TSTP Solution File: NUM405+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM405+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 : Mon Jul 18 08:44:11 EDT 2022
% Result : Theorem 28.92s 7.88s
% Output : Proof 54.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM405+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 12:31:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.47/0.60 ____ _
% 0.47/0.60 ___ / __ \_____(_)___ ________ __________
% 0.47/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.60
% 0.47/0.60 A Theorem Prover for First-Order Logic
% 0.47/0.60 (ePrincess v.1.0)
% 0.47/0.60
% 0.47/0.60 (c) Philipp Rümmer, 2009-2015
% 0.47/0.60 (c) Peter Backeman, 2014-2015
% 0.47/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.60 Bug reports to peter@backeman.se
% 0.47/0.60
% 0.47/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.60
% 0.47/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.67/0.95 Prover 0: Preprocessing ...
% 1.99/1.07 Prover 0: Warning: ignoring some quantifiers
% 2.06/1.09 Prover 0: Constructing countermodel ...
% 3.13/1.41 Prover 0: gave up
% 3.13/1.41 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.42/1.44 Prover 1: Preprocessing ...
% 3.98/1.55 Prover 1: Warning: ignoring some quantifiers
% 3.98/1.55 Prover 1: Constructing countermodel ...
% 4.96/1.77 Prover 1: gave up
% 4.96/1.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.96/1.79 Prover 2: Preprocessing ...
% 5.44/1.88 Prover 2: Warning: ignoring some quantifiers
% 5.44/1.89 Prover 2: Constructing countermodel ...
% 7.32/2.31 Prover 2: gave up
% 7.32/2.32 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 7.32/2.33 Prover 3: Preprocessing ...
% 7.54/2.35 Prover 3: Warning: ignoring some quantifiers
% 7.54/2.35 Prover 3: Constructing countermodel ...
% 7.82/2.43 Prover 3: gave up
% 7.82/2.43 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 7.82/2.45 Prover 4: Preprocessing ...
% 8.09/2.51 Prover 4: Warning: ignoring some quantifiers
% 8.09/2.52 Prover 4: Constructing countermodel ...
% 12.77/3.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 12.86/3.61 Prover 5: Preprocessing ...
% 12.94/3.69 Prover 5: Warning: ignoring some quantifiers
% 12.94/3.69 Prover 5: Constructing countermodel ...
% 15.53/4.33 Prover 5: gave up
% 15.53/4.33 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 15.95/4.35 Prover 6: Preprocessing ...
% 15.95/4.38 Prover 6: Warning: ignoring some quantifiers
% 15.95/4.39 Prover 6: Constructing countermodel ...
% 17.46/4.68 Prover 6: gave up
% 17.46/4.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 17.46/4.70 Prover 7: Preprocessing ...
% 17.46/4.71 Prover 7: Proving ...
% 28.92/7.87 Prover 7: proved (3192ms)
% 28.92/7.88 Prover 4: stopped
% 28.92/7.88
% 28.92/7.88 % SZS status Theorem for theBenchmark
% 28.92/7.88
% 28.92/7.88 Generating proof ... found it (size 32)
% 54.94/22.68
% 54.94/22.68 % SZS output start Proof for theBenchmark
% 54.94/22.68 Assumed formulas after preprocessing and simplification:
% 54.94/22.68 | (0) ? [v0] : (relation_empty_yielding(v0) & one_to_one(v0) & relation(v0) & epsilon_connected(v0) & epsilon_transitive(v0) & ordinal(v0) & function(v0) & empty(v0) & ! [v1] : ! [v2] : (v2 = v1 | ~ empty(v2) | ~ empty(v1)) & ! [v1] : ! [v2] : ( ~ element(v1, v2) | empty(v2) | in(v1, v2)) & ! [v1] : ! [v2] : ( ~ empty(v2) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ in(v1, v2) | element(v1, v2)) & ? [v1] : ! [v2] : ( ~ ordinal(v2) | in(v2, v1)) & ! [v1] : (v1 = v0 | ~ empty(v1)) & ! [v1] : ( ~ relation(v1) | ~ function(v1) | ~ empty(v1) | one_to_one(v1)) & ! [v1] : ( ~ epsilon_connected(v1) | ~ epsilon_transitive(v1) | ordinal(v1)) & ! [v1] : ( ~ ordinal(v1) | (epsilon_connected(v1) & epsilon_transitive(v1))) & ! [v1] : ( ~ empty(v1) | relation(v1)) & ! [v1] : ( ~ empty(v1) | function(v1)) & ! [v1] : ( ~ empty(v1) | (epsilon_connected(v1) & epsilon_transitive(v1) & ordinal(v1))) & ! [v1] : ? [v2] : element(v2, v1) & ! [v1] : ? [v2] : ( ! [v3] : ( ~ ordinal(v3) | ~ in(v3, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | (ordinal(v3) & in(v3, v1)))) & ! [v1] : ? [v2] : (( ~ ordinal(v2) | ~ in(v2, v1)) & (ordinal(v2) | in(v2, v1))) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1) & ? [v1] : (relation_non_empty(v1) & relation(v1) & function(v1)) & ? [v1] : (relation_empty_yielding(v1) & relation(v1) & function(v1)) & ? [v1] : (relation_empty_yielding(v1) & relation(v1)) & ? [v1] : (one_to_one(v1) & relation(v1) & epsilon_connected(v1) & epsilon_transitive(v1) & ordinal(v1) & function(v1) & empty(v1)) & ? [v1] : (one_to_one(v1) & relation(v1) & function(v1)) & ? [v1] : (relation(v1) & function(v1) & empty(v1)) & ? [v1] : (relation(v1) & function(v1)) & ? [v1] : (relation(v1) & empty(v1)) & ? [v1] : (relation(v1) & ~ empty(v1)) & ? [v1] : (epsilon_connected(v1) & epsilon_transitive(v1) & ordinal(v1) & ~ empty(v1)) & ? [v1] : (epsilon_connected(v1) & epsilon_transitive(v1) & ordinal(v1)))
% 54.94/22.68 | Instantiating (0) with all_0_0_0 yields:
% 54.94/22.68 | (1) relation_empty_yielding(all_0_0_0) & one_to_one(all_0_0_0) & relation(all_0_0_0) & epsilon_connected(all_0_0_0) & epsilon_transitive(all_0_0_0) & ordinal(all_0_0_0) & function(all_0_0_0) & empty(all_0_0_0) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ? [v0] : ! [v1] : ( ~ ordinal(v1) | in(v1, v0)) & ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) & ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) & ! [v0] : ( ~ ordinal(v0) | (epsilon_connected(v0) & epsilon_transitive(v0))) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ( ~ empty(v0) | (epsilon_connected(v0) & epsilon_transitive(v0) & ordinal(v0))) & ! [v0] : ? [v1] : element(v1, v0) & ! [v0] : ? [v1] : ( ! [v2] : ( ~ ordinal(v2) | ~ in(v2, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | (ordinal(v2) & in(v2, v0)))) & ! [v0] : ? [v1] : (( ~ ordinal(v1) | ~ in(v1, v0)) & (ordinal(v1) | in(v1, v0))) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) & ? [v0] : (relation_non_empty(v0) & relation(v0) & function(v0)) & ? [v0] : (relation_empty_yielding(v0) & relation(v0) & function(v0)) & ? [v0] : (relation_empty_yielding(v0) & relation(v0)) & ? [v0] : (one_to_one(v0) & relation(v0) & epsilon_connected(v0) & epsilon_transitive(v0) & ordinal(v0) & function(v0) & empty(v0)) & ? [v0] : (one_to_one(v0) & relation(v0) & function(v0)) & ? [v0] : (relation(v0) & function(v0) & empty(v0)) & ? [v0] : (relation(v0) & function(v0)) & ? [v0] : (relation(v0) & empty(v0)) & ? [v0] : (relation(v0) & ~ empty(v0)) & ? [v0] : (epsilon_connected(v0) & epsilon_transitive(v0) & ordinal(v0) & ~ empty(v0)) & ? [v0] : (epsilon_connected(v0) & epsilon_transitive(v0) & ordinal(v0))
% 54.94/22.69 |
% 54.94/22.69 | Applying alpha-rule on (1) yields:
% 54.94/22.69 | (2) ? [v0] : (relation(v0) & empty(v0))
% 54.94/22.69 | (3) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0))
% 54.94/22.69 | (4) ordinal(all_0_0_0)
% 54.94/22.69 | (5) ! [v0] : ( ~ empty(v0) | (epsilon_connected(v0) & epsilon_transitive(v0) & ordinal(v0)))
% 54.94/22.69 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 54.94/22.69 | (7) ? [v0] : (relation_empty_yielding(v0) & relation(v0))
% 54.94/22.69 | (8) one_to_one(all_0_0_0)
% 54.94/22.69 | (9) ? [v0] : ! [v1] : ( ~ ordinal(v1) | in(v1, v0))
% 54.94/22.69 | (10) ? [v0] : (relation_non_empty(v0) & relation(v0) & function(v0))
% 54.94/22.69 | (11) ! [v0] : ( ~ ordinal(v0) | (epsilon_connected(v0) & epsilon_transitive(v0)))
% 54.94/22.69 | (12) ? [v0] : (epsilon_connected(v0) & epsilon_transitive(v0) & ordinal(v0) & ~ empty(v0))
% 54.94/22.69 | (13) ? [v0] : (relation(v0) & function(v0))
% 54.94/22.69 | (14) ? [v0] : (relation_empty_yielding(v0) & relation(v0) & function(v0))
% 54.94/22.69 | (15) ! [v0] : ? [v1] : ( ! [v2] : ( ~ ordinal(v2) | ~ in(v2, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | (ordinal(v2) & in(v2, v0))))
% 54.94/22.69 | (16) ! [v0] : ? [v1] : (( ~ ordinal(v1) | ~ in(v1, v0)) & (ordinal(v1) | in(v1, v0)))
% 54.94/22.69 | (17) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 54.94/22.69 | (18) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 54.94/22.69 | (19) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 54.94/22.69 | (20) empty(all_0_0_0)
% 54.94/22.69 | (21) ? [v0] : (relation(v0) & function(v0) & empty(v0))
% 54.94/22.69 | (22) epsilon_transitive(all_0_0_0)
% 54.94/22.69 | (23) ? [v0] : empty(v0)
% 54.94/22.69 | (24) ? [v0] : (one_to_one(v0) & relation(v0) & function(v0))
% 54.94/22.69 | (25) relation(all_0_0_0)
% 54.94/22.69 | (26) ? [v0] : (relation(v0) & ~ empty(v0))
% 54.94/22.69 | (27) ? [v0] : ~ empty(v0)
% 54.94/22.69 | (28) ? [v0] : (one_to_one(v0) & relation(v0) & epsilon_connected(v0) & epsilon_transitive(v0) & ordinal(v0) & function(v0) & empty(v0))
% 54.94/22.69 | (29) ! [v0] : ( ~ empty(v0) | relation(v0))
% 54.94/22.69 | (30) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 54.94/22.69 | (31) ? [v0] : (epsilon_connected(v0) & epsilon_transitive(v0) & ordinal(v0))
% 54.94/22.69 | (32) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0))
% 54.94/22.69 | (33) epsilon_connected(all_0_0_0)
% 54.94/22.69 | (34) relation_empty_yielding(all_0_0_0)
% 54.94/22.69 | (35) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 54.94/22.69 | (36) ! [v0] : ? [v1] : element(v1, v0)
% 54.94/22.69 | (37) ! [v0] : ( ~ empty(v0) | function(v0))
% 54.94/22.69 | (38) function(all_0_0_0)
% 54.94/22.69 |
% 54.94/22.69 | Instantiating (9) with all_25_0_12 yields:
% 54.94/22.69 | (39) ! [v0] : ( ~ ordinal(v0) | in(v0, all_25_0_12))
% 54.94/22.69 |
% 54.94/22.69 | Introducing new symbol ex_57_0_15 defined by:
% 54.94/22.69 | (40) ex_57_0_15 = all_25_0_12
% 54.94/22.69 |
% 54.94/22.69 | Instantiating formula (15) with ex_57_0_15 yields:
% 54.94/22.69 | (41) ? [v0] : ( ! [v1] : ( ~ ordinal(v1) | ~ in(v1, ex_57_0_15) | in(v1, v0)) & ! [v1] : ( ~ in(v1, v0) | (ordinal(v1) & in(v1, ex_57_0_15))))
% 54.94/22.69 |
% 54.94/22.69 | Instantiating (41) with all_58_0_16 yields:
% 54.94/22.69 | (42) ! [v0] : ( ~ ordinal(v0) | ~ in(v0, ex_57_0_15) | in(v0, all_58_0_16)) & ! [v0] : ( ~ in(v0, all_58_0_16) | (ordinal(v0) & in(v0, ex_57_0_15)))
% 54.94/22.69 |
% 54.94/22.69 | Applying alpha-rule on (42) yields:
% 54.94/22.69 | (43) ! [v0] : ( ~ ordinal(v0) | ~ in(v0, ex_57_0_15) | in(v0, all_58_0_16))
% 54.94/22.69 | (44) ! [v0] : ( ~ in(v0, all_58_0_16) | (ordinal(v0) & in(v0, ex_57_0_15)))
% 54.94/22.70 |
% 54.94/22.70 | Introducing new symbol ex_153_0_49 defined by:
% 54.94/22.70 | (45) ex_153_0_49 = all_58_0_16
% 54.94/22.70 |
% 54.94/22.70 | Instantiating formula (16) with ex_153_0_49 yields:
% 54.94/22.70 | (46) ? [v0] : (( ~ ordinal(v0) | ~ in(v0, ex_153_0_49)) & (ordinal(v0) | in(v0, ex_153_0_49)))
% 54.94/22.70 |
% 54.94/22.70 | Instantiating (46) with all_154_0_50 yields:
% 54.94/22.70 | (47) ( ~ ordinal(all_154_0_50) | ~ in(all_154_0_50, ex_153_0_49)) & (ordinal(all_154_0_50) | in(all_154_0_50, ex_153_0_49))
% 54.94/22.70 |
% 54.94/22.70 | Applying alpha-rule on (47) yields:
% 54.94/22.70 | (48) ~ ordinal(all_154_0_50) | ~ in(all_154_0_50, ex_153_0_49)
% 54.94/22.70 | (49) ordinal(all_154_0_50) | in(all_154_0_50, ex_153_0_49)
% 54.94/22.70 |
% 54.94/22.70 +-Applying beta-rule and splitting (49), into two cases.
% 54.94/22.70 |-Branch one:
% 54.94/22.70 | (50) ordinal(all_154_0_50)
% 54.94/22.70 |
% 54.94/22.70 +-Applying beta-rule and splitting (48), into two cases.
% 54.94/22.70 |-Branch one:
% 54.94/22.70 | (51) ~ ordinal(all_154_0_50)
% 54.94/22.70 |
% 54.94/22.70 | Using (50) and (51) yields:
% 54.94/22.70 | (52) $false
% 54.94/22.70 |
% 54.94/22.70 |-The branch is then unsatisfiable
% 54.94/22.70 |-Branch two:
% 54.94/22.70 | (53) ~ in(all_154_0_50, ex_153_0_49)
% 54.94/22.70 |
% 54.94/22.70 | Instantiating formula (39) with all_154_0_50 and discharging atoms ordinal(all_154_0_50), yields:
% 54.94/22.70 | (54) in(all_154_0_50, all_25_0_12)
% 54.94/22.70 |
% 54.94/22.70 | Instantiating formula (43) with all_154_0_50 and discharging atoms ordinal(all_154_0_50), yields:
% 54.94/22.70 | (55) ~ in(all_154_0_50, ex_57_0_15) | in(all_154_0_50, all_58_0_16)
% 54.94/22.70 |
% 54.94/22.70 +-Applying beta-rule and splitting (55), into two cases.
% 54.94/22.70 |-Branch one:
% 54.94/22.70 | (56) ~ in(all_154_0_50, ex_57_0_15)
% 54.94/22.70 |
% 54.94/22.70 | From (40) and (56) follows:
% 54.94/22.70 | (57) ~ in(all_154_0_50, all_25_0_12)
% 54.94/22.70 |
% 54.94/22.70 | Using (54) and (57) yields:
% 54.94/22.70 | (52) $false
% 54.94/22.70 |
% 54.94/22.70 |-The branch is then unsatisfiable
% 54.94/22.70 |-Branch two:
% 54.94/22.70 | (59) in(all_154_0_50, all_58_0_16)
% 54.94/22.70 |
% 54.94/22.70 | From (45) and (53) follows:
% 54.94/22.70 | (60) ~ in(all_154_0_50, all_58_0_16)
% 54.94/22.70 |
% 54.94/22.70 | Using (59) and (60) yields:
% 54.94/22.70 | (52) $false
% 54.94/22.70 |
% 54.94/22.70 |-The branch is then unsatisfiable
% 54.94/22.70 |-Branch two:
% 54.94/22.70 | (51) ~ ordinal(all_154_0_50)
% 54.94/22.70 | (63) in(all_154_0_50, ex_153_0_49)
% 54.94/22.70 |
% 54.94/22.70 | Instantiating formula (44) with all_154_0_50 yields:
% 54.94/22.70 | (64) ~ in(all_154_0_50, all_58_0_16) | (ordinal(all_154_0_50) & in(all_154_0_50, ex_57_0_15))
% 54.94/22.70 |
% 54.94/22.70 +-Applying beta-rule and splitting (64), into two cases.
% 54.94/22.70 |-Branch one:
% 54.94/22.70 | (60) ~ in(all_154_0_50, all_58_0_16)
% 54.94/22.70 |
% 54.94/22.70 | From (45) and (63) follows:
% 54.94/22.70 | (59) in(all_154_0_50, all_58_0_16)
% 54.94/22.70 |
% 54.94/22.70 | Using (59) and (60) yields:
% 54.94/22.70 | (52) $false
% 54.94/22.70 |
% 54.94/22.70 |-The branch is then unsatisfiable
% 54.94/22.70 |-Branch two:
% 54.94/22.70 | (68) ordinal(all_154_0_50) & in(all_154_0_50, ex_57_0_15)
% 54.94/22.70 |
% 54.94/22.70 | Applying alpha-rule on (68) yields:
% 54.94/22.70 | (50) ordinal(all_154_0_50)
% 54.94/22.70 | (70) in(all_154_0_50, ex_57_0_15)
% 54.94/22.70 |
% 54.94/22.70 | Using (50) and (51) yields:
% 54.94/22.70 | (52) $false
% 54.94/22.70 |
% 54.94/22.70 |-The branch is then unsatisfiable
% 54.94/22.70 % SZS output end Proof for theBenchmark
% 54.94/22.70
% 54.94/22.70 22093ms
%------------------------------------------------------------------------------