TSTP Solution File: SEU120+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU120+1 : TPTP v8.1.0. Released v3.3.0.
% 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 08:46:42 EDT 2022
% Result : Theorem 27.47s 13.12s
% Output : Proof 28.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU120+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 23:59:48 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.19/0.56 ____ _
% 0.19/0.56 ___ / __ \_____(_)___ ________ __________
% 0.19/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.56
% 0.19/0.56 A Theorem Prover for First-Order Logic
% 0.19/0.56 (ePrincess v.1.0)
% 0.19/0.56
% 0.19/0.56 (c) Philipp Rümmer, 2009-2015
% 0.19/0.56 (c) Peter Backeman, 2014-2015
% 0.19/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.56 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.56 Bug reports to peter@backeman.se
% 0.19/0.56
% 0.19/0.56 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.56
% 0.19/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/0.86 Prover 0: Preprocessing ...
% 1.64/0.98 Prover 0: Warning: ignoring some quantifiers
% 1.64/0.99 Prover 0: Constructing countermodel ...
% 2.22/1.13 Prover 0: gave up
% 2.22/1.13 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.22/1.15 Prover 1: Preprocessing ...
% 2.49/1.21 Prover 1: Warning: ignoring some quantifiers
% 2.49/1.21 Prover 1: Constructing countermodel ...
% 2.72/1.30 Prover 1: gave up
% 2.72/1.30 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.72/1.31 Prover 2: Preprocessing ...
% 2.72/1.37 Prover 2: Warning: ignoring some quantifiers
% 2.72/1.37 Prover 2: Constructing countermodel ...
% 3.24/1.45 Prover 2: gave up
% 3.24/1.46 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.24/1.47 Prover 3: Preprocessing ...
% 3.24/1.48 Prover 3: Warning: ignoring some quantifiers
% 3.24/1.48 Prover 3: Constructing countermodel ...
% 3.57/1.52 Prover 3: gave up
% 3.57/1.52 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.57/1.53 Prover 4: Preprocessing ...
% 3.57/1.57 Prover 4: Warning: ignoring some quantifiers
% 3.57/1.57 Prover 4: Constructing countermodel ...
% 4.29/1.68 Prover 4: gave up
% 4.37/1.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.37/1.69 Prover 5: Preprocessing ...
% 4.52/1.72 Prover 5: Warning: ignoring some quantifiers
% 4.52/1.72 Prover 5: Constructing countermodel ...
% 4.60/1.77 Prover 5: gave up
% 4.60/1.77 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.60/1.78 Prover 6: Preprocessing ...
% 4.60/1.80 Prover 6: Warning: ignoring some quantifiers
% 4.60/1.81 Prover 6: Constructing countermodel ...
% 5.00/1.85 Prover 6: gave up
% 5.00/1.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.00/1.86 Prover 7: Preprocessing ...
% 5.00/1.87 Prover 7: Proving ...
% 26.25/12.77 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 26.25/12.79 Prover 8: Preprocessing ...
% 26.68/12.82 Prover 8: Proving ...
% 27.47/13.12 Prover 8: proved (344ms)
% 27.47/13.12 Prover 7: stopped
% 27.47/13.12
% 27.47/13.12 % SZS status Theorem for theBenchmark
% 27.47/13.12
% 27.47/13.12 Generating proof ... found it (size 34)
% 28.64/13.54
% 28.64/13.54 % SZS output start Proof for theBenchmark
% 28.64/13.54 Assumed formulas after preprocessing and simplification:
% 28.64/13.54 | (0) ? [v0] : (empty(v0) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (disjoint(v4, v3) = v2) | ~ (disjoint(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_intersection2(v4, v3) = v2) | ~ (set_intersection2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (in(v4, v3) = v2) | ~ (in(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = v3) | ? [v4] : ( ~ (v4 = v0) & set_intersection2(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (empty(v3) = v2) | ~ (empty(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | set_intersection2(v2, v1) = v3) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_intersection2(v1, v1) = v2)) & ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | disjoint(v2, v1) = 0) & ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | set_intersection2(v1, v2) = v0) & ! [v1] : ! [v2] : ( ~ (in(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v1] : (v1 = v0 | ? [v2] : in(v2, v1) = 0) & ! [v1] : ~ (in(v1, v0) = 0) & ? [v1] : ? [v2] : ? [v3] : ? [v4] : (disjoint(v1, v2) = v3 & set_intersection2(v1, v2) = v4 & ((v3 = 0 & ? [v5] : in(v5, v4) = 0) | ( ~ (v3 = 0) & ! [v5] : ~ (in(v5, v4) = 0)))) & ? [v1] : ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2) & ? [v1] : empty(v1) = 0)
% 28.64/13.56 | Instantiating (0) with all_0_0_0 yields:
% 28.64/13.56 | (1) empty(all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = all_0_0_0) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = all_0_0_0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0) = 0) & ! [v0] : ~ (in(v0, all_0_0_0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (disjoint(v0, v1) = v2 & set_intersection2(v0, v1) = v3 & ((v2 = 0 & ? [v4] : in(v4, v3) = 0) | ( ~ (v2 = 0) & ! [v4] : ~ (in(v4, v3) = 0)))) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) & ? [v0] : empty(v0) = 0
% 28.64/13.57 |
% 28.64/13.57 | Applying alpha-rule on (1) yields:
% 28.64/13.57 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 28.64/13.57 | (3) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 28.64/13.57 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = all_0_0_0) & set_intersection2(v0, v1) = v3))
% 28.64/13.57 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 28.64/13.57 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 28.64/13.57 | (7) ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0) = 0)
% 28.64/13.57 | (8) empty(all_0_0_0) = 0
% 28.64/13.57 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 28.64/13.58 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 28.64/13.58 | (11) ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1)
% 28.64/13.58 | (12) ! [v0] : ~ (in(v0, all_0_0_0) = 0)
% 28.64/13.58 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 28.64/13.58 | (14) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 28.64/13.58 | (15) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (disjoint(v0, v1) = v2 & set_intersection2(v0, v1) = v3 & ((v2 = 0 & ? [v4] : in(v4, v3) = 0) | ( ~ (v2 = 0) & ! [v4] : ~ (in(v4, v3) = 0))))
% 28.64/13.58 | (16) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = all_0_0_0)
% 28.64/13.58 | (17) ? [v0] : empty(v0) = 0
% 28.64/13.58 |
% 28.64/13.58 | Instantiating (15) with all_7_0_4, all_7_1_5, all_7_2_6, all_7_3_7 yields:
% 28.64/13.58 | (18) disjoint(all_7_3_7, all_7_2_6) = all_7_1_5 & set_intersection2(all_7_3_7, all_7_2_6) = all_7_0_4 & ((all_7_1_5 = 0 & ? [v0] : in(v0, all_7_0_4) = 0) | ( ~ (all_7_1_5 = 0) & ! [v0] : ~ (in(v0, all_7_0_4) = 0)))
% 28.64/13.58 |
% 28.64/13.58 | Applying alpha-rule on (18) yields:
% 28.64/13.58 | (19) disjoint(all_7_3_7, all_7_2_6) = all_7_1_5
% 28.64/13.58 | (20) set_intersection2(all_7_3_7, all_7_2_6) = all_7_0_4
% 28.64/13.58 | (21) (all_7_1_5 = 0 & ? [v0] : in(v0, all_7_0_4) = 0) | ( ~ (all_7_1_5 = 0) & ! [v0] : ~ (in(v0, all_7_0_4) = 0))
% 28.64/13.58 |
% 28.64/13.58 | Instantiating formula (4) with all_7_1_5, all_7_2_6, all_7_3_7 and discharging atoms disjoint(all_7_3_7, all_7_2_6) = all_7_1_5, yields:
% 28.64/13.58 | (22) all_7_1_5 = 0 | ? [v0] : ( ~ (v0 = all_0_0_0) & set_intersection2(all_7_3_7, all_7_2_6) = v0)
% 28.64/13.58 |
% 28.64/13.58 +-Applying beta-rule and splitting (21), into two cases.
% 28.64/13.58 |-Branch one:
% 28.64/13.58 | (23) all_7_1_5 = 0 & ? [v0] : in(v0, all_7_0_4) = 0
% 28.64/13.58 |
% 28.64/13.58 | Applying alpha-rule on (23) yields:
% 28.64/13.58 | (24) all_7_1_5 = 0
% 28.64/13.58 | (25) ? [v0] : in(v0, all_7_0_4) = 0
% 28.64/13.58 |
% 28.64/13.58 | Instantiating (25) with all_22_0_8 yields:
% 28.64/13.58 | (26) in(all_22_0_8, all_7_0_4) = 0
% 28.64/13.58 |
% 28.64/13.58 | From (24) and (19) follows:
% 28.64/13.58 | (27) disjoint(all_7_3_7, all_7_2_6) = 0
% 28.64/13.58 |
% 28.64/13.58 | Instantiating formula (16) with all_7_2_6, all_7_3_7 and discharging atoms disjoint(all_7_3_7, all_7_2_6) = 0, yields:
% 28.64/13.58 | (28) set_intersection2(all_7_3_7, all_7_2_6) = all_0_0_0
% 28.64/13.58 |
% 28.64/13.58 | Instantiating formula (5) with all_7_3_7, all_7_2_6, all_0_0_0, all_7_0_4 and discharging atoms set_intersection2(all_7_3_7, all_7_2_6) = all_7_0_4, set_intersection2(all_7_3_7, all_7_2_6) = all_0_0_0, yields:
% 28.64/13.58 | (29) all_7_0_4 = all_0_0_0
% 28.64/13.58 |
% 28.64/13.58 | From (29) and (26) follows:
% 28.64/13.58 | (30) in(all_22_0_8, all_0_0_0) = 0
% 28.64/13.58 |
% 28.64/13.58 | Instantiating formula (12) with all_22_0_8 and discharging atoms in(all_22_0_8, all_0_0_0) = 0, yields:
% 28.64/13.58 | (31) $false
% 28.64/13.58 |
% 28.64/13.59 |-The branch is then unsatisfiable
% 28.64/13.59 |-Branch two:
% 28.64/13.59 | (32) ~ (all_7_1_5 = 0) & ! [v0] : ~ (in(v0, all_7_0_4) = 0)
% 28.64/13.59 |
% 28.64/13.59 | Applying alpha-rule on (32) yields:
% 28.64/13.59 | (33) ~ (all_7_1_5 = 0)
% 28.64/13.59 | (34) ! [v0] : ~ (in(v0, all_7_0_4) = 0)
% 28.64/13.59 |
% 28.64/13.59 +-Applying beta-rule and splitting (22), into two cases.
% 28.64/13.59 |-Branch one:
% 28.64/13.59 | (24) all_7_1_5 = 0
% 28.64/13.59 |
% 28.64/13.59 | Equations (24) can reduce 33 to:
% 28.64/13.59 | (36) $false
% 28.64/13.59 |
% 28.64/13.59 |-The branch is then unsatisfiable
% 28.64/13.59 |-Branch two:
% 28.64/13.59 | (37) ? [v0] : ( ~ (v0 = all_0_0_0) & set_intersection2(all_7_3_7, all_7_2_6) = v0)
% 28.64/13.59 |
% 28.64/13.59 | Instantiating (37) with all_27_0_10 yields:
% 28.64/13.59 | (38) ~ (all_27_0_10 = all_0_0_0) & set_intersection2(all_7_3_7, all_7_2_6) = all_27_0_10
% 28.64/13.59 |
% 28.64/13.59 | Applying alpha-rule on (38) yields:
% 28.64/13.59 | (39) ~ (all_27_0_10 = all_0_0_0)
% 28.64/13.59 | (40) set_intersection2(all_7_3_7, all_7_2_6) = all_27_0_10
% 28.64/13.59 |
% 28.64/13.59 | Instantiating formula (5) with all_7_3_7, all_7_2_6, all_27_0_10, all_7_0_4 and discharging atoms set_intersection2(all_7_3_7, all_7_2_6) = all_27_0_10, set_intersection2(all_7_3_7, all_7_2_6) = all_7_0_4, yields:
% 28.64/13.59 | (41) all_27_0_10 = all_7_0_4
% 28.64/13.59 |
% 28.64/13.59 | Equations (41) can reduce 39 to:
% 28.64/13.59 | (42) ~ (all_7_0_4 = all_0_0_0)
% 28.64/13.59 |
% 28.64/13.59 | Introducing new symbol ex_39_0_11 defined by:
% 28.64/13.59 | (43) ex_39_0_11 = all_7_0_4
% 28.64/13.59 |
% 28.64/13.59 | Instantiating formula (7) with ex_39_0_11 yields:
% 28.64/13.59 | (44) ex_39_0_11 = all_0_0_0 | ? [v0] : in(v0, ex_39_0_11) = 0
% 28.98/13.59 |
% 28.98/13.59 +-Applying beta-rule and splitting (44), into two cases.
% 28.98/13.59 |-Branch one:
% 28.98/13.59 | (45) ex_39_0_11 = all_0_0_0
% 28.98/13.59 |
% 28.98/13.59 | Combining equations (43,45) yields a new equation:
% 28.98/13.59 | (46) all_7_0_4 = all_0_0_0
% 28.98/13.59 |
% 28.98/13.59 | Simplifying 46 yields:
% 28.98/13.59 | (29) all_7_0_4 = all_0_0_0
% 28.98/13.59 |
% 28.98/13.59 | Equations (29) can reduce 42 to:
% 28.98/13.59 | (36) $false
% 28.98/13.59 |
% 28.98/13.59 |-The branch is then unsatisfiable
% 28.98/13.59 |-Branch two:
% 28.98/13.59 | (49) ? [v0] : in(v0, ex_39_0_11) = 0
% 28.98/13.59 |
% 28.98/13.59 | Instantiating (49) with all_42_0_12 yields:
% 28.98/13.59 | (50) in(all_42_0_12, ex_39_0_11) = 0
% 28.98/13.59 |
% 28.98/13.59 | Instantiating formula (34) with all_42_0_12 yields:
% 28.98/13.59 | (51) ~ (in(all_42_0_12, all_7_0_4) = 0)
% 28.98/13.59 |
% 28.98/13.59 | From (43) and (50) follows:
% 28.98/13.59 | (52) in(all_42_0_12, all_7_0_4) = 0
% 28.98/13.59 |
% 28.98/13.59 | Using (52) and (51) yields:
% 28.98/13.59 | (31) $false
% 28.98/13.59 |
% 28.98/13.59 |-The branch is then unsatisfiable
% 28.98/13.59 % SZS output end Proof for theBenchmark
% 28.98/13.59
% 28.98/13.59 13016ms
%------------------------------------------------------------------------------