TSTP Solution File: SET900+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET900+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 4.91s 1.99s
% Output : Proof 6.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET900+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n026.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 : Sun Jul 10 01:07:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.58/0.60 ____ _
% 0.58/0.60 ___ / __ \_____(_)___ ________ __________
% 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.60
% 0.58/0.60 A Theorem Prover for First-Order Logic
% 0.58/0.60 (ePrincess v.1.0)
% 0.58/0.60
% 0.58/0.60 (c) Philipp Rümmer, 2009-2015
% 0.58/0.60 (c) Peter Backeman, 2014-2015
% 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.60 Bug reports to peter@backeman.se
% 0.58/0.60
% 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.60
% 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.35/0.90 Prover 0: Preprocessing ...
% 1.47/0.99 Prover 0: Warning: ignoring some quantifiers
% 1.47/1.00 Prover 0: Constructing countermodel ...
% 1.85/1.12 Prover 0: gave up
% 1.85/1.12 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.85/1.14 Prover 1: Preprocessing ...
% 2.24/1.18 Prover 1: Warning: ignoring some quantifiers
% 2.24/1.18 Prover 1: Constructing countermodel ...
% 2.32/1.23 Prover 1: gave up
% 2.32/1.23 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.38/1.24 Prover 2: Preprocessing ...
% 2.38/1.28 Prover 2: Warning: ignoring some quantifiers
% 2.38/1.28 Prover 2: Constructing countermodel ...
% 2.77/1.33 Prover 2: gave up
% 2.77/1.33 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.77/1.34 Prover 3: Preprocessing ...
% 2.77/1.35 Prover 3: Warning: ignoring some quantifiers
% 2.77/1.35 Prover 3: Constructing countermodel ...
% 2.77/1.37 Prover 3: gave up
% 2.77/1.37 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.77/1.38 Prover 4: Preprocessing ...
% 3.01/1.42 Prover 4: Warning: ignoring some quantifiers
% 3.01/1.42 Prover 4: Constructing countermodel ...
% 3.31/1.49 Prover 4: gave up
% 3.31/1.49 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.31/1.49 Prover 5: Preprocessing ...
% 3.45/1.51 Prover 5: Warning: ignoring some quantifiers
% 3.45/1.52 Prover 5: Constructing countermodel ...
% 3.57/1.54 Prover 5: gave up
% 3.57/1.54 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.57/1.55 Prover 6: Preprocessing ...
% 3.57/1.57 Prover 6: Warning: ignoring some quantifiers
% 3.57/1.57 Prover 6: Constructing countermodel ...
% 3.57/1.60 Prover 6: gave up
% 3.57/1.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.57/1.60 Prover 7: Preprocessing ...
% 3.57/1.62 Prover 7: Proving ...
% 4.91/1.99 Prover 7: proved (393ms)
% 4.91/1.99
% 4.91/1.99 % SZS status Theorem for theBenchmark
% 4.91/1.99
% 4.91/1.99 Generating proof ... found it (size 26)
% 6.32/2.39
% 6.32/2.39 % SZS output start Proof for theBenchmark
% 6.32/2.39 Assumed formulas after preprocessing and simplification:
% 6.32/2.39 | (0) ? [v0] : (empty(v0) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v3) = v2) | ~ (singleton(v3) = v1)) & ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | ! [v3] : (v3 = v2 | v3 = v0 | ? [v4] : ( ~ (v4 = v1) & in(v4, v3)))) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v1) & ~ (v1 = v0) & singleton(v2) = v3 & ! [v4] : (v4 = v2 | ~ in(v4, v1))) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1))
% 6.32/2.41 | Instantiating (0) with all_0_0_0 yields:
% 6.32/2.41 | (1) empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | v2 = all_0_0_0 | ? [v3] : ( ~ (v3 = v0) & in(v3, v2)))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v0) & ~ (v0 = all_0_0_0) & singleton(v1) = v2 & ! [v3] : (v3 = v1 | ~ in(v3, v0))) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0)
% 6.32/2.41 |
% 6.32/2.41 | Applying alpha-rule on (1) yields:
% 6.32/2.41 | (2) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | v2 = all_0_0_0 | ? [v3] : ( ~ (v3 = v0) & in(v3, v2))))
% 6.32/2.41 | (3) ? [v0] : empty(v0)
% 6.32/2.41 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.32/2.41 | (5) ? [v0] : ~ empty(v0)
% 6.32/2.41 | (6) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 6.73/2.41 | (7) empty(all_0_0_0)
% 6.73/2.41 | (8) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v0) & ~ (v0 = all_0_0_0) & singleton(v1) = v2 & ! [v3] : (v3 = v1 | ~ in(v3, v0)))
% 6.73/2.41 |
% 6.73/2.41 | Instantiating (8) with all_7_0_3, all_7_1_4, all_7_2_5 yields:
% 6.73/2.41 | (9) ~ (all_7_0_3 = all_7_2_5) & ~ (all_7_2_5 = all_0_0_0) & singleton(all_7_1_4) = all_7_0_3 & ! [v0] : (v0 = all_7_1_4 | ~ in(v0, all_7_2_5))
% 6.73/2.41 |
% 6.73/2.41 | Applying alpha-rule on (9) yields:
% 6.73/2.41 | (10) ~ (all_7_0_3 = all_7_2_5)
% 6.73/2.41 | (11) ~ (all_7_2_5 = all_0_0_0)
% 6.73/2.41 | (12) singleton(all_7_1_4) = all_7_0_3
% 6.73/2.41 | (13) ! [v0] : (v0 = all_7_1_4 | ~ in(v0, all_7_2_5))
% 6.73/2.41 |
% 6.73/2.41 | Instantiating formula (2) with all_7_0_3, all_7_1_4 and discharging atoms singleton(all_7_1_4) = all_7_0_3, yields:
% 6.73/2.41 | (14) ! [v0] : (v0 = all_7_0_3 | v0 = all_0_0_0 | ? [v1] : ( ~ (v1 = all_7_1_4) & in(v1, v0)))
% 6.73/2.42 |
% 6.73/2.42 | Introducing new symbol ex_16_0_6 defined by:
% 6.73/2.42 | (15) ex_16_0_6 = all_7_2_5
% 6.73/2.42 |
% 6.73/2.42 | Instantiating formula (14) with ex_16_0_6 yields:
% 6.73/2.42 | (16) ex_16_0_6 = all_7_0_3 | ex_16_0_6 = all_0_0_0 | ? [v0] : ( ~ (v0 = all_7_1_4) & in(v0, ex_16_0_6))
% 6.73/2.42 |
% 6.73/2.42 +-Applying beta-rule and splitting (16), into two cases.
% 6.73/2.42 |-Branch one:
% 6.73/2.42 | (17) ex_16_0_6 = all_7_0_3
% 6.73/2.42 |
% 6.73/2.42 | Combining equations (17,15) yields a new equation:
% 6.73/2.42 | (18) all_7_0_3 = all_7_2_5
% 6.73/2.42 |
% 6.73/2.42 | Simplifying 18 yields:
% 6.73/2.42 | (19) all_7_0_3 = all_7_2_5
% 6.73/2.42 |
% 6.73/2.42 | Equations (19) can reduce 10 to:
% 6.73/2.42 | (20) $false
% 6.73/2.42 |
% 6.73/2.42 |-The branch is then unsatisfiable
% 6.73/2.42 |-Branch two:
% 6.73/2.42 | (21) ex_16_0_6 = all_0_0_0 | ? [v0] : ( ~ (v0 = all_7_1_4) & in(v0, ex_16_0_6))
% 6.73/2.42 |
% 6.73/2.42 +-Applying beta-rule and splitting (21), into two cases.
% 6.73/2.42 |-Branch one:
% 6.73/2.42 | (22) ex_16_0_6 = all_0_0_0
% 6.73/2.42 |
% 6.73/2.42 | Combining equations (15,22) yields a new equation:
% 6.73/2.42 | (23) all_7_2_5 = all_0_0_0
% 6.73/2.42 |
% 6.73/2.42 | Simplifying 23 yields:
% 6.73/2.42 | (24) all_7_2_5 = all_0_0_0
% 6.73/2.42 |
% 6.73/2.42 | Equations (24) can reduce 11 to:
% 6.73/2.42 | (20) $false
% 6.73/2.42 |
% 6.73/2.42 |-The branch is then unsatisfiable
% 6.73/2.42 |-Branch two:
% 6.73/2.42 | (26) ? [v0] : ( ~ (v0 = all_7_1_4) & in(v0, ex_16_0_6))
% 6.73/2.42 |
% 6.73/2.42 | Instantiating (26) with all_26_0_8 yields:
% 6.73/2.42 | (27) ~ (all_26_0_8 = all_7_1_4) & in(all_26_0_8, ex_16_0_6)
% 6.73/2.42 |
% 6.73/2.42 | Applying alpha-rule on (27) yields:
% 6.73/2.42 | (28) ~ (all_26_0_8 = all_7_1_4)
% 6.73/2.42 | (29) in(all_26_0_8, ex_16_0_6)
% 6.73/2.42 |
% 6.73/2.42 | Instantiating formula (13) with all_26_0_8 yields:
% 6.73/2.42 | (30) all_26_0_8 = all_7_1_4 | ~ in(all_26_0_8, all_7_2_5)
% 6.73/2.42 |
% 6.73/2.42 +-Applying beta-rule and splitting (30), into two cases.
% 6.73/2.42 |-Branch one:
% 6.73/2.42 | (31) ~ in(all_26_0_8, all_7_2_5)
% 6.73/2.42 |
% 6.73/2.42 | From (15) and (29) follows:
% 6.73/2.42 | (32) in(all_26_0_8, all_7_2_5)
% 6.73/2.42 |
% 6.73/2.42 | Using (32) and (31) yields:
% 6.73/2.42 | (33) $false
% 6.73/2.42 |
% 6.73/2.42 |-The branch is then unsatisfiable
% 6.73/2.42 |-Branch two:
% 6.73/2.42 | (34) all_26_0_8 = all_7_1_4
% 6.73/2.42 |
% 6.73/2.42 | Equations (34) can reduce 28 to:
% 6.73/2.42 | (20) $false
% 6.73/2.42 |
% 6.73/2.42 |-The branch is then unsatisfiable
% 6.73/2.42 % SZS output end Proof for theBenchmark
% 6.73/2.42
% 6.73/2.42 1812ms
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