.72/1.43 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.96/1.44 Prover 3: Preprocessing ...
% 2.96/1.46 Prover 3: Warning: ignoring some quantifiers
% 2.96/1.46 Prover 3: Constructing countermodel ...
% 3.07/1.48 Prover 3: gave up
% 3.07/1.48 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.07/1.49 Prover 4: Preprocessing ...
% 3.31/1.55 Prover 4: Warning: ignoring some quantifiers
% 3.31/1.55 Prover 4: Constructing countermodel ...
% 4.13/1.76 Prover 4: gave up
% 4.13/1.76 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.46/1.77 Prover 5: Preprocessing ...
% 4.46/1.80 Prover 5: Warning: ignoring some quantifiers
% 4.61/1.80 Prover 5: Constructing countermodel ...
% 4.76/1.83 Prover 5: gave up
% 4.76/1.83 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.76/1.83 Prover 6: Preprocessing ...
% 4.76/1.86 Prover 6: Warning: ignoring some quantifiers
% 4.76/1.86 Prover 6: Constructing countermodel ...
% 4.76/1.89 Prover 6: gave up
% 4.76/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 4.76/1.89 Prover 7: Preprocessing ...
% 4.76/1.91 Prover 7: Proving ...
% 6.47/2.27 Prover 7: proved (385ms)
% 6.47/2.27
% 6.47/2.27 % SZS status Theorem for theBenchmark
% 6.47/2.27
% 6.47/2.27 Generating proof ... found it (size 23)
% 7.92/2.65
% 7.92/2.65 % SZS output start Proof for theBenchmark
% 7.92/2.66 Assumed formulas after preprocessing and simplification:
% 7.92/2.66 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (union(v3) = v2) | ~ (union(v3) = v1)) & ? [v1] : ( ~ (v1 = v0) & union(v0) = v1 & empty(v0) & ! [v2] : ! [v3] : ( ~ (union(v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ! [v6] : ( ~ in(v6, v2) | ~ in(v5, v6))) & (in(v5, v4) | ? [v6] : (in(v6, v2) & in(v5, v6)))))) & ! [v2] : ! [v3] : ( ~ (union(v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | ? [v5] : (in(v5, v2) & in(v4, v5))) & ! [v4] : (in(v4, v3) | ! [v5] : ( ~ in(v5, v2) | ~ in(v4, v5))))) & ! [v2] : ! [v3] : ( ~ in(v3, v2) | ~ in(v2, v3)) & ! [v2] : (v2 = v0 | ? [v3] : in(v3, v2)) & ! [v2] : ~ in(v2, v0) & ? [v2] : ~ empty(v2) & ? [v2] : empty(v2)))
% 7.92/2.68 | Instantiating (0) with all_0_0_0 yields:
% 7.92/2.68 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ? [v0] : ( ~ (v0 = all_0_0_0) & union(all_0_0_0) = v0 & empty(all_0_0_0) & ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ! [v5] : ( ~ in(v5, v1) | ~ in(v4, v5))) & (in(v4, v3) | ? [v5] : (in(v5, v1) & in(v4, v5)))))) & ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | ? [v4] : (in(v4, v1) & in(v3, v4))) & ! [v3] : (in(v3, v2) | ! [v4] : ( ~ in(v4, v1) | ~ in(v3, v4))))) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : (v1 = all_0_0_0 | ? [v2] : in(v2, v1)) & ! [v1] : ~ in(v1, all_0_0_0) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1))
% 7.92/2.68 |
% 7.92/2.68 | Applying alpha-rule on (1) yields:
% 7.92/2.68 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 7.92/2.68 | (3) ? [v0] : ( ~ (v0 = all_0_0_0) & union(all_0_0_0) = v0 & empty(all_0_0_0) & ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ! [v5] : ( ~ in(v5, v1) | ~ in(v4, v5))) & (in(v4, v3) | ? [v5] : (in(v5, v1) & in(v4, v5)))))) & ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | ? [v4] : (in(v4, v1) & in(v3, v4))) & ! [v3] : (in(v3, v2) | ! [v4] : ( ~ in(v4, v1) | ~ in(v3, v4))))) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : (v1 = all_0_0_0 | ? [v2] : in(v2, v1)) & ! [v1] : ~ in(v1, all_0_0_0) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1))
% 7.92/2.68 |
% 7.92/2.68 | Instantiating (3) with all_2_0_1 yields:
% 7.92/2.68 | (4) ~ (all_2_0_1 = all_0_0_0) & union(all_0_0_0) = all_2_0_1 & empty(all_0_0_0) & ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ! [v4] : ( ~ in(v4, v0) | ~ in(v3, v4))) & (in(v3, v2) | ? [v4] : (in(v4, v0) & in(v3, v4)))))) & ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ( ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) & ! [v2] : (in(v2, v1) | ! [v3] : ( ~ in(v3, v0) | ~ in(v2, v3))))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0)) & ! [v0] : ~ in(v0, all_0_0_0) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0)
% 7.92/2.69 |
% 7.92/2.69 | Applying alpha-rule on (4) yields:
% 7.92/2.69 | (5) ~ (all_2_0_1 = all_0_0_0)
% 7.92/2.69 | (6) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 7.92/2.69 | (7) ? [v0] : ~ empty(v0)
% 7.92/2.69 | (8) empty(all_0_0_0)
% 7.92/2.69 | (9) union(all_0_0_0) = all_2_0_1
% 7.92/2.69 | (10) ? [v0] : empty(v0)
% 7.92/2.69 | (11) ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0))
% 7.92/2.69 | (12) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ( ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) & ! [v2] : (in(v2, v1) | ! [v3] : ( ~ in(v3, v0) | ~ in(v2, v3)))))
% 7.92/2.69 | (13) ! [v0] : ~ in(v0, all_0_0_0)
% 7.92/2.69 | (14) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ! [v4] : ( ~ in(v4, v0) | ~ in(v3, v4))) & (in(v3, v2) | ? [v4] : (in(v4, v0) & in(v3, v4))))))
% 7.92/2.69 |
% 7.92/2.69 | Instantiating formula (12) with all_2_0_1, all_0_0_0 and discharging atoms union(all_0_0_0) = all_2_0_1, yields:
% 7.92/2.69 | (15) ! [v0] : ( ~ in(v0, all_2_0_1) | ? [v1] : (in(v1, all_0_0_0) & in(v0, v1))) & ! [v0] : (in(v0, all_2_0_1) | ! [v1] : ( ~ in(v1, all_0_0_0) | ~ in(v0, v1)))
% 7.92/2.69 |
% 7.92/2.69 | Applying alpha-rule on (15) yields:
% 7.92/2.69 | (16) ! [v0] : ( ~ in(v0, all_2_0_1) | ? [v1] : (in(v1, all_0_0_0) & in(v0, v1)))
% 7.92/2.69 | (17) ! [v0] : (in(v0, all_2_0_1) | ! [v1] : ( ~ in(v1, all_0_0_0) | ~ in(v0, v1)))
% 7.92/2.69 |
% 7.92/2.69 | Introducing new symbol ex_17_0_4 defined by:
% 7.92/2.69 | (18) ex_17_0_4 = all_2_0_1
% 7.92/2.69 |
% 7.92/2.69 | Instantiating formula (11) with ex_17_0_4 yields:
% 7.92/2.69 | (19) ex_17_0_4 = all_0_0_0 | ? [v0] : in(v0, ex_17_0_4)
% 7.92/2.69 |
% 7.92/2.69 +-Applying beta-rule and splitting (19), into two cases.
% 7.92/2.69 |-Branch one:
% 7.92/2.69 | (20) ex_17_0_4 = all_0_0_0
% 7.92/2.69 |
% 7.92/2.69 | Combining equations (18,20) yields a new equation:
% 7.92/2.69 | (21) all_2_0_1 = all_0_0_0
% 7.92/2.69 |
% 7.92/2.69 | Simplifying 21 yields:
% 7.92/2.69 | (22) all_2_0_1 = all_0_0_0
% 7.92/2.69 |
% 7.92/2.69 | Equations (22) can reduce 5 to:
% 7.92/2.69 | (23) $false
% 7.92/2.69 |
% 7.92/2.69 |-The branch is then unsatisfiable
% 7.92/2.69 |-Branch two:
% 7.92/2.69 | (24) ? [v0] : in(v0, ex_17_0_4)
% 7.92/2.69 |
% 7.92/2.69 | Instantiating (24) with all_20_0_5 yields:
% 7.92/2.69 | (25) in(all_20_0_5, ex_17_0_4)
% 7.92/2.69 |
% 7.92/2.69 | Instantiating formula (16) with all_20_0_5 yields:
% 7.92/2.69 | (26) ~ in(all_20_0_5, all_2_0_1) | ? [v0] : (in(v0, all_0_0_0) & in(all_20_0_5, v0))
% 7.92/2.69 |
% 7.92/2.69 +-Applying beta-rule and splitting (26), into two cases.
% 7.92/2.69 |-Branch one:
% 7.92/2.69 | (27) ~ in(all_20_0_5, all_2_0_1)
% 7.92/2.69 |
% 7.92/2.69 | From (18) and (25) follows:
% 7.92/2.70 | (28) in(all_20_0_5, all_2_0_1)
% 7.92/2.70 |
% 7.92/2.70 | Using (28) and (27) yields:
% 7.92/2.70 | (29) $false
% 7.92/2.70 |
% 7.92/2.70 |-The branch is then unsatisfiable
% 7.92/2.70 |-Branch two:
% 7.92/2.70 | (30) ? [v0] : (in(v0, all_0_0_0) & in(all_20_0_5, v0))
% 7.92/2.70 |
% 7.92/2.70 | Instantiating (30) with all_28_0_7 yields:
% 7.92/2.70 | (31) in(all_28_0_7, all_0_0_0) & in(all_20_0_5, all_28_0_7)
% 7.92/2.70 |
% 7.92/2.70 | Applying alpha-rule on (31) yields:
% 7.92/2.70 | (32) in(all_28_0_7, all_0_0_0)
% 7.92/2.70 | (33) in(all_20_0_5, all_28_0_7)
% 7.92/2.70 |
% 7.92/2.70 | Instantiating formula (13) with all_28_0_7 and discharging atoms in(all_28_0_7, all_0_0_0), yields:
% 7.92/2.70 | (29) $false
% 7.92/2.70 |
% 7.92/2.70 |-The branch is then unsatisfiable
% 7.92/2.70 % SZS output end Proof for theBenchmark
% 7.92/2.70
% 7.92/2.70 2086ms
%------------------------------------------------------------------------------