TSTP Solution File: SYN334+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN334+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : Thu Jul 21 05:01:29 EDT 2022
% Result : Theorem 140.64s 104.16s
% Output : Proof 179.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN334+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n027.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 : Mon Jul 11 20:35:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.59 ____ _
% 0.21/0.59 ___ / __ \_____(_)___ ________ __________
% 0.21/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.21/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.21/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.21/0.59
% 0.21/0.59 A Theorem Prover for First-Order Logic
% 0.21/0.60 (ePrincess v.1.0)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2015
% 0.21/0.60 (c) Peter Backeman, 2014-2015
% 0.21/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.21/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.21/0.60 Bug reports to peter@backeman.se
% 0.21/0.60
% 0.21/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.31/0.91 Prover 0: Preprocessing ...
% 1.39/0.96 Prover 0: Warning: ignoring some quantifiers
% 1.39/0.97 Prover 0: Constructing countermodel ...
% 1.67/1.07 Prover 0: gave up
% 1.67/1.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.67/1.09 Prover 1: Preprocessing ...
% 1.67/1.15 Prover 1: Constructing countermodel ...
% 1.67/1.16 Prover 1: gave up
% 1.67/1.16 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.67/1.17 Prover 2: Preprocessing ...
% 2.18/1.22 Prover 2: Warning: ignoring some quantifiers
% 2.30/1.22 Prover 2: Constructing countermodel ...
% 2.30/1.25 Prover 2: gave up
% 2.30/1.25 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.37/1.26 Prover 3: Preprocessing ...
% 2.37/1.27 Prover 3: Warning: ignoring some quantifiers
% 2.37/1.27 Prover 3: Constructing countermodel ...
% 2.37/1.29 Prover 3: gave up
% 2.37/1.29 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.37/1.30 Prover 4: Preprocessing ...
% 2.37/1.33 Prover 4: Warning: ignoring some quantifiers
% 2.63/1.33 Prover 4: Constructing countermodel ...
% 7.96/2.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 7.96/2.61 Prover 5: Preprocessing ...
% 7.96/2.63 Prover 5: Constructing countermodel ...
% 7.96/2.63 Prover 5: gave up
% 7.96/2.63 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 7.96/2.64 Prover 6: Preprocessing ...
% 8.24/2.66 Prover 6: Warning: ignoring some quantifiers
% 8.24/2.67 Prover 6: Constructing countermodel ...
% 8.24/2.67 Prover 6: gave up
% 8.24/2.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 8.24/2.68 Prover 7: Preprocessing ...
% 8.24/2.69 Prover 7: Proving ...
% 29.70/13.14 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 29.70/13.15 Prover 8: Preprocessing ...
% 29.70/13.17 Prover 8: Constructing countermodel ...
% 29.70/13.17 Prover 8: gave up
% 29.70/13.17 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal
% 29.92/13.18 Prover 9: Preprocessing ...
% 29.92/13.18 Prover 9: Proving ...
% 62.52/37.14 Prover 9: stopped
% 63.22/37.35 Prover 10: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 63.22/37.35 Prover 10: Preprocessing ...
% 63.22/37.36 Prover 10: Warning: ignoring some quantifiers
% 63.22/37.36 Prover 10: Constructing countermodel ...
% 63.22/37.37 Prover 10: gave up
% 63.22/37.37 Prover 11: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 63.22/37.37 Prover 11: Preprocessing ...
% 63.22/37.38 Prover 11: Warning: ignoring some quantifiers
% 63.22/37.38 Prover 11: Constructing countermodel ...
% 63.22/37.39 Prover 11: gave up
% 63.22/37.39 Prover 12: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 63.22/37.39 Prover 12: Preprocessing ...
% 63.22/37.41 Prover 12: Constructing countermodel ...
% 63.22/37.41 Prover 12: gave up
% 63.22/37.41 Prover 13: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 63.22/37.41 Prover 13: Preprocessing ...
% 63.22/37.42 Prover 13: Warning: ignoring some quantifiers
% 63.22/37.42 Prover 13: Constructing countermodel ...
% 63.70/37.44 Prover 13: gave up
% 63.70/37.44 Prover 14: Options: -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 63.70/37.45 Prover 14: Preprocessing ...
% 63.70/37.45 Prover 14: Warning: ignoring some quantifiers
% 63.70/37.45 Prover 14: Constructing countermodel ...
% 63.70/37.45 Prover 14: gave up
% 63.70/37.45 Prover 15: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 63.70/37.46 Prover 15: Preprocessing ...
% 63.70/37.47 Prover 15: Constructing countermodel ...
% 63.70/37.47 Prover 15: gave up
% 63.70/37.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 63.70/37.47 Prover 16: Preprocessing ...
% 63.70/37.48 Prover 16: Constructing countermodel ...
% 63.70/37.48 Prover 16: gave up
% 63.70/37.48 Prover 17: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 63.70/37.48 Prover 17: Preprocessing ...
% 63.70/37.48 Prover 17: Warning: ignoring some quantifiers
% 63.70/37.48 Prover 17: Constructing countermodel ...
% 63.70/37.49 Prover 17: gave up
% 63.70/37.49 Prover 18: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 63.70/37.49 Prover 18: Preprocessing ...
% 63.70/37.50 Prover 18: Warning: ignoring some quantifiers
% 63.70/37.50 Prover 18: Constructing countermodel ...
% 63.70/37.50 Prover 18: gave up
% 63.70/37.50 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 63.70/37.50 Prover 19: Preprocessing ...
% 63.70/37.51 Prover 19: Constructing countermodel ...
% 63.70/37.51 Prover 19: gave up
% 134.86/98.98 Prover 4: stopped
% 140.64/104.16 Prover 7: proved (47724ms)
% 140.64/104.16
% 140.64/104.16 % SZS status Theorem for theBenchmark
% 140.64/104.16
% 140.64/104.16 Generating proof ... found it (size 155)
% 179.68/136.58
% 179.68/136.58 % SZS output start Proof for theBenchmark
% 179.68/136.58 Assumed formulas after preprocessing and simplification:
% 179.68/136.58 | (0) ! [v0] : ! [v1] : ? [v2] : (( ~ big_g(v2, v2) | ~ big_g(v0, v1)) & ( ~ big_f(v2, v2) | ~ big_f(v0, v1) | big_g(v2, v2)) & ( ~ big_f(v0, v1) | (( ~ big_g(v1, v2) | big_f(v0, v2)) & ( ~ big_f(v0, v2) | big_g(v1, v2)))) & (big_g(v2, v2) | big_g(v0, v1)) & (big_f(v0, v1) | (big_f(v2, v2) & ~ big_g(v2, v2))))
% 179.68/136.58 | Introducing new symbol ex_0_1_1 defined by:
% 179.68/136.58 | (1) ex_0_1_1 = arbitrary_constant
% 179.68/136.59 |
% 179.68/136.59 | Introducing new symbol ex_0_0_0 defined by:
% 179.68/136.59 | (2) ex_0_0_0 = arbitrary_constant
% 179.68/136.59 |
% 179.68/136.59 | Instantiating formula (0) with ex_0_0_0, ex_0_1_1 yields:
% 179.68/136.59 | (3) ? [v0] : (( ~ big_g(v0, v0) | ~ big_g(ex_0_1_1, ex_0_0_0)) & ( ~ big_f(v0, v0) | ~ big_f(ex_0_1_1, ex_0_0_0) | big_g(v0, v0)) & ( ~ big_f(ex_0_1_1, ex_0_0_0) | (( ~ big_g(ex_0_0_0, v0) | big_f(ex_0_1_1, v0)) & ( ~ big_f(ex_0_1_1, v0) | big_g(ex_0_0_0, v0)))) & (big_g(v0, v0) | big_g(ex_0_1_1, ex_0_0_0)) & (big_f(ex_0_1_1, ex_0_0_0) | (big_f(v0, v0) & ~ big_g(v0, v0))))
% 179.68/136.59 |
% 179.68/136.59 | Instantiating (3) with all_1_0_2 yields:
% 179.68/136.59 | (4) ( ~ big_g(all_1_0_2, all_1_0_2) | ~ big_g(ex_0_1_1, ex_0_0_0)) & ( ~ big_f(all_1_0_2, all_1_0_2) | ~ big_f(ex_0_1_1, ex_0_0_0) | big_g(all_1_0_2, all_1_0_2)) & ( ~ big_f(ex_0_1_1, ex_0_0_0) | (( ~ big_g(ex_0_0_0, all_1_0_2) | big_f(ex_0_1_1, all_1_0_2)) & ( ~ big_f(ex_0_1_1, all_1_0_2) | big_g(ex_0_0_0, all_1_0_2)))) & (big_g(all_1_0_2, all_1_0_2) | big_g(ex_0_1_1, ex_0_0_0)) & (big_f(ex_0_1_1, ex_0_0_0) | (big_f(all_1_0_2, all_1_0_2) & ~ big_g(all_1_0_2, all_1_0_2)))
% 179.68/136.59 |
% 179.68/136.59 | Applying alpha-rule on (4) yields:
% 179.68/136.59 | (5) big_f(ex_0_1_1, ex_0_0_0) | (big_f(all_1_0_2, all_1_0_2) & ~ big_g(all_1_0_2, all_1_0_2))
% 179.68/136.59 | (6) ~ big_g(all_1_0_2, all_1_0_2) | ~ big_g(ex_0_1_1, ex_0_0_0)
% 179.68/136.59 | (7) ~ big_f(all_1_0_2, all_1_0_2) | ~ big_f(ex_0_1_1, ex_0_0_0) | big_g(all_1_0_2, all_1_0_2)
% 179.68/136.59 | (8) ~ big_f(ex_0_1_1, ex_0_0_0) | (( ~ big_g(ex_0_0_0, all_1_0_2) | big_f(ex_0_1_1, all_1_0_2)) & ( ~ big_f(ex_0_1_1, all_1_0_2) | big_g(ex_0_0_0, all_1_0_2)))
% 179.68/136.59 | (9) big_g(all_1_0_2, all_1_0_2) | big_g(ex_0_1_1, ex_0_0_0)
% 179.68/136.59 |
% 179.68/136.59 +-Applying beta-rule and splitting (9), into two cases.
% 179.68/136.59 |-Branch one:
% 179.68/136.59 | (10) big_g(all_1_0_2, all_1_0_2)
% 179.68/136.59 |
% 179.68/136.59 +-Applying beta-rule and splitting (5), into two cases.
% 179.68/136.59 |-Branch one:
% 179.68/136.59 | (11) big_f(ex_0_1_1, ex_0_0_0)
% 179.68/136.59 |
% 179.68/136.59 +-Applying beta-rule and splitting (8), into two cases.
% 179.68/136.59 |-Branch one:
% 179.68/136.59 | (12) ~ big_f(ex_0_1_1, ex_0_0_0)
% 179.68/136.59 |
% 179.68/136.59 | Using (11) and (12) yields:
% 179.68/136.59 | (13) $false
% 179.68/136.59 |
% 179.68/136.59 |-The branch is then unsatisfiable
% 179.68/136.59 |-Branch two:
% 179.68/136.59 | (14) ( ~ big_g(ex_0_0_0, all_1_0_2) | big_f(ex_0_1_1, all_1_0_2)) & ( ~ big_f(ex_0_1_1, all_1_0_2) | big_g(ex_0_0_0, all_1_0_2))
% 179.68/136.59 |
% 179.68/136.59 | Applying alpha-rule on (14) yields:
% 179.68/136.59 | (15) ~ big_g(ex_0_0_0, all_1_0_2) | big_f(ex_0_1_1, all_1_0_2)
% 179.68/136.59 | (16) ~ big_f(ex_0_1_1, all_1_0_2) | big_g(ex_0_0_0, all_1_0_2)
% 179.68/136.59 |
% 179.68/136.59 +-Applying beta-rule and splitting (16), into two cases.
% 179.68/136.59 |-Branch one:
% 179.68/136.59 | (17) big_g(ex_0_0_0, all_1_0_2)
% 179.68/136.59 |
% 179.68/136.59 +-Applying beta-rule and splitting (15), into two cases.
% 179.68/136.59 |-Branch one:
% 179.68/136.59 | (18) ~ big_g(ex_0_0_0, all_1_0_2)
% 179.68/136.59 |
% 179.68/136.59 | Using (17) and (18) yields:
% 179.68/136.59 | (13) $false
% 179.68/136.59 |
% 179.68/136.59 |-The branch is then unsatisfiable
% 179.68/136.59 |-Branch two:
% 179.68/136.59 | (20) big_f(ex_0_1_1, all_1_0_2)
% 179.68/136.59 |
% 179.68/136.59 | Introducing new symbol ex_30_1_4 defined by:
% 179.68/136.59 | (21) ex_30_1_4 = arbitrary_constant
% 179.68/136.59 |
% 179.68/136.59 | Introducing new symbol ex_30_0_3 defined by:
% 179.68/136.59 | (22) ex_30_0_3 = all_1_0_2
% 179.68/136.59 |
% 179.68/136.59 | Instantiating formula (0) with ex_30_0_3, ex_30_1_4 yields:
% 179.68/136.59 | (23) ? [v0] : (( ~ big_g(v0, v0) | ~ big_g(ex_30_1_4, ex_30_0_3)) & ( ~ big_f(v0, v0) | ~ big_f(ex_30_1_4, ex_30_0_3) | big_g(v0, v0)) & ( ~ big_f(ex_30_1_4, ex_30_0_3) | (( ~ big_g(ex_30_0_3, v0) | big_f(ex_30_1_4, v0)) & ( ~ big_f(ex_30_1_4, v0) | big_g(ex_30_0_3, v0)))) & (big_g(v0, v0) | big_g(ex_30_1_4, ex_30_0_3)) & (big_f(ex_30_1_4, ex_30_0_3) | (big_f(v0, v0) & ~ big_g(v0, v0))))
% 179.68/136.59 |
% 179.68/136.59 | Instantiating (23) with all_31_0_5 yields:
% 179.68/136.59 | (24) ( ~ big_g(all_31_0_5, all_31_0_5) | ~ big_g(ex_30_1_4, ex_30_0_3)) & ( ~ big_f(all_31_0_5, all_31_0_5) | ~ big_f(ex_30_1_4, ex_30_0_3) | big_g(all_31_0_5, all_31_0_5)) & ( ~ big_f(ex_30_1_4, ex_30_0_3) | (( ~ big_g(ex_30_0_3, all_31_0_5) | big_f(ex_30_1_4, all_31_0_5)) & ( ~ big_f(ex_30_1_4, all_31_0_5) | big_g(ex_30_0_3, all_31_0_5)))) & (big_g(all_31_0_5, all_31_0_5) | big_g(ex_30_1_4, ex_30_0_3)) & (big_f(ex_30_1_4, ex_30_0_3) | (big_f(all_31_0_5, all_31_0_5) & ~ big_g(all_31_0_5, all_31_0_5)))
% 179.68/136.59 |
% 179.68/136.59 | Applying alpha-rule on (24) yields:
% 179.68/136.59 | (25) ~ big_f(ex_30_1_4, ex_30_0_3) | (( ~ big_g(ex_30_0_3, all_31_0_5) | big_f(ex_30_1_4, all_31_0_5)) & ( ~ big_f(ex_30_1_4, all_31_0_5) | big_g(ex_30_0_3, all_31_0_5)))
% 179.68/136.59 | (26) big_g(all_31_0_5, all_31_0_5) | big_g(ex_30_1_4, ex_30_0_3)
% 179.68/136.59 | (27) ~ big_g(all_31_0_5, all_31_0_5) | ~ big_g(ex_30_1_4, ex_30_0_3)
% 179.68/136.59 | (28) big_f(ex_30_1_4, ex_30_0_3) | (big_f(all_31_0_5, all_31_0_5) & ~ big_g(all_31_0_5, all_31_0_5))
% 179.68/136.59 | (29) ~ big_f(all_31_0_5, all_31_0_5) | ~ big_f(ex_30_1_4, ex_30_0_3) | big_g(all_31_0_5, all_31_0_5)
% 179.68/136.59 |
% 179.68/136.59 +-Applying beta-rule and splitting (26), into two cases.
% 179.68/136.59 |-Branch one:
% 179.68/136.59 | (30) big_g(all_31_0_5, all_31_0_5)
% 179.68/136.59 |
% 179.68/136.59 +-Applying beta-rule and splitting (27), into two cases.
% 179.68/136.59 |-Branch one:
% 179.68/136.59 | (31) ~ big_g(all_31_0_5, all_31_0_5)
% 179.68/136.59 |
% 179.68/136.59 | Using (30) and (31) yields:
% 179.68/136.59 | (13) $false
% 179.68/136.59 |
% 179.68/136.59 |-The branch is then unsatisfiable
% 179.68/136.59 |-Branch two:
% 179.68/136.59 | (33) ~ big_g(ex_30_1_4, ex_30_0_3)
% 179.68/136.59 |
% 179.68/136.59 | From (2) and (17) follows:
% 179.68/136.60 | (34) big_g(arbitrary_constant, all_1_0_2)
% 179.68/136.60 |
% 179.68/136.60 | From (21)(22) and (33) follows:
% 179.68/136.60 | (35) ~ big_g(arbitrary_constant, all_1_0_2)
% 179.68/136.60 |
% 179.68/136.60 | Using (34) and (35) yields:
% 179.68/136.60 | (13) $false
% 179.68/136.60 |
% 179.68/136.60 |-The branch is then unsatisfiable
% 179.68/136.60 |-Branch two:
% 179.68/136.60 | (31) ~ big_g(all_31_0_5, all_31_0_5)
% 179.68/136.60 | (38) big_g(ex_30_1_4, ex_30_0_3)
% 179.68/136.60 |
% 179.68/136.60 +-Applying beta-rule and splitting (29), into two cases.
% 179.68/136.60 |-Branch one:
% 179.68/136.60 | (30) big_g(all_31_0_5, all_31_0_5)
% 179.68/136.60 |
% 179.68/136.60 | Using (30) and (31) yields:
% 179.68/136.60 | (13) $false
% 179.68/136.60 |
% 179.68/136.60 |-The branch is then unsatisfiable
% 179.68/136.60 |-Branch two:
% 179.68/136.60 | (41) ~ big_f(all_31_0_5, all_31_0_5) | ~ big_f(ex_30_1_4, ex_30_0_3)
% 179.68/136.60 |
% 179.68/136.60 +-Applying beta-rule and splitting (28), into two cases.
% 179.68/136.60 |-Branch one:
% 179.68/136.60 | (42) big_f(ex_30_1_4, ex_30_0_3)
% 179.68/136.60 |
% 179.68/136.60 +-Applying beta-rule and splitting (41), into two cases.
% 179.68/136.60 |-Branch one:
% 179.68/136.60 | (43) ~ big_f(all_31_0_5, all_31_0_5)
% 179.68/136.60 |
% 179.68/136.60 | Introducing new symbol ex_70_1_25 defined by:
% 179.68/136.60 | (44) ex_70_1_25 = all_31_0_5
% 179.68/136.60 |
% 179.68/136.60 | Introducing new symbol ex_70_0_24 defined by:
% 179.68/136.60 | (45) ex_70_0_24 = all_31_0_5
% 179.68/136.60 |
% 179.68/136.60 | Instantiating formula (0) with ex_70_0_24, ex_70_1_25 yields:
% 179.68/136.60 | (46) ? [v0] : (( ~ big_g(v0, v0) | ~ big_g(ex_70_1_25, ex_70_0_24)) & ( ~ big_f(v0, v0) | ~ big_f(ex_70_1_25, ex_70_0_24) | big_g(v0, v0)) & ( ~ big_f(ex_70_1_25, ex_70_0_24) | (( ~ big_g(ex_70_0_24, v0) | big_f(ex_70_1_25, v0)) & ( ~ big_f(ex_70_1_25, v0) | big_g(ex_70_0_24, v0)))) & (big_g(v0, v0) | big_g(ex_70_1_25, ex_70_0_24)) & (big_f(ex_70_1_25, ex_70_0_24) | (big_f(v0, v0) & ~ big_g(v0, v0))))
% 179.68/136.60 |
% 179.68/136.60 | Instantiating (46) with all_71_0_26 yields:
% 179.68/136.60 | (47) ( ~ big_g(all_71_0_26, all_71_0_26) | ~ big_g(ex_70_1_25, ex_70_0_24)) & ( ~ big_f(all_71_0_26, all_71_0_26) | ~ big_f(ex_70_1_25, ex_70_0_24) | big_g(all_71_0_26, all_71_0_26)) & ( ~ big_f(ex_70_1_25, ex_70_0_24) | (( ~ big_g(ex_70_0_24, all_71_0_26) | big_f(ex_70_1_25, all_71_0_26)) & ( ~ big_f(ex_70_1_25, all_71_0_26) | big_g(ex_70_0_24, all_71_0_26)))) & (big_g(all_71_0_26, all_71_0_26) | big_g(ex_70_1_25, ex_70_0_24)) & (big_f(ex_70_1_25, ex_70_0_24) | (big_f(all_71_0_26, all_71_0_26) & ~ big_g(all_71_0_26, all_71_0_26)))
% 179.68/136.60 |
% 179.68/136.60 | Applying alpha-rule on (47) yields:
% 179.68/136.60 | (48) ~ big_f(all_71_0_26, all_71_0_26) | ~ big_f(ex_70_1_25, ex_70_0_24) | big_g(all_71_0_26, all_71_0_26)
% 179.68/136.60 | (49) ~ big_g(all_71_0_26, all_71_0_26) | ~ big_g(ex_70_1_25, ex_70_0_24)
% 179.68/136.60 | (50) ~ big_f(ex_70_1_25, ex_70_0_24) | (( ~ big_g(ex_70_0_24, all_71_0_26) | big_f(ex_70_1_25, all_71_0_26)) & ( ~ big_f(ex_70_1_25, all_71_0_26) | big_g(ex_70_0_24, all_71_0_26)))
% 179.68/136.60 | (51) big_f(ex_70_1_25, ex_70_0_24) | (big_f(all_71_0_26, all_71_0_26) & ~ big_g(all_71_0_26, all_71_0_26))
% 179.68/136.60 | (52) big_g(all_71_0_26, all_71_0_26) | big_g(ex_70_1_25, ex_70_0_24)
% 179.68/136.60 |
% 179.68/136.60 +-Applying beta-rule and splitting (52), into two cases.
% 179.68/136.60 |-Branch one:
% 179.68/136.60 | (53) big_g(all_71_0_26, all_71_0_26)
% 179.68/136.60 |
% 179.68/136.60 +-Applying beta-rule and splitting (51), into two cases.
% 179.68/136.60 |-Branch one:
% 179.68/136.60 | (54) big_f(ex_70_1_25, ex_70_0_24)
% 179.68/136.60 |
% 179.68/136.60 | From (44)(45) and (54) follows:
% 179.68/136.60 | (55) big_f(all_31_0_5, all_31_0_5)
% 179.68/136.60 |
% 179.68/136.60 | Using (55) and (43) yields:
% 179.68/136.60 | (13) $false
% 179.68/136.60 |
% 179.68/136.60 |-The branch is then unsatisfiable
% 179.68/136.60 |-Branch two:
% 179.68/136.60 | (57) big_f(all_71_0_26, all_71_0_26) & ~ big_g(all_71_0_26, all_71_0_26)
% 179.68/136.60 |
% 179.68/136.60 | Applying alpha-rule on (57) yields:
% 179.68/136.60 | (58) big_f(all_71_0_26, all_71_0_26)
% 179.68/136.60 | (59) ~ big_g(all_71_0_26, all_71_0_26)
% 179.68/136.60 |
% 179.68/136.60 | Using (53) and (59) yields:
% 179.68/136.60 | (13) $false
% 179.68/136.60 |
% 179.68/136.60 |-The branch is then unsatisfiable
% 179.68/136.60 |-Branch two:
% 179.68/136.60 | (61) big_g(ex_70_1_25, ex_70_0_24)
% 179.68/136.60 |
% 179.68/136.60 | From (44)(45) and (61) follows:
% 179.68/136.60 | (30) big_g(all_31_0_5, all_31_0_5)
% 179.68/136.60 |
% 179.68/136.60 | Using (30) and (31) yields:
% 179.68/136.60 | (13) $false
% 179.68/136.60 |
% 179.68/136.60 |-The branch is then unsatisfiable
% 179.68/136.60 |-Branch two:
% 179.68/136.60 | (64) ~ big_f(ex_30_1_4, ex_30_0_3)
% 179.68/136.60 |
% 179.68/136.60 | Using (42) and (64) yields:
% 179.68/136.60 | (13) $false
% 179.68/136.60 |
% 179.68/136.60 |-The branch is then unsatisfiable
% 179.68/136.60 |-Branch two:
% 179.68/136.60 | (64) ~ big_f(ex_30_1_4, ex_30_0_3)
% 179.68/136.60 | (67) big_f(all_31_0_5, all_31_0_5) & ~ big_g(all_31_0_5, all_31_0_5)
% 179.68/136.60 |
% 179.68/136.60 | From (1) and (20) follows:
% 179.68/136.60 | (68) big_f(arbitrary_constant, all_1_0_2)
% 179.68/136.60 |
% 179.68/136.60 | From (21)(22) and (64) follows:
% 179.68/136.60 | (69) ~ big_f(arbitrary_constant, all_1_0_2)
% 179.68/136.60 |
% 179.68/136.60 | Using (68) and (69) yields:
% 179.68/136.60 | (13) $false
% 179.68/136.60 |
% 179.68/136.60 |-The branch is then unsatisfiable
% 179.68/136.60 |-Branch two:
% 179.68/136.60 | (18) ~ big_g(ex_0_0_0, all_1_0_2)
% 179.68/136.60 | (72) ~ big_f(ex_0_1_1, all_1_0_2)
% 179.68/136.60 |
% 179.68/136.60 | Introducing new symbol ex_30_1_31 defined by:
% 179.68/136.60 | (73) ex_30_1_31 = arbitrary_constant
% 179.68/136.60 |
% 179.68/136.60 | Introducing new symbol ex_30_0_30 defined by:
% 179.68/136.60 | (74) ex_30_0_30 = all_1_0_2
% 179.68/136.60 |
% 179.68/136.60 | Instantiating formula (0) with ex_30_0_30, ex_30_1_31 yields:
% 179.68/136.60 | (75) ? [v0] : (( ~ big_g(v0, v0) | ~ big_g(ex_30_1_31, ex_30_0_30)) & ( ~ big_f(v0, v0) | ~ big_f(ex_30_1_31, ex_30_0_30) | big_g(v0, v0)) & ( ~ big_f(ex_30_1_31, ex_30_0_30) | (( ~ big_g(ex_30_0_30, v0) | big_f(ex_30_1_31, v0)) & ( ~ big_f(ex_30_1_31, v0) | big_g(ex_30_0_30, v0)))) & (big_g(v0, v0) | big_g(ex_30_1_31, ex_30_0_30)) & (big_f(ex_30_1_31, ex_30_0_30) | (big_f(v0, v0) & ~ big_g(v0, v0))))
% 179.80/136.60 |
% 179.80/136.60 | Instantiating (75) with all_31_0_32 yields:
% 179.80/136.60 | (76) ( ~ big_g(all_31_0_32, all_31_0_32) | ~ big_g(ex_30_1_31, ex_30_0_30)) & ( ~ big_f(all_31_0_32, all_31_0_32) | ~ big_f(ex_30_1_31, ex_30_0_30) | big_g(all_31_0_32, all_31_0_32)) & ( ~ big_f(ex_30_1_31, ex_30_0_30) | (( ~ big_g(ex_30_0_30, all_31_0_32) | big_f(ex_30_1_31, all_31_0_32)) & ( ~ big_f(ex_30_1_31, all_31_0_32) | big_g(ex_30_0_30, all_31_0_32)))) & (big_g(all_31_0_32, all_31_0_32) | big_g(ex_30_1_31, ex_30_0_30)) & (big_f(ex_30_1_31, ex_30_0_30) | (big_f(all_31_0_32, all_31_0_32) & ~ big_g(all_31_0_32, all_31_0_32)))
% 179.80/136.60 |
% 179.80/136.60 | Applying alpha-rule on (76) yields:
% 179.80/136.60 | (77) ~ big_g(all_31_0_32, all_31_0_32) | ~ big_g(ex_30_1_31, ex_30_0_30)
% 179.80/136.60 | (78) big_g(all_31_0_32, all_31_0_32) | big_g(ex_30_1_31, ex_30_0_30)
% 179.80/136.60 | (79) ~ big_f(all_31_0_32, all_31_0_32) | ~ big_f(ex_30_1_31, ex_30_0_30) | big_g(all_31_0_32, all_31_0_32)
% 179.80/136.60 | (80) ~ big_f(ex_30_1_31, ex_30_0_30) | (( ~ big_g(ex_30_0_30, all_31_0_32) | big_f(ex_30_1_31, all_31_0_32)) & ( ~ big_f(ex_30_1_31, all_31_0_32) | big_g(ex_30_0_30, all_31_0_32)))
% 179.80/136.60 | (81) big_f(ex_30_1_31, ex_30_0_30) | (big_f(all_31_0_32, all_31_0_32) & ~ big_g(all_31_0_32, all_31_0_32))
% 179.80/136.60 |
% 179.80/136.60 +-Applying beta-rule and splitting (78), into two cases.
% 179.80/136.60 |-Branch one:
% 179.80/136.60 | (82) big_g(all_31_0_32, all_31_0_32)
% 179.80/136.60 |
% 179.80/136.60 +-Applying beta-rule and splitting (81), into two cases.
% 179.80/136.60 |-Branch one:
% 179.80/136.60 | (83) big_f(ex_30_1_31, ex_30_0_30)
% 179.80/136.60 |
% 179.80/136.60 | From (73)(74) and (83) follows:
% 179.80/136.60 | (68) big_f(arbitrary_constant, all_1_0_2)
% 179.80/136.60 |
% 179.80/136.60 | From (1) and (72) follows:
% 179.80/136.60 | (69) ~ big_f(arbitrary_constant, all_1_0_2)
% 179.80/136.60 |
% 179.80/136.60 | Using (68) and (69) yields:
% 179.80/136.60 | (13) $false
% 179.80/136.61 |
% 179.80/136.61 |-The branch is then unsatisfiable
% 179.80/136.61 |-Branch two:
% 179.80/136.61 | (87) big_f(all_31_0_32, all_31_0_32) & ~ big_g(all_31_0_32, all_31_0_32)
% 179.80/136.61 |
% 179.80/136.61 | Applying alpha-rule on (87) yields:
% 179.80/136.61 | (88) big_f(all_31_0_32, all_31_0_32)
% 179.80/136.61 | (89) ~ big_g(all_31_0_32, all_31_0_32)
% 179.80/136.61 |
% 179.80/136.61 | Using (82) and (89) yields:
% 179.80/136.61 | (13) $false
% 179.80/136.61 |
% 179.80/136.61 |-The branch is then unsatisfiable
% 179.80/136.61 |-Branch two:
% 179.80/136.61 | (91) big_g(ex_30_1_31, ex_30_0_30)
% 179.80/136.61 |
% 179.80/136.61 | From (73)(74) and (91) follows:
% 179.80/136.61 | (34) big_g(arbitrary_constant, all_1_0_2)
% 179.80/136.61 |
% 179.80/136.61 | From (2) and (18) follows:
% 179.80/136.61 | (35) ~ big_g(arbitrary_constant, all_1_0_2)
% 179.80/136.61 |
% 179.80/136.61 | Using (34) and (35) yields:
% 179.80/136.61 | (13) $false
% 179.80/136.61 |
% 179.80/136.61 |-The branch is then unsatisfiable
% 179.80/136.61 |-Branch two:
% 179.80/136.61 | (95) big_f(all_1_0_2, all_1_0_2) & ~ big_g(all_1_0_2, all_1_0_2)
% 179.80/136.61 |
% 179.80/136.61 | Applying alpha-rule on (95) yields:
% 179.80/136.61 | (96) big_f(all_1_0_2, all_1_0_2)
% 179.80/136.61 | (97) ~ big_g(all_1_0_2, all_1_0_2)
% 179.80/136.61 |
% 179.80/136.61 | Using (10) and (97) yields:
% 179.80/136.61 | (13) $false
% 179.80/136.61 |
% 179.80/136.61 |-The branch is then unsatisfiable
% 179.80/136.61 |-Branch two:
% 179.80/136.61 | (97) ~ big_g(all_1_0_2, all_1_0_2)
% 179.80/136.61 | (100) big_g(ex_0_1_1, ex_0_0_0)
% 179.80/136.61 |
% 179.80/136.61 | Introducing new symbol ex_28_1_40 defined by:
% 179.80/136.61 | (101) ex_28_1_40 = all_1_0_2
% 179.80/136.61 |
% 179.80/136.61 | Introducing new symbol ex_28_0_39 defined by:
% 179.80/136.61 | (102) ex_28_0_39 = all_1_0_2
% 179.80/136.61 |
% 179.80/136.61 | Instantiating formula (0) with ex_28_0_39, ex_28_1_40 yields:
% 179.80/136.61 | (103) ? [v0] : (( ~ big_g(v0, v0) | ~ big_g(ex_28_1_40, ex_28_0_39)) & ( ~ big_f(v0, v0) | ~ big_f(ex_28_1_40, ex_28_0_39) | big_g(v0, v0)) & ( ~ big_f(ex_28_1_40, ex_28_0_39) | (( ~ big_g(ex_28_0_39, v0) | big_f(ex_28_1_40, v0)) & ( ~ big_f(ex_28_1_40, v0) | big_g(ex_28_0_39, v0)))) & (big_g(v0, v0) | big_g(ex_28_1_40, ex_28_0_39)) & (big_f(ex_28_1_40, ex_28_0_39) | (big_f(v0, v0) & ~ big_g(v0, v0))))
% 179.80/136.61 |
% 179.80/136.61 | Instantiating (103) with all_29_0_41 yields:
% 179.80/136.61 | (104) ( ~ big_g(all_29_0_41, all_29_0_41) | ~ big_g(ex_28_1_40, ex_28_0_39)) & ( ~ big_f(all_29_0_41, all_29_0_41) | ~ big_f(ex_28_1_40, ex_28_0_39) | big_g(all_29_0_41, all_29_0_41)) & ( ~ big_f(ex_28_1_40, ex_28_0_39) | (( ~ big_g(ex_28_0_39, all_29_0_41) | big_f(ex_28_1_40, all_29_0_41)) & ( ~ big_f(ex_28_1_40, all_29_0_41) | big_g(ex_28_0_39, all_29_0_41)))) & (big_g(all_29_0_41, all_29_0_41) | big_g(ex_28_1_40, ex_28_0_39)) & (big_f(ex_28_1_40, ex_28_0_39) | (big_f(all_29_0_41, all_29_0_41) & ~ big_g(all_29_0_41, all_29_0_41)))
% 179.80/136.61 |
% 179.80/136.61 | Applying alpha-rule on (104) yields:
% 179.80/136.61 | (105) big_g(all_29_0_41, all_29_0_41) | big_g(ex_28_1_40, ex_28_0_39)
% 179.80/136.61 | (106) big_f(ex_28_1_40, ex_28_0_39) | (big_f(all_29_0_41, all_29_0_41) & ~ big_g(all_29_0_41, all_29_0_41))
% 179.80/136.61 | (107) ~ big_g(all_29_0_41, all_29_0_41) | ~ big_g(ex_28_1_40, ex_28_0_39)
% 179.80/136.61 | (108) ~ big_f(ex_28_1_40, ex_28_0_39) | (( ~ big_g(ex_28_0_39, all_29_0_41) | big_f(ex_28_1_40, all_29_0_41)) & ( ~ big_f(ex_28_1_40, all_29_0_41) | big_g(ex_28_0_39, all_29_0_41)))
% 179.80/136.61 | (109) ~ big_f(all_29_0_41, all_29_0_41) | ~ big_f(ex_28_1_40, ex_28_0_39) | big_g(all_29_0_41, all_29_0_41)
% 179.80/136.61 |
% 179.80/136.61 +-Applying beta-rule and splitting (105), into two cases.
% 179.80/136.61 |-Branch one:
% 179.80/136.61 | (110) big_g(all_29_0_41, all_29_0_41)
% 179.80/136.61 |
% 179.80/136.61 +-Applying beta-rule and splitting (106), into two cases.
% 179.80/136.61 |-Branch one:
% 179.80/136.61 | (111) big_f(ex_28_1_40, ex_28_0_39)
% 179.80/136.61 |
% 179.80/136.61 +-Applying beta-rule and splitting (108), into two cases.
% 179.80/136.61 |-Branch one:
% 179.80/136.61 | (112) ~ big_f(ex_28_1_40, ex_28_0_39)
% 179.80/136.61 |
% 179.80/136.61 | Using (111) and (112) yields:
% 179.80/136.61 | (13) $false
% 179.80/136.61 |
% 179.80/136.61 |-The branch is then unsatisfiable
% 179.80/136.61 |-Branch two:
% 179.80/136.61 | (114) ( ~ big_g(ex_28_0_39, all_29_0_41) | big_f(ex_28_1_40, all_29_0_41)) & ( ~ big_f(ex_28_1_40, all_29_0_41) | big_g(ex_28_0_39, all_29_0_41))
% 179.80/136.61 |
% 179.80/136.61 | Applying alpha-rule on (114) yields:
% 179.80/136.61 | (115) ~ big_g(ex_28_0_39, all_29_0_41) | big_f(ex_28_1_40, all_29_0_41)
% 179.80/136.61 | (116) ~ big_f(ex_28_1_40, all_29_0_41) | big_g(ex_28_0_39, all_29_0_41)
% 179.80/136.61 |
% 179.80/136.61 +-Applying beta-rule and splitting (116), into two cases.
% 179.80/136.61 |-Branch one:
% 179.80/136.61 | (117) big_g(ex_28_0_39, all_29_0_41)
% 179.80/136.61 |
% 179.80/136.61 +-Applying beta-rule and splitting (115), into two cases.
% 179.80/136.61 |-Branch one:
% 179.80/136.61 | (118) ~ big_g(ex_28_0_39, all_29_0_41)
% 179.80/136.61 |
% 179.80/136.61 | Using (117) and (118) yields:
% 179.80/136.61 | (13) $false
% 179.80/136.61 |
% 179.80/136.61 |-The branch is then unsatisfiable
% 179.80/136.61 |-Branch two:
% 179.80/136.61 | (120) big_f(ex_28_1_40, all_29_0_41)
% 179.80/136.61 |
% 179.80/136.61 | Introducing new symbol ex_58_1_49 defined by:
% 179.80/136.61 | (121) ex_58_1_49 = all_1_0_2
% 179.80/136.61 |
% 179.80/136.61 | Introducing new symbol ex_58_0_48 defined by:
% 179.80/136.61 | (122) ex_58_0_48 = all_29_0_41
% 179.80/136.61 |
% 179.80/136.61 | Instantiating formula (0) with ex_58_0_48, ex_58_1_49 yields:
% 179.80/136.61 | (123) ? [v0] : (( ~ big_g(v0, v0) | ~ big_g(ex_58_1_49, ex_58_0_48)) & ( ~ big_f(v0, v0) | ~ big_f(ex_58_1_49, ex_58_0_48) | big_g(v0, v0)) & ( ~ big_f(ex_58_1_49, ex_58_0_48) | (( ~ big_g(ex_58_0_48, v0) | big_f(ex_58_1_49, v0)) & ( ~ big_f(ex_58_1_49, v0) | big_g(ex_58_0_48, v0)))) & (big_g(v0, v0) | big_g(ex_58_1_49, ex_58_0_48)) & (big_f(ex_58_1_49, ex_58_0_48) | (big_f(v0, v0) & ~ big_g(v0, v0))))
% 179.80/136.61 |
% 179.80/136.61 | Instantiating (123) with all_59_0_50 yields:
% 179.80/136.61 | (124) ( ~ big_g(all_59_0_50, all_59_0_50) | ~ big_g(ex_58_1_49, ex_58_0_48)) & ( ~ big_f(all_59_0_50, all_59_0_50) | ~ big_f(ex_58_1_49, ex_58_0_48) | big_g(all_59_0_50, all_59_0_50)) & ( ~ big_f(ex_58_1_49, ex_58_0_48) | (( ~ big_g(ex_58_0_48, all_59_0_50) | big_f(ex_58_1_49, all_59_0_50)) & ( ~ big_f(ex_58_1_49, all_59_0_50) | big_g(ex_58_0_48, all_59_0_50)))) & (big_g(all_59_0_50, all_59_0_50) | big_g(ex_58_1_49, ex_58_0_48)) & (big_f(ex_58_1_49, ex_58_0_48) | (big_f(all_59_0_50, all_59_0_50) & ~ big_g(all_59_0_50, all_59_0_50)))
% 179.80/136.61 |
% 179.80/136.61 | Applying alpha-rule on (124) yields:
% 179.80/136.61 | (125) ~ big_f(all_59_0_50, all_59_0_50) | ~ big_f(ex_58_1_49, ex_58_0_48) | big_g(all_59_0_50, all_59_0_50)
% 179.80/136.61 | (126) big_g(all_59_0_50, all_59_0_50) | big_g(ex_58_1_49, ex_58_0_48)
% 179.80/136.61 | (127) ~ big_g(all_59_0_50, all_59_0_50) | ~ big_g(ex_58_1_49, ex_58_0_48)
% 179.80/136.61 | (128) big_f(ex_58_1_49, ex_58_0_48) | (big_f(all_59_0_50, all_59_0_50) & ~ big_g(all_59_0_50, all_59_0_50))
% 179.80/136.61 | (129) ~ big_f(ex_58_1_49, ex_58_0_48) | (( ~ big_g(ex_58_0_48, all_59_0_50) | big_f(ex_58_1_49, all_59_0_50)) & ( ~ big_f(ex_58_1_49, all_59_0_50) | big_g(ex_58_0_48, all_59_0_50)))
% 179.80/136.61 |
% 179.80/136.61 +-Applying beta-rule and splitting (126), into two cases.
% 179.80/136.61 |-Branch one:
% 179.80/136.61 | (130) big_g(all_59_0_50, all_59_0_50)
% 179.80/136.61 |
% 179.80/136.61 +-Applying beta-rule and splitting (127), into two cases.
% 179.80/136.61 |-Branch one:
% 179.80/136.61 | (131) ~ big_g(all_59_0_50, all_59_0_50)
% 179.80/136.61 |
% 179.80/136.61 | Using (130) and (131) yields:
% 179.80/136.61 | (13) $false
% 179.80/136.62 |
% 179.80/136.62 |-The branch is then unsatisfiable
% 179.80/136.62 |-Branch two:
% 179.80/136.62 | (133) ~ big_g(ex_58_1_49, ex_58_0_48)
% 179.80/136.62 |
% 179.80/136.62 | From (102) and (117) follows:
% 179.80/136.62 | (134) big_g(all_1_0_2, all_29_0_41)
% 179.80/136.62 |
% 179.80/136.62 | From (121)(122) and (133) follows:
% 179.80/136.62 | (135) ~ big_g(all_1_0_2, all_29_0_41)
% 179.80/136.62 |
% 179.80/136.62 | Using (134) and (135) yields:
% 179.80/136.62 | (13) $false
% 179.80/136.62 |
% 179.80/136.62 |-The branch is then unsatisfiable
% 179.80/136.62 |-Branch two:
% 179.80/136.62 | (131) ~ big_g(all_59_0_50, all_59_0_50)
% 179.80/136.62 | (138) big_g(ex_58_1_49, ex_58_0_48)
% 179.80/136.62 |
% 179.80/136.62 +-Applying beta-rule and splitting (125), into two cases.
% 179.80/136.62 |-Branch one:
% 179.80/136.62 | (130) big_g(all_59_0_50, all_59_0_50)
% 179.80/136.62 |
% 179.80/136.62 | Using (130) and (131) yields:
% 179.80/136.62 | (13) $false
% 179.80/136.62 |
% 179.80/136.62 |-The branch is then unsatisfiable
% 179.80/136.62 |-Branch two:
% 179.80/136.62 | (141) ~ big_f(all_59_0_50, all_59_0_50) | ~ big_f(ex_58_1_49, ex_58_0_48)
% 179.80/136.62 |
% 179.80/136.62 +-Applying beta-rule and splitting (128), into two cases.
% 179.80/136.62 |-Branch one:
% 179.80/136.62 | (142) big_f(ex_58_1_49, ex_58_0_48)
% 179.80/136.62 |
% 179.80/136.62 +-Applying beta-rule and splitting (141), into two cases.
% 179.80/136.62 |-Branch one:
% 179.80/136.62 | (143) ~ big_f(all_59_0_50, all_59_0_50)
% 179.80/136.62 |
% 179.80/136.62 | Introducing new symbol ex_98_1_100 defined by:
% 179.80/136.62 | (144) ex_98_1_100 = all_59_0_50
% 179.80/136.62 |
% 179.80/136.62 | Introducing new symbol ex_98_0_99 defined by:
% 179.80/136.62 | (145) ex_98_0_99 = all_59_0_50
% 179.80/136.62 |
% 179.80/136.62 | Instantiating formula (0) with ex_98_0_99, ex_98_1_100 yields:
% 179.80/136.62 | (146) ? [v0] : (( ~ big_g(v0, v0) | ~ big_g(ex_98_1_100, ex_98_0_99)) & ( ~ big_f(v0, v0) | ~ big_f(ex_98_1_100, ex_98_0_99) | big_g(v0, v0)) & ( ~ big_f(ex_98_1_100, ex_98_0_99) | (( ~ big_g(ex_98_0_99, v0) | big_f(ex_98_1_100, v0)) & ( ~ big_f(ex_98_1_100, v0) | big_g(ex_98_0_99, v0)))) & (big_g(v0, v0) | big_g(ex_98_1_100, ex_98_0_99)) & (big_f(ex_98_1_100, ex_98_0_99) | (big_f(v0, v0) & ~ big_g(v0, v0))))
% 179.80/136.62 |
% 179.80/136.62 | Instantiating (146) with all_99_0_101 yields:
% 179.80/136.62 | (147) ( ~ big_g(all_99_0_101, all_99_0_101) | ~ big_g(ex_98_1_100, ex_98_0_99)) & ( ~ big_f(all_99_0_101, all_99_0_101) | ~ big_f(ex_98_1_100, ex_98_0_99) | big_g(all_99_0_101, all_99_0_101)) & ( ~ big_f(ex_98_1_100, ex_98_0_99) | (( ~ big_g(ex_98_0_99, all_99_0_101) | big_f(ex_98_1_100, all_99_0_101)) & ( ~ big_f(ex_98_1_100, all_99_0_101) | big_g(ex_98_0_99, all_99_0_101)))) & (big_g(all_99_0_101, all_99_0_101) | big_g(ex_98_1_100, ex_98_0_99)) & (big_f(ex_98_1_100, ex_98_0_99) | (big_f(all_99_0_101, all_99_0_101) & ~ big_g(all_99_0_101, all_99_0_101)))
% 179.80/136.62 |
% 179.80/136.62 | Applying alpha-rule on (147) yields:
% 179.80/136.62 | (148) big_g(all_99_0_101, all_99_0_101) | big_g(ex_98_1_100, ex_98_0_99)
% 179.80/136.62 | (149) ~ big_f(ex_98_1_100, ex_98_0_99) | (( ~ big_g(ex_98_0_99, all_99_0_101) | big_f(ex_98_1_100, all_99_0_101)) & ( ~ big_f(ex_98_1_100, all_99_0_101) | big_g(ex_98_0_99, all_99_0_101)))
% 179.80/136.62 | (150) ~ big_g(all_99_0_101, all_99_0_101) | ~ big_g(ex_98_1_100, ex_98_0_99)
% 179.80/136.62 | (151) ~ big_f(all_99_0_101, all_99_0_101) | ~ big_f(ex_98_1_100, ex_98_0_99) | big_g(all_99_0_101, all_99_0_101)
% 179.80/136.62 | (152) big_f(ex_98_1_100, ex_98_0_99) | (big_f(all_99_0_101, all_99_0_101) & ~ big_g(all_99_0_101, all_99_0_101))
% 179.80/136.62 |
% 179.80/136.62 +-Applying beta-rule and splitting (148), into two cases.
% 179.80/136.62 |-Branch one:
% 179.80/136.62 | (153) big_g(all_99_0_101, all_99_0_101)
% 179.80/136.62 |
% 179.80/136.62 +-Applying beta-rule and splitting (152), into two cases.
% 179.80/136.62 |-Branch one:
% 179.80/136.62 | (154) big_f(ex_98_1_100, ex_98_0_99)
% 179.80/136.62 |
% 179.80/136.62 | From (144)(145) and (154) follows:
% 179.80/136.62 | (155) big_f(all_59_0_50, all_59_0_50)
% 179.80/136.62 |
% 179.80/136.62 | Using (155) and (143) yields:
% 179.80/136.62 | (13) $false
% 179.80/136.62 |
% 179.80/136.62 |-The branch is then unsatisfiable
% 179.80/136.62 |-Branch two:
% 179.80/136.62 | (157) big_f(all_99_0_101, all_99_0_101) & ~ big_g(all_99_0_101, all_99_0_101)
% 179.80/136.62 |
% 179.80/136.62 | Applying alpha-rule on (157) yields:
% 179.80/136.62 | (158) big_f(all_99_0_101, all_99_0_101)
% 179.80/136.62 | (159) ~ big_g(all_99_0_101, all_99_0_101)
% 179.80/136.62 |
% 179.80/136.62 | Using (153) and (159) yields:
% 179.80/136.62 | (13) $false
% 179.80/136.62 |
% 179.80/136.62 |-The branch is then unsatisfiable
% 179.80/136.62 |-Branch two:
% 179.80/136.62 | (161) big_g(ex_98_1_100, ex_98_0_99)
% 179.80/136.62 |
% 179.80/136.62 | From (144)(145) and (161) follows:
% 179.80/136.62 | (130) big_g(all_59_0_50, all_59_0_50)
% 179.80/136.62 |
% 179.80/136.62 | Using (130) and (131) yields:
% 179.80/136.62 | (13) $false
% 179.80/136.62 |
% 179.80/136.62 |-The branch is then unsatisfiable
% 179.80/136.62 |-Branch two:
% 179.80/136.62 | (164) ~ big_f(ex_58_1_49, ex_58_0_48)
% 179.80/136.62 |
% 179.80/136.62 | Using (142) and (164) yields:
% 179.80/136.62 | (13) $false
% 179.80/136.62 |
% 179.80/136.62 |-The branch is then unsatisfiable
% 179.80/136.62 |-Branch two:
% 179.80/136.62 | (164) ~ big_f(ex_58_1_49, ex_58_0_48)
% 179.80/136.62 | (167) big_f(all_59_0_50, all_59_0_50) & ~ big_g(all_59_0_50, all_59_0_50)
% 179.80/136.62 |
% 179.80/136.62 | From (101) and (120) follows:
% 179.80/136.62 | (168) big_f(all_1_0_2, all_29_0_41)
% 179.80/136.62 |
% 179.80/136.62 | From (121)(122) and (164) follows:
% 179.80/136.62 | (169) ~ big_f(all_1_0_2, all_29_0_41)
% 179.80/136.62 |
% 179.80/136.62 | Using (168) and (169) yields:
% 179.80/136.62 | (13) $false
% 179.80/136.62 |
% 179.80/136.62 |-The branch is then unsatisfiable
% 179.80/136.62 |-Branch two:
% 179.80/136.62 | (118) ~ big_g(ex_28_0_39, all_29_0_41)
% 179.80/136.62 | (172) ~ big_f(ex_28_1_40, all_29_0_41)
% 179.80/136.62 |
% 179.80/136.62 | Introducing new symbol ex_58_1_43 defined by:
% 179.90/136.62 | (173) ex_58_1_43 = all_1_0_2
% 179.90/136.62 |
% 179.90/136.62 | Introducing new symbol ex_58_0_42 defined by:
% 179.90/136.62 | (174) ex_58_0_42 = all_29_0_41
% 179.90/136.62 |
% 179.90/136.62 | Instantiating formula (0) with ex_58_0_42, ex_58_1_43 yields:
% 179.90/136.62 | (175) ? [v0] : (( ~ big_g(v0, v0) | ~ big_g(ex_58_1_43, ex_58_0_42)) & ( ~ big_f(v0, v0) | ~ big_f(ex_58_1_43, ex_58_0_42) | big_g(v0, v0)) & ( ~ big_f(ex_58_1_43, ex_58_0_42) | (( ~ big_g(ex_58_0_42, v0) | big_f(ex_58_1_43, v0)) & ( ~ big_f(ex_58_1_43, v0) | big_g(ex_58_0_42, v0)))) & (big_g(v0, v0) | big_g(ex_58_1_43, ex_58_0_42)) & (big_f(ex_58_1_43, ex_58_0_42) | (big_f(v0, v0) & ~ big_g(v0, v0))))
% 179.90/136.62 |
% 179.90/136.62 | Instantiating (175) with all_59_0_44 yields:
% 179.90/136.62 | (176) ( ~ big_g(all_59_0_44, all_59_0_44) | ~ big_g(ex_58_1_43, ex_58_0_42)) & ( ~ big_f(all_59_0_44, all_59_0_44) | ~ big_f(ex_58_1_43, ex_58_0_42) | big_g(all_59_0_44, all_59_0_44)) & ( ~ big_f(ex_58_1_43, ex_58_0_42) | (( ~ big_g(ex_58_0_42, all_59_0_44) | big_f(ex_58_1_43, all_59_0_44)) & ( ~ big_f(ex_58_1_43, all_59_0_44) | big_g(ex_58_0_42, all_59_0_44)))) & (big_g(all_59_0_44, all_59_0_44) | big_g(ex_58_1_43, ex_58_0_42)) & (big_f(ex_58_1_43, ex_58_0_42) | (big_f(all_59_0_44, all_59_0_44) & ~ big_g(all_59_0_44, all_59_0_44)))
% 179.90/136.63 |
% 179.90/136.63 | Applying alpha-rule on (176) yields:
% 179.90/136.63 | (177) ~ big_g(all_59_0_44, all_59_0_44) | ~ big_g(ex_58_1_43, ex_58_0_42)
% 179.90/136.63 | (178) big_f(ex_58_1_43, ex_58_0_42) | (big_f(all_59_0_44, all_59_0_44) & ~ big_g(all_59_0_44, all_59_0_44))
% 179.90/136.63 | (179) ~ big_f(all_59_0_44, all_59_0_44) | ~ big_f(ex_58_1_43, ex_58_0_42) | big_g(all_59_0_44, all_59_0_44)
% 179.90/136.63 | (180) ~ big_f(ex_58_1_43, ex_58_0_42) | (( ~ big_g(ex_58_0_42, all_59_0_44) | big_f(ex_58_1_43, all_59_0_44)) & ( ~ big_f(ex_58_1_43, all_59_0_44) | big_g(ex_58_0_42, all_59_0_44)))
% 179.90/136.63 | (181) big_g(all_59_0_44, all_59_0_44) | big_g(ex_58_1_43, ex_58_0_42)
% 179.90/136.63 |
% 179.90/136.63 +-Applying beta-rule and splitting (181), into two cases.
% 179.90/136.63 |-Branch one:
% 179.90/136.63 | (182) big_g(all_59_0_44, all_59_0_44)
% 179.90/136.63 |
% 179.90/136.63 +-Applying beta-rule and splitting (178), into two cases.
% 179.90/136.63 |-Branch one:
% 179.90/136.63 | (183) big_f(ex_58_1_43, ex_58_0_42)
% 179.90/136.63 |
% 179.90/136.63 | From (173)(174) and (183) follows:
% 179.90/136.63 | (168) big_f(all_1_0_2, all_29_0_41)
% 179.90/136.63 |
% 179.90/136.63 | From (101) and (172) follows:
% 179.90/136.63 | (169) ~ big_f(all_1_0_2, all_29_0_41)
% 179.90/136.63 |
% 179.90/136.63 | Using (168) and (169) yields:
% 179.90/136.63 | (13) $false
% 179.90/136.63 |
% 179.90/136.63 |-The branch is then unsatisfiable
% 179.90/136.63 |-Branch two:
% 179.90/136.63 | (187) big_f(all_59_0_44, all_59_0_44) & ~ big_g(all_59_0_44, all_59_0_44)
% 179.90/136.63 |
% 179.90/136.63 | Applying alpha-rule on (187) yields:
% 179.90/136.63 | (188) big_f(all_59_0_44, all_59_0_44)
% 179.90/136.63 | (189) ~ big_g(all_59_0_44, all_59_0_44)
% 179.90/136.63 |
% 179.90/136.63 | Using (182) and (189) yields:
% 179.90/136.63 | (13) $false
% 179.90/136.63 |
% 179.90/136.63 |-The branch is then unsatisfiable
% 179.90/136.63 |-Branch two:
% 179.90/136.63 | (191) big_g(ex_58_1_43, ex_58_0_42)
% 179.90/136.63 |
% 179.90/136.63 | From (173)(174) and (191) follows:
% 179.90/136.63 | (134) big_g(all_1_0_2, all_29_0_41)
% 179.90/136.63 |
% 179.90/136.63 | From (102) and (118) follows:
% 179.90/136.63 | (135) ~ big_g(all_1_0_2, all_29_0_41)
% 179.90/136.63 |
% 179.90/136.63 | Using (134) and (135) yields:
% 179.90/136.63 | (13) $false
% 179.90/136.63 |
% 179.90/136.63 |-The branch is then unsatisfiable
% 179.90/136.63 |-Branch two:
% 179.90/136.63 | (195) big_f(all_29_0_41, all_29_0_41) & ~ big_g(all_29_0_41, all_29_0_41)
% 179.90/136.63 |
% 179.90/136.63 | Applying alpha-rule on (195) yields:
% 179.90/136.63 | (196) big_f(all_29_0_41, all_29_0_41)
% 179.90/136.63 | (197) ~ big_g(all_29_0_41, all_29_0_41)
% 179.90/136.63 |
% 179.90/136.63 | Using (110) and (197) yields:
% 179.90/136.63 | (13) $false
% 179.90/136.63 |
% 179.90/136.63 |-The branch is then unsatisfiable
% 179.90/136.63 |-Branch two:
% 179.90/136.63 | (199) big_g(ex_28_1_40, ex_28_0_39)
% 179.90/136.63 |
% 179.90/136.63 | From (101)(102) and (199) follows:
% 179.90/136.63 | (10) big_g(all_1_0_2, all_1_0_2)
% 179.90/136.63 |
% 179.90/136.63 | Using (10) and (97) yields:
% 179.90/136.63 | (13) $false
% 179.90/136.63 |
% 179.90/136.63 |-The branch is then unsatisfiable
% 179.90/136.63 % SZS output end Proof for theBenchmark
% 179.90/136.63
% 179.90/136.63 136024ms
%------------------------------------------------------------------------------