TSTP Solution File: SYN345+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN345+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 05:01:37 EDT 2022
% Result : Theorem 7.26s 2.64s
% Output : Proof 9.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN345+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.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 : Mon Jul 11 18:47:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/0.59 ____ _
% 0.60/0.59 ___ / __ \_____(_)___ ________ __________
% 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.59
% 0.60/0.59 A Theorem Prover for First-Order Logic
% 0.60/0.59 (ePrincess v.1.0)
% 0.60/0.59
% 0.60/0.59 (c) Philipp Rümmer, 2009-2015
% 0.60/0.59 (c) Peter Backeman, 2014-2015
% 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.59 Bug reports to peter@backeman.se
% 0.60/0.59
% 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.59
% 0.60/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.38/0.91 Prover 0: Preprocessing ...
% 1.41/0.96 Prover 0: Warning: ignoring some quantifiers
% 1.41/0.98 Prover 0: Constructing countermodel ...
% 1.59/1.07 Prover 0: gave up
% 1.59/1.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.80/1.10 Prover 1: Preprocessing ...
% 1.80/1.15 Prover 1: Constructing countermodel ...
% 2.31/1.22 Prover 1: gave up
% 2.31/1.22 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.31/1.23 Prover 2: Preprocessing ...
% 2.31/1.26 Prover 2: Warning: ignoring some quantifiers
% 2.31/1.26 Prover 2: Constructing countermodel ...
% 2.31/1.30 Prover 2: gave up
% 2.31/1.30 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.60/1.31 Prover 3: Preprocessing ...
% 2.60/1.31 Prover 3: Warning: ignoring some quantifiers
% 2.60/1.31 Prover 3: Constructing countermodel ...
% 2.60/1.33 Prover 3: gave up
% 2.60/1.33 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.60/1.34 Prover 4: Preprocessing ...
% 2.60/1.37 Prover 4: Warning: ignoring some quantifiers
% 2.60/1.37 Prover 4: Constructing countermodel ...
% 3.48/1.53 Prover 4: gave up
% 3.48/1.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.48/1.54 Prover 5: Preprocessing ...
% 3.48/1.55 Prover 5: Constructing countermodel ...
% 3.48/1.58 Prover 5: gave up
% 3.48/1.58 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.48/1.59 Prover 6: Preprocessing ...
% 3.48/1.60 Prover 6: Warning: ignoring some quantifiers
% 3.48/1.60 Prover 6: Constructing countermodel ...
% 3.48/1.62 Prover 6: gave up
% 3.48/1.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.48/1.62 Prover 7: Preprocessing ...
% 3.96/1.63 Prover 7: Proving ...
% 7.26/2.64 Prover 7: proved (1007ms)
% 7.26/2.64
% 7.26/2.64 % SZS status Theorem for theBenchmark
% 7.26/2.64
% 7.26/2.64 Generating proof ... found it (size 98)
% 9.90/3.65
% 9.90/3.65 % SZS output start Proof for theBenchmark
% 9.90/3.65 Assumed formulas after preprocessing and simplification:
% 9.90/3.65 | (0) ? [v0] : ? [v1] : ! [v2] : ! [v3] : ? [v4] : (big_f(v2, v3, v4) & ( ~ big_f(v1, v1, v2) | (( ~ big_f(v0, v1, v1) | ~ big_f(v0, v0, v1)) & (big_f(v0, v1, v1) | big_f(v0, v0, v1)))) & ( ~ big_f(v0, v1, v1) | big_f(v0, v0, v1) | (big_f(v1, v2, v3) & ~ big_f(v2, v4, v4))) & ( ~ big_f(v0, v0, v1) | big_f(v0, v1, v1) | (big_f(v0, v1, v2) & ~ big_f(v3, v2, v4))))
% 9.90/3.65 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 9.90/3.65 | (1) ! [v0] : ! [v1] : ? [v2] : (big_f(v0, v1, v2) & ( ~ big_f(all_0_0_0, all_0_0_0, v0) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))) & ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, v0, v1) & ~ big_f(v0, v2, v2))) & ( ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, v0) & ~ big_f(v1, v0, v2))))
% 9.90/3.65 |
% 9.90/3.65 | Introducing new symbol ex_2_1_3 defined by:
% 9.90/3.65 | (2) ex_2_1_3 = all_0_0_0
% 9.90/3.65 |
% 9.90/3.65 | Introducing new symbol ex_2_0_2 defined by:
% 9.90/3.65 | (3) ex_2_0_2 = all_0_0_0
% 9.90/3.65 |
% 9.90/3.65 | Instantiating formula (1) with ex_2_0_2, ex_2_1_3 yields:
% 9.90/3.65 | (4) ? [v0] : (big_f(ex_2_1_3, ex_2_0_2, v0) & ( ~ big_f(all_0_0_0, all_0_0_0, ex_2_1_3) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))) & ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_2_1_3, ex_2_0_2) & ~ big_f(ex_2_1_3, v0, v0))) & ( ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_2_1_3) & ~ big_f(ex_2_0_2, ex_2_1_3, v0))))
% 9.90/3.66 |
% 9.90/3.66 | Instantiating (4) with all_3_0_4 yields:
% 9.90/3.66 | (5) big_f(ex_2_1_3, ex_2_0_2, all_3_0_4) & ( ~ big_f(all_0_0_0, all_0_0_0, ex_2_1_3) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))) & ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_2_1_3, ex_2_0_2) & ~ big_f(ex_2_1_3, all_3_0_4, all_3_0_4))) & ( ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_2_1_3) & ~ big_f(ex_2_0_2, ex_2_1_3, all_3_0_4)))
% 9.90/3.66 |
% 9.90/3.66 | Applying alpha-rule on (5) yields:
% 9.90/3.66 | (6) big_f(ex_2_1_3, ex_2_0_2, all_3_0_4)
% 9.90/3.66 | (7) ~ big_f(all_0_0_0, all_0_0_0, ex_2_1_3) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))
% 9.90/3.66 | (8) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_2_1_3, ex_2_0_2) & ~ big_f(ex_2_1_3, all_3_0_4, all_3_0_4))
% 9.90/3.66 | (9) ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_2_1_3) & ~ big_f(ex_2_0_2, ex_2_1_3, all_3_0_4))
% 9.90/3.66 |
% 9.90/3.66 +-Applying beta-rule and splitting (7), into two cases.
% 9.90/3.66 |-Branch one:
% 9.90/3.66 | (10) ~ big_f(all_0_0_0, all_0_0_0, ex_2_1_3)
% 9.90/3.66 |
% 9.90/3.66 +-Applying beta-rule and splitting (9), into two cases.
% 9.90/3.66 |-Branch one:
% 9.90/3.66 | (11) ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.66 |
% 9.90/3.66 +-Applying beta-rule and splitting (8), into two cases.
% 9.90/3.66 |-Branch one:
% 9.90/3.66 | (12) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.66 |
% 9.90/3.66 | Introducing new symbol ex_32_1_6 defined by:
% 9.90/3.66 | (13) ex_32_1_6 = all_3_0_4
% 9.90/3.66 |
% 9.90/3.66 | Instantiating formula (1) with ex_32_0_5, ex_32_1_6 yields:
% 9.90/3.66 | (14) ? [v0] : (big_f(ex_32_1_6, ex_32_0_5, v0) & ( ~ big_f(all_0_0_0, all_0_0_0, ex_32_1_6) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))) & ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_32_1_6, ex_32_0_5) & ~ big_f(ex_32_1_6, v0, v0))) & ( ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_32_1_6) & ~ big_f(ex_32_0_5, ex_32_1_6, v0))))
% 9.90/3.66 |
% 9.90/3.66 | Instantiating (14) with all_33_0_7 yields:
% 9.90/3.66 | (15) big_f(ex_32_1_6, ex_32_0_5, all_33_0_7) & ( ~ big_f(all_0_0_0, all_0_0_0, ex_32_1_6) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))) & ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_32_1_6, ex_32_0_5) & ~ big_f(ex_32_1_6, all_33_0_7, all_33_0_7))) & ( ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_32_1_6) & ~ big_f(ex_32_0_5, ex_32_1_6, all_33_0_7)))
% 9.90/3.66 |
% 9.90/3.66 | Applying alpha-rule on (15) yields:
% 9.90/3.66 | (16) big_f(ex_32_1_6, ex_32_0_5, all_33_0_7)
% 9.90/3.66 | (17) ~ big_f(all_0_0_0, all_0_0_0, ex_32_1_6) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))
% 9.90/3.66 | (18) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_32_1_6, ex_32_0_5) & ~ big_f(ex_32_1_6, all_33_0_7, all_33_0_7))
% 9.90/3.66 | (19) ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_32_1_6) & ~ big_f(ex_32_0_5, ex_32_1_6, all_33_0_7))
% 9.90/3.66 |
% 9.90/3.66 +-Applying beta-rule and splitting (17), into two cases.
% 9.90/3.66 |-Branch one:
% 9.90/3.66 | (20) ~ big_f(all_0_0_0, all_0_0_0, ex_32_1_6)
% 9.90/3.66 |
% 9.90/3.66 | From (2)(3) and (6) follows:
% 9.90/3.66 | (21) big_f(all_0_0_0, all_0_0_0, all_3_0_4)
% 9.90/3.66 |
% 9.90/3.66 | From (13) and (20) follows:
% 9.90/3.66 | (22) ~ big_f(all_0_0_0, all_0_0_0, all_3_0_4)
% 9.90/3.66 |
% 9.90/3.66 | Using (21) and (22) yields:
% 9.90/3.66 | (23) $false
% 9.90/3.66 |
% 9.90/3.66 |-The branch is then unsatisfiable
% 9.90/3.66 |-Branch two:
% 9.90/3.66 | (24) ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0))
% 9.90/3.67 |
% 9.90/3.67 | Applying alpha-rule on (24) yields:
% 9.90/3.67 | (25) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.67 | (26) big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.67 |
% 9.90/3.67 +-Applying beta-rule and splitting (26), into two cases.
% 9.90/3.67 |-Branch one:
% 9.90/3.67 | (27) big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.67 |
% 9.90/3.67 | Using (27) and (12) yields:
% 9.90/3.67 | (23) $false
% 9.90/3.67 |
% 9.90/3.67 |-The branch is then unsatisfiable
% 9.90/3.67 |-Branch two:
% 9.90/3.67 | (29) big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.67 |
% 9.90/3.67 | Using (29) and (11) yields:
% 9.90/3.67 | (23) $false
% 9.90/3.67 |
% 9.90/3.67 |-The branch is then unsatisfiable
% 9.90/3.67 |-Branch two:
% 9.90/3.67 | (31) big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_2_1_3, ex_2_0_2) & ~ big_f(ex_2_1_3, all_3_0_4, all_3_0_4))
% 9.90/3.67 |
% 9.90/3.67 +-Applying beta-rule and splitting (31), into two cases.
% 9.90/3.67 |-Branch one:
% 9.90/3.67 | (29) big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.67 |
% 9.90/3.67 | Using (29) and (11) yields:
% 9.90/3.67 | (23) $false
% 9.90/3.67 |
% 9.90/3.67 |-The branch is then unsatisfiable
% 9.90/3.67 |-Branch two:
% 9.90/3.67 | (34) big_f(all_0_0_0, ex_2_1_3, ex_2_0_2) & ~ big_f(ex_2_1_3, all_3_0_4, all_3_0_4)
% 9.90/3.67 |
% 9.90/3.67 | Applying alpha-rule on (34) yields:
% 9.90/3.67 | (35) big_f(all_0_0_0, ex_2_1_3, ex_2_0_2)
% 9.90/3.67 | (36) ~ big_f(ex_2_1_3, all_3_0_4, all_3_0_4)
% 9.90/3.67 |
% 9.90/3.67 | From (2)(3) and (35) follows:
% 9.90/3.67 | (37) big_f(all_0_0_0, all_0_0_0, all_0_0_0)
% 9.90/3.67 |
% 9.90/3.67 | From (2) and (10) follows:
% 9.90/3.67 | (38) ~ big_f(all_0_0_0, all_0_0_0, all_0_0_0)
% 9.90/3.67 |
% 9.90/3.67 | Using (37) and (38) yields:
% 9.90/3.67 | (23) $false
% 9.90/3.67 |
% 9.90/3.67 |-The branch is then unsatisfiable
% 9.90/3.67 |-Branch two:
% 9.90/3.67 | (29) big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.67 | (41) big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_2_1_3) & ~ big_f(ex_2_0_2, ex_2_1_3, all_3_0_4))
% 9.90/3.67 |
% 9.90/3.67 +-Applying beta-rule and splitting (8), into two cases.
% 9.90/3.67 |-Branch one:
% 9.90/3.67 | (12) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.67 |
% 9.90/3.67 +-Applying beta-rule and splitting (41), into two cases.
% 9.90/3.67 |-Branch one:
% 9.90/3.67 | (27) big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.67 |
% 9.90/3.67 | Using (27) and (12) yields:
% 9.90/3.67 | (23) $false
% 9.90/3.67 |
% 9.90/3.67 |-The branch is then unsatisfiable
% 9.90/3.67 |-Branch two:
% 9.90/3.67 | (45) big_f(all_0_1_1, all_0_0_0, ex_2_1_3) & ~ big_f(ex_2_0_2, ex_2_1_3, all_3_0_4)
% 9.90/3.67 |
% 9.90/3.67 | Applying alpha-rule on (45) yields:
% 9.90/3.67 | (46) big_f(all_0_1_1, all_0_0_0, ex_2_1_3)
% 9.90/3.67 | (47) ~ big_f(ex_2_0_2, ex_2_1_3, all_3_0_4)
% 9.90/3.67 |
% 9.90/3.67 | From (2)(3) and (6) follows:
% 9.90/3.67 | (21) big_f(all_0_0_0, all_0_0_0, all_3_0_4)
% 9.90/3.67 |
% 9.90/3.67 | From (3)(2) and (47) follows:
% 9.90/3.67 | (22) ~ big_f(all_0_0_0, all_0_0_0, all_3_0_4)
% 9.90/3.67 |
% 9.90/3.67 | Using (21) and (22) yields:
% 9.90/3.67 | (23) $false
% 9.90/3.67 |
% 9.90/3.67 |-The branch is then unsatisfiable
% 9.90/3.67 |-Branch two:
% 9.90/3.67 | (27) big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.67 | (31) big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_2_1_3, ex_2_0_2) & ~ big_f(ex_2_1_3, all_3_0_4, all_3_0_4))
% 9.90/3.67 |
% 9.90/3.67 | Introducing new symbol ex_34_1_9 defined by:
% 9.90/3.67 | (53) ex_34_1_9 = all_3_0_4
% 9.90/3.67 |
% 9.90/3.67 | Instantiating formula (1) with ex_34_0_8, ex_34_1_9 yields:
% 9.90/3.67 | (54) ? [v0] : (big_f(ex_34_1_9, ex_34_0_8, v0) & ( ~ big_f(all_0_0_0, all_0_0_0, ex_34_1_9) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))) & ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_34_1_9, ex_34_0_8) & ~ big_f(ex_34_1_9, v0, v0))) & ( ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_34_1_9) & ~ big_f(ex_34_0_8, ex_34_1_9, v0))))
% 9.90/3.67 |
% 9.90/3.67 | Instantiating (54) with all_35_0_10 yields:
% 9.90/3.67 | (55) big_f(ex_34_1_9, ex_34_0_8, all_35_0_10) & ( ~ big_f(all_0_0_0, all_0_0_0, ex_34_1_9) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))) & ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_34_1_9, ex_34_0_8) & ~ big_f(ex_34_1_9, all_35_0_10, all_35_0_10))) & ( ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_34_1_9) & ~ big_f(ex_34_0_8, ex_34_1_9, all_35_0_10)))
% 9.90/3.67 |
% 9.90/3.67 | Applying alpha-rule on (55) yields:
% 9.90/3.67 | (56) big_f(ex_34_1_9, ex_34_0_8, all_35_0_10)
% 9.90/3.67 | (57) ~ big_f(all_0_0_0, all_0_0_0, ex_34_1_9) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))
% 9.90/3.67 | (58) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_34_1_9, ex_34_0_8) & ~ big_f(ex_34_1_9, all_35_0_10, all_35_0_10))
% 9.90/3.67 | (59) ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_34_1_9) & ~ big_f(ex_34_0_8, ex_34_1_9, all_35_0_10))
% 9.90/3.67 |
% 9.90/3.67 +-Applying beta-rule and splitting (57), into two cases.
% 9.90/3.67 |-Branch one:
% 9.90/3.67 | (60) ~ big_f(all_0_0_0, all_0_0_0, ex_34_1_9)
% 9.90/3.67 |
% 9.90/3.67 | From (2)(3) and (6) follows:
% 9.90/3.67 | (21) big_f(all_0_0_0, all_0_0_0, all_3_0_4)
% 9.90/3.67 |
% 9.90/3.67 | From (53) and (60) follows:
% 9.90/3.67 | (22) ~ big_f(all_0_0_0, all_0_0_0, all_3_0_4)
% 9.90/3.67 |
% 9.90/3.67 | Using (21) and (22) yields:
% 9.90/3.67 | (23) $false
% 9.90/3.67 |
% 9.90/3.67 |-The branch is then unsatisfiable
% 9.90/3.67 |-Branch two:
% 9.90/3.67 | (24) ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0))
% 9.90/3.67 |
% 9.90/3.68 | Applying alpha-rule on (24) yields:
% 9.90/3.68 | (25) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.68 | (26) big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 +-Applying beta-rule and splitting (25), into two cases.
% 9.90/3.68 |-Branch one:
% 9.90/3.68 | (12) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 | Using (27) and (12) yields:
% 9.90/3.68 | (23) $false
% 9.90/3.68 |
% 9.90/3.68 |-The branch is then unsatisfiable
% 9.90/3.68 |-Branch two:
% 9.90/3.68 | (11) ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 | Using (29) and (11) yields:
% 9.90/3.68 | (23) $false
% 9.90/3.68 |
% 9.90/3.68 |-The branch is then unsatisfiable
% 9.90/3.68 |-Branch two:
% 9.90/3.68 | (24) ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0))
% 9.90/3.68 |
% 9.90/3.68 | Applying alpha-rule on (24) yields:
% 9.90/3.68 | (25) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.68 | (26) big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 +-Applying beta-rule and splitting (8), into two cases.
% 9.90/3.68 |-Branch one:
% 9.90/3.68 | (12) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 +-Applying beta-rule and splitting (26), into two cases.
% 9.90/3.68 |-Branch one:
% 9.90/3.68 | (27) big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 | Using (27) and (12) yields:
% 9.90/3.68 | (23) $false
% 9.90/3.68 |
% 9.90/3.68 |-The branch is then unsatisfiable
% 9.90/3.68 |-Branch two:
% 9.90/3.68 | (29) big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 +-Applying beta-rule and splitting (9), into two cases.
% 9.90/3.68 |-Branch one:
% 9.90/3.68 | (11) ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 | Using (29) and (11) yields:
% 9.90/3.68 | (23) $false
% 9.90/3.68 |
% 9.90/3.68 |-The branch is then unsatisfiable
% 9.90/3.68 |-Branch two:
% 9.90/3.68 | (41) big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_2_1_3) & ~ big_f(ex_2_0_2, ex_2_1_3, all_3_0_4))
% 9.90/3.68 |
% 9.90/3.68 +-Applying beta-rule and splitting (41), into two cases.
% 9.90/3.68 |-Branch one:
% 9.90/3.68 | (27) big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 | Using (27) and (12) yields:
% 9.90/3.68 | (23) $false
% 9.90/3.68 |
% 9.90/3.68 |-The branch is then unsatisfiable
% 9.90/3.68 |-Branch two:
% 9.90/3.68 | (45) big_f(all_0_1_1, all_0_0_0, ex_2_1_3) & ~ big_f(ex_2_0_2, ex_2_1_3, all_3_0_4)
% 9.90/3.68 |
% 9.90/3.68 | Applying alpha-rule on (45) yields:
% 9.90/3.68 | (46) big_f(all_0_1_1, all_0_0_0, ex_2_1_3)
% 9.90/3.68 | (47) ~ big_f(ex_2_0_2, ex_2_1_3, all_3_0_4)
% 9.90/3.68 |
% 9.90/3.68 | From (2)(3) and (6) follows:
% 9.90/3.68 | (21) big_f(all_0_0_0, all_0_0_0, all_3_0_4)
% 9.90/3.68 |
% 9.90/3.68 | From (3)(2) and (47) follows:
% 9.90/3.68 | (22) ~ big_f(all_0_0_0, all_0_0_0, all_3_0_4)
% 9.90/3.68 |
% 9.90/3.68 | Using (21) and (22) yields:
% 9.90/3.68 | (23) $false
% 9.90/3.68 |
% 9.90/3.68 |-The branch is then unsatisfiable
% 9.90/3.68 |-Branch two:
% 9.90/3.68 | (27) big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.68 | (31) big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_2_1_3, ex_2_0_2) & ~ big_f(ex_2_1_3, all_3_0_4, all_3_0_4))
% 9.90/3.68 |
% 9.90/3.68 +-Applying beta-rule and splitting (9), into two cases.
% 9.90/3.68 |-Branch one:
% 9.90/3.68 | (11) ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 +-Applying beta-rule and splitting (31), into two cases.
% 9.90/3.68 |-Branch one:
% 9.90/3.68 | (29) big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 | Using (29) and (11) yields:
% 9.90/3.68 | (23) $false
% 9.90/3.68 |
% 9.90/3.68 |-The branch is then unsatisfiable
% 9.90/3.68 |-Branch two:
% 9.90/3.68 | (34) big_f(all_0_0_0, ex_2_1_3, ex_2_0_2) & ~ big_f(ex_2_1_3, all_3_0_4, all_3_0_4)
% 9.90/3.68 |
% 9.90/3.68 | Applying alpha-rule on (34) yields:
% 9.90/3.68 | (35) big_f(all_0_0_0, ex_2_1_3, ex_2_0_2)
% 9.90/3.68 | (36) ~ big_f(ex_2_1_3, all_3_0_4, all_3_0_4)
% 9.90/3.68 |
% 9.90/3.68 | Introducing new symbol ex_28_1_12 defined by:
% 9.90/3.68 | (97) ex_28_1_12 = all_3_0_4
% 9.90/3.68 |
% 9.90/3.68 | Introducing new symbol ex_28_0_11 defined by:
% 9.90/3.68 | (98) ex_28_0_11 = all_3_0_4
% 9.90/3.68 |
% 9.90/3.68 | Instantiating formula (1) with ex_28_0_11, ex_28_1_12 yields:
% 9.90/3.68 | (99) ? [v0] : (big_f(ex_28_1_12, ex_28_0_11, v0) & ( ~ big_f(all_0_0_0, all_0_0_0, ex_28_1_12) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))) & ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_28_1_12, ex_28_0_11) & ~ big_f(ex_28_1_12, v0, v0))) & ( ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_28_1_12) & ~ big_f(ex_28_0_11, ex_28_1_12, v0))))
% 9.90/3.68 |
% 9.90/3.68 | Instantiating (99) with all_29_0_13 yields:
% 9.90/3.68 | (100) big_f(ex_28_1_12, ex_28_0_11, all_29_0_13) & ( ~ big_f(all_0_0_0, all_0_0_0, ex_28_1_12) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))) & ( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_28_1_12, ex_28_0_11) & ~ big_f(ex_28_1_12, all_29_0_13, all_29_0_13))) & ( ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_28_1_12) & ~ big_f(ex_28_0_11, ex_28_1_12, all_29_0_13)))
% 9.90/3.68 |
% 9.90/3.68 | Applying alpha-rule on (100) yields:
% 9.90/3.68 | (101) big_f(ex_28_1_12, ex_28_0_11, all_29_0_13)
% 9.90/3.68 | (102) ~ big_f(all_0_0_0, all_0_0_0, ex_28_1_12) | (( ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)) & (big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0)))
% 9.90/3.68 | (103) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0) | big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_28_1_12, ex_28_0_11) & ~ big_f(ex_28_1_12, all_29_0_13, all_29_0_13))
% 9.90/3.68 | (104) ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0) | big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_28_1_12) & ~ big_f(ex_28_0_11, ex_28_1_12, all_29_0_13))
% 9.90/3.68 |
% 9.90/3.68 +-Applying beta-rule and splitting (103), into two cases.
% 9.90/3.68 |-Branch one:
% 9.90/3.68 | (12) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.68 |
% 9.90/3.68 | Using (27) and (12) yields:
% 9.90/3.68 | (23) $false
% 9.90/3.68 |
% 9.90/3.68 |-The branch is then unsatisfiable
% 9.90/3.68 |-Branch two:
% 9.90/3.68 | (107) big_f(all_0_1_1, all_0_1_1, all_0_0_0) | (big_f(all_0_0_0, ex_28_1_12, ex_28_0_11) & ~ big_f(ex_28_1_12, all_29_0_13, all_29_0_13))
% 9.90/3.68 |
% 9.90/3.69 +-Applying beta-rule and splitting (107), into two cases.
% 9.90/3.69 |-Branch one:
% 9.90/3.69 | (29) big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.69 |
% 9.90/3.69 | Using (29) and (11) yields:
% 9.90/3.69 | (23) $false
% 9.90/3.69 |
% 9.90/3.69 |-The branch is then unsatisfiable
% 9.90/3.69 |-Branch two:
% 9.90/3.69 | (110) big_f(all_0_0_0, ex_28_1_12, ex_28_0_11) & ~ big_f(ex_28_1_12, all_29_0_13, all_29_0_13)
% 9.90/3.69 |
% 9.90/3.69 | Applying alpha-rule on (110) yields:
% 9.90/3.69 | (111) big_f(all_0_0_0, ex_28_1_12, ex_28_0_11)
% 9.90/3.69 | (112) ~ big_f(ex_28_1_12, all_29_0_13, all_29_0_13)
% 9.90/3.69 |
% 9.90/3.69 | From (97)(98) and (111) follows:
% 9.90/3.69 | (113) big_f(all_0_0_0, all_3_0_4, all_3_0_4)
% 9.90/3.69 |
% 9.90/3.69 | From (2) and (36) follows:
% 9.90/3.69 | (114) ~ big_f(all_0_0_0, all_3_0_4, all_3_0_4)
% 9.90/3.69 |
% 9.90/3.69 | Using (113) and (114) yields:
% 9.90/3.69 | (23) $false
% 9.90/3.69 |
% 9.90/3.69 |-The branch is then unsatisfiable
% 9.90/3.69 |-Branch two:
% 9.90/3.69 | (29) big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.69 | (41) big_f(all_0_1_1, all_0_0_0, all_0_0_0) | (big_f(all_0_1_1, all_0_0_0, ex_2_1_3) & ~ big_f(ex_2_0_2, ex_2_1_3, all_3_0_4))
% 9.90/3.69 |
% 9.90/3.69 +-Applying beta-rule and splitting (25), into two cases.
% 9.90/3.69 |-Branch one:
% 9.90/3.69 | (12) ~ big_f(all_0_1_1, all_0_0_0, all_0_0_0)
% 9.90/3.69 |
% 9.90/3.69 | Using (27) and (12) yields:
% 9.90/3.69 | (23) $false
% 9.90/3.69 |
% 9.90/3.69 |-The branch is then unsatisfiable
% 9.90/3.69 |-Branch two:
% 9.90/3.69 | (11) ~ big_f(all_0_1_1, all_0_1_1, all_0_0_0)
% 9.90/3.69 |
% 9.90/3.69 | Using (29) and (11) yields:
% 9.90/3.69 | (23) $false
% 9.90/3.69 |
% 9.90/3.69 |-The branch is then unsatisfiable
% 9.90/3.69 % SZS output end Proof for theBenchmark
% 9.90/3.69
% 9.90/3.69 3085ms
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