TSTP Solution File: SYN347+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN347+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 05:01:38 EDT 2022
% Result : Theorem 7.14s 2.79s
% Output : Proof 12.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN347+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n011.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 20:45:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.24/0.88 Prover 0: Preprocessing ...
% 1.31/0.92 Prover 0: Warning: ignoring some quantifiers
% 1.39/0.94 Prover 0: Constructing countermodel ...
% 1.54/1.04 Prover 0: gave up
% 1.54/1.04 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.54/1.06 Prover 1: Preprocessing ...
% 1.85/1.10 Prover 1: Warning: ignoring some quantifiers
% 1.85/1.10 Prover 1: Constructing countermodel ...
% 2.17/1.22 Prover 1: gave up
% 2.17/1.22 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.17/1.22 Prover 2: Preprocessing ...
% 2.26/1.25 Prover 2: Warning: ignoring some quantifiers
% 2.26/1.25 Prover 2: Constructing countermodel ...
% 2.26/1.31 Prover 2: gave up
% 2.26/1.31 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.26/1.32 Prover 3: Preprocessing ...
% 2.61/1.32 Prover 3: Warning: ignoring some quantifiers
% 2.61/1.32 Prover 3: Constructing countermodel ...
% 2.61/1.34 Prover 3: gave up
% 2.61/1.34 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.61/1.35 Prover 4: Preprocessing ...
% 2.61/1.37 Prover 4: Warning: ignoring some quantifiers
% 2.61/1.37 Prover 4: Constructing countermodel ...
% 2.90/1.42 Prover 4: gave up
% 2.90/1.42 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.90/1.43 Prover 5: Preprocessing ...
% 2.90/1.44 Prover 5: Warning: ignoring some quantifiers
% 2.90/1.44 Prover 5: Constructing countermodel ...
% 3.16/1.49 Prover 5: gave up
% 3.16/1.49 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.16/1.49 Prover 6: Preprocessing ...
% 3.16/1.50 Prover 6: Warning: ignoring some quantifiers
% 3.16/1.51 Prover 6: Constructing countermodel ...
% 3.30/1.54 Prover 6: gave up
% 3.30/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.30/1.54 Prover 7: Preprocessing ...
% 3.30/1.55 Prover 7: Proving ...
% 7.14/2.79 Prover 7: proved (1250ms)
% 7.14/2.79
% 7.14/2.79 % SZS status Theorem for theBenchmark
% 7.14/2.79
% 7.14/2.79 Generating proof ... found it (size 60)
% 12.55/4.48
% 12.55/4.48 % SZS output start Proof for theBenchmark
% 12.55/4.48 Assumed formulas after preprocessing and simplification:
% 12.55/4.48 | (0) ? [v0] : ? [v1] : ! [v2] : ! [v3] : ? [v4] : (( ~ big_f(v1, v4) | ~ big_f(v0, v4)) & ( ~ big_f(v0, v1) | (( ~ big_f(v3, v4) | ~ big_f(v2, v4)) & (big_f(v3, v4) | big_f(v2, v4)))) & (big_f(v1, v4) | big_f(v0, v4)) & (big_f(v0, v1) | (( ~ big_f(v3, v4) | big_f(v2, v4)) & ( ~ big_f(v2, v4) | big_f(v3, v4)))))
% 12.55/4.48 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 12.55/4.48 | (1) ! [v0] : ! [v1] : ? [v2] : (( ~ big_f(all_0_0_0, v2) | ~ big_f(all_0_1_1, v2)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(v1, v2) | ~ big_f(v0, v2)) & (big_f(v1, v2) | big_f(v0, v2)))) & (big_f(all_0_0_0, v2) | big_f(all_0_1_1, v2)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(v1, v2) | big_f(v0, v2)) & ( ~ big_f(v0, v2) | big_f(v1, v2)))))
% 12.55/4.48 |
% 12.55/4.48 | Instantiating formula (1) with ex_2_0_2, ex_2_1_3 yields:
% 12.55/4.48 | (2) ? [v0] : (( ~ big_f(all_0_0_0, v0) | ~ big_f(all_0_1_1, v0)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, v0) | ~ big_f(ex_2_1_3, v0)) & (big_f(ex_2_0_2, v0) | big_f(ex_2_1_3, v0)))) & (big_f(all_0_0_0, v0) | big_f(all_0_1_1, v0)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, v0) | big_f(ex_2_1_3, v0)) & ( ~ big_f(ex_2_1_3, v0) | big_f(ex_2_0_2, v0)))))
% 12.55/4.49 |
% 12.55/4.49 | Instantiating (2) with all_3_0_4 yields:
% 12.55/4.49 | (3) ( ~ big_f(all_0_0_0, all_3_0_4) | ~ big_f(all_0_1_1, all_3_0_4)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, all_3_0_4) | ~ big_f(ex_2_1_3, all_3_0_4)) & (big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4)))) & (big_f(all_0_0_0, all_3_0_4) | big_f(all_0_1_1, all_3_0_4)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4)) & ( ~ big_f(ex_2_1_3, all_3_0_4) | big_f(ex_2_0_2, all_3_0_4))))
% 12.55/4.49 |
% 12.55/4.49 | Applying alpha-rule on (3) yields:
% 12.55/4.49 | (4) ~ big_f(all_0_0_0, all_3_0_4) | ~ big_f(all_0_1_1, all_3_0_4)
% 12.55/4.49 | (5) ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, all_3_0_4) | ~ big_f(ex_2_1_3, all_3_0_4)) & (big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4)))
% 12.55/4.49 | (6) big_f(all_0_0_0, all_3_0_4) | big_f(all_0_1_1, all_3_0_4)
% 12.55/4.49 | (7) big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4)) & ( ~ big_f(ex_2_1_3, all_3_0_4) | big_f(ex_2_0_2, all_3_0_4)))
% 12.55/4.49 |
% 12.55/4.49 +-Applying beta-rule and splitting (7), into two cases.
% 12.55/4.49 |-Branch one:
% 12.55/4.49 | (8) big_f(all_0_1_1, all_0_0_0)
% 12.55/4.49 |
% 12.55/4.49 | Introducing new symbol ex_35_1_6 defined by:
% 12.55/4.49 | (9) ex_35_1_6 = arbitrary_constant
% 12.55/4.49 |
% 12.55/4.49 | Introducing new symbol ex_35_0_5 defined by:
% 12.55/4.49 | (10) ex_35_0_5 = arbitrary_constant
% 12.55/4.49 |
% 12.55/4.49 | Instantiating formula (1) with ex_35_0_5, ex_35_1_6 yields:
% 12.55/4.49 | (11) ? [v0] : (( ~ big_f(all_0_0_0, v0) | ~ big_f(all_0_1_1, v0)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, v0) | ~ big_f(ex_35_1_6, v0)) & (big_f(ex_35_0_5, v0) | big_f(ex_35_1_6, v0)))) & (big_f(all_0_0_0, v0) | big_f(all_0_1_1, v0)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, v0) | big_f(ex_35_1_6, v0)) & ( ~ big_f(ex_35_1_6, v0) | big_f(ex_35_0_5, v0)))))
% 12.55/4.49 |
% 12.55/4.49 | Instantiating (11) with all_36_0_7 yields:
% 12.55/4.49 | (12) ( ~ big_f(all_0_0_0, all_36_0_7) | ~ big_f(all_0_1_1, all_36_0_7)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, all_36_0_7) | ~ big_f(ex_35_1_6, all_36_0_7)) & (big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7)))) & (big_f(all_0_0_0, all_36_0_7) | big_f(all_0_1_1, all_36_0_7)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7)) & ( ~ big_f(ex_35_1_6, all_36_0_7) | big_f(ex_35_0_5, all_36_0_7))))
% 12.55/4.49 |
% 12.55/4.49 | Applying alpha-rule on (12) yields:
% 12.55/4.49 | (13) ~ big_f(all_0_0_0, all_36_0_7) | ~ big_f(all_0_1_1, all_36_0_7)
% 12.55/4.49 | (14) ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, all_36_0_7) | ~ big_f(ex_35_1_6, all_36_0_7)) & (big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7)))
% 12.55/4.49 | (15) big_f(all_0_0_0, all_36_0_7) | big_f(all_0_1_1, all_36_0_7)
% 12.55/4.49 | (16) big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7)) & ( ~ big_f(ex_35_1_6, all_36_0_7) | big_f(ex_35_0_5, all_36_0_7)))
% 12.55/4.49 |
% 12.55/4.49 +-Applying beta-rule and splitting (14), into two cases.
% 12.55/4.49 |-Branch one:
% 12.55/4.49 | (17) ~ big_f(all_0_1_1, all_0_0_0)
% 12.55/4.49 |
% 12.55/4.49 | Using (8) and (17) yields:
% 12.55/4.49 | (18) $false
% 12.55/4.49 |
% 12.55/4.49 |-The branch is then unsatisfiable
% 12.55/4.49 |-Branch two:
% 12.55/4.49 | (19) ( ~ big_f(ex_35_0_5, all_36_0_7) | ~ big_f(ex_35_1_6, all_36_0_7)) & (big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7))
% 12.55/4.49 |
% 12.55/4.49 | Applying alpha-rule on (19) yields:
% 12.55/4.49 | (20) ~ big_f(ex_35_0_5, all_36_0_7) | ~ big_f(ex_35_1_6, all_36_0_7)
% 12.55/4.49 | (21) big_f(ex_35_0_5, all_36_0_7) | big_f(ex_35_1_6, all_36_0_7)
% 12.55/4.49 |
% 12.55/4.49 +-Applying beta-rule and splitting (21), into two cases.
% 12.55/4.49 |-Branch one:
% 12.55/4.49 | (22) big_f(ex_35_0_5, all_36_0_7)
% 12.55/4.49 |
% 12.55/4.49 +-Applying beta-rule and splitting (20), into two cases.
% 12.55/4.49 |-Branch one:
% 12.55/4.49 | (23) ~ big_f(ex_35_0_5, all_36_0_7)
% 12.55/4.49 |
% 12.55/4.49 | Using (22) and (23) yields:
% 12.55/4.49 | (18) $false
% 12.55/4.49 |
% 12.55/4.49 |-The branch is then unsatisfiable
% 12.55/4.49 |-Branch two:
% 12.55/4.49 | (25) ~ big_f(ex_35_1_6, all_36_0_7)
% 12.55/4.49 |
% 12.55/4.49 | From (10) and (22) follows:
% 12.55/4.49 | (26) big_f(arbitrary_constant, all_36_0_7)
% 12.55/4.49 |
% 12.55/4.49 | From (9) and (25) follows:
% 12.55/4.49 | (27) ~ big_f(arbitrary_constant, all_36_0_7)
% 12.55/4.49 |
% 12.55/4.49 | Using (26) and (27) yields:
% 12.55/4.49 | (18) $false
% 12.55/4.49 |
% 12.55/4.49 |-The branch is then unsatisfiable
% 12.55/4.49 |-Branch two:
% 12.55/4.49 | (23) ~ big_f(ex_35_0_5, all_36_0_7)
% 12.55/4.49 | (30) big_f(ex_35_1_6, all_36_0_7)
% 12.55/4.49 |
% 12.55/4.49 | From (9) and (30) follows:
% 12.55/4.49 | (26) big_f(arbitrary_constant, all_36_0_7)
% 12.55/4.49 |
% 12.55/4.49 | From (10) and (23) follows:
% 12.55/4.49 | (27) ~ big_f(arbitrary_constant, all_36_0_7)
% 12.55/4.50 |
% 12.55/4.50 | Using (26) and (27) yields:
% 12.55/4.50 | (18) $false
% 12.55/4.50 |
% 12.55/4.50 |-The branch is then unsatisfiable
% 12.55/4.50 |-Branch two:
% 12.55/4.50 | (17) ~ big_f(all_0_1_1, all_0_0_0)
% 12.55/4.50 | (35) ( ~ big_f(ex_2_0_2, all_3_0_4) | big_f(ex_2_1_3, all_3_0_4)) & ( ~ big_f(ex_2_1_3, all_3_0_4) | big_f(ex_2_0_2, all_3_0_4))
% 12.55/4.50 |
% 12.55/4.50 | Introducing new symbol ex_35_1_12 defined by:
% 12.55/4.50 | (36) ex_35_1_12 = all_0_0_0
% 12.55/4.50 |
% 12.55/4.50 | Introducing new symbol ex_35_0_11 defined by:
% 12.55/4.50 | (37) ex_35_0_11 = all_0_1_1
% 12.55/4.50 |
% 12.55/4.50 | Instantiating formula (1) with ex_35_0_11, ex_35_1_12 yields:
% 12.55/4.50 | (38) ? [v0] : (( ~ big_f(all_0_0_0, v0) | ~ big_f(all_0_1_1, v0)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, v0) | ~ big_f(ex_35_1_12, v0)) & (big_f(ex_35_0_11, v0) | big_f(ex_35_1_12, v0)))) & (big_f(all_0_0_0, v0) | big_f(all_0_1_1, v0)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, v0) | big_f(ex_35_1_12, v0)) & ( ~ big_f(ex_35_1_12, v0) | big_f(ex_35_0_11, v0)))))
% 12.55/4.50 |
% 12.55/4.50 | Instantiating (38) with all_36_0_13 yields:
% 12.55/4.50 | (39) ( ~ big_f(all_0_0_0, all_36_0_13) | ~ big_f(all_0_1_1, all_36_0_13)) & ( ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, all_36_0_13) | ~ big_f(ex_35_1_12, all_36_0_13)) & (big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)))) & (big_f(all_0_0_0, all_36_0_13) | big_f(all_0_1_1, all_36_0_13)) & (big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)) & ( ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13))))
% 12.55/4.50 |
% 12.55/4.50 | Applying alpha-rule on (39) yields:
% 12.55/4.50 | (40) ~ big_f(all_0_0_0, all_36_0_13) | ~ big_f(all_0_1_1, all_36_0_13)
% 12.55/4.50 | (41) ~ big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, all_36_0_13) | ~ big_f(ex_35_1_12, all_36_0_13)) & (big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)))
% 12.55/4.50 | (42) big_f(all_0_0_0, all_36_0_13) | big_f(all_0_1_1, all_36_0_13)
% 12.55/4.50 | (43) big_f(all_0_1_1, all_0_0_0) | (( ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)) & ( ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13)))
% 12.88/4.50 |
% 12.88/4.50 +-Applying beta-rule and splitting (42), into two cases.
% 12.88/4.50 |-Branch one:
% 12.88/4.50 | (44) big_f(all_0_0_0, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 +-Applying beta-rule and splitting (40), into two cases.
% 12.88/4.50 |-Branch one:
% 12.88/4.50 | (45) ~ big_f(all_0_0_0, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | Using (44) and (45) yields:
% 12.88/4.50 | (18) $false
% 12.88/4.50 |
% 12.88/4.50 |-The branch is then unsatisfiable
% 12.88/4.50 |-Branch two:
% 12.88/4.50 | (47) ~ big_f(all_0_1_1, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 +-Applying beta-rule and splitting (43), into two cases.
% 12.88/4.50 |-Branch one:
% 12.88/4.50 | (8) big_f(all_0_1_1, all_0_0_0)
% 12.88/4.50 |
% 12.88/4.50 | Using (8) and (17) yields:
% 12.88/4.50 | (18) $false
% 12.88/4.50 |
% 12.88/4.50 |-The branch is then unsatisfiable
% 12.88/4.50 |-Branch two:
% 12.88/4.50 | (50) ( ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)) & ( ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13))
% 12.88/4.50 |
% 12.88/4.50 | Applying alpha-rule on (50) yields:
% 12.88/4.50 | (51) ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)
% 12.88/4.50 | (52) ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 +-Applying beta-rule and splitting (52), into two cases.
% 12.88/4.50 |-Branch one:
% 12.88/4.50 | (53) ~ big_f(ex_35_1_12, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | From (36) and (53) follows:
% 12.88/4.50 | (45) ~ big_f(all_0_0_0, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | Using (44) and (45) yields:
% 12.88/4.50 | (18) $false
% 12.88/4.50 |
% 12.88/4.50 |-The branch is then unsatisfiable
% 12.88/4.50 |-Branch two:
% 12.88/4.50 | (56) big_f(ex_35_0_11, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | From (37) and (56) follows:
% 12.88/4.50 | (57) big_f(all_0_1_1, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | Using (57) and (47) yields:
% 12.88/4.50 | (18) $false
% 12.88/4.50 |
% 12.88/4.50 |-The branch is then unsatisfiable
% 12.88/4.50 |-Branch two:
% 12.88/4.50 | (45) ~ big_f(all_0_0_0, all_36_0_13)
% 12.88/4.50 | (57) big_f(all_0_1_1, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 +-Applying beta-rule and splitting (43), into two cases.
% 12.88/4.50 |-Branch one:
% 12.88/4.50 | (8) big_f(all_0_1_1, all_0_0_0)
% 12.88/4.50 |
% 12.88/4.50 | Using (8) and (17) yields:
% 12.88/4.50 | (18) $false
% 12.88/4.50 |
% 12.88/4.50 |-The branch is then unsatisfiable
% 12.88/4.50 |-Branch two:
% 12.88/4.50 | (50) ( ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)) & ( ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13))
% 12.88/4.50 |
% 12.88/4.50 | Applying alpha-rule on (50) yields:
% 12.88/4.50 | (51) ~ big_f(ex_35_0_11, all_36_0_13) | big_f(ex_35_1_12, all_36_0_13)
% 12.88/4.50 | (52) ~ big_f(ex_35_1_12, all_36_0_13) | big_f(ex_35_0_11, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 +-Applying beta-rule and splitting (52), into two cases.
% 12.88/4.50 |-Branch one:
% 12.88/4.50 | (53) ~ big_f(ex_35_1_12, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 +-Applying beta-rule and splitting (51), into two cases.
% 12.88/4.50 |-Branch one:
% 12.88/4.50 | (67) ~ big_f(ex_35_0_11, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | From (37) and (67) follows:
% 12.88/4.50 | (47) ~ big_f(all_0_1_1, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | Using (57) and (47) yields:
% 12.88/4.50 | (18) $false
% 12.88/4.50 |
% 12.88/4.50 |-The branch is then unsatisfiable
% 12.88/4.50 |-Branch two:
% 12.88/4.50 | (70) big_f(ex_35_1_12, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | Using (70) and (53) yields:
% 12.88/4.50 | (18) $false
% 12.88/4.50 |
% 12.88/4.50 |-The branch is then unsatisfiable
% 12.88/4.50 |-Branch two:
% 12.88/4.50 | (70) big_f(ex_35_1_12, all_36_0_13)
% 12.88/4.50 | (56) big_f(ex_35_0_11, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | From (36) and (70) follows:
% 12.88/4.50 | (44) big_f(all_0_0_0, all_36_0_13)
% 12.88/4.50 |
% 12.88/4.50 | Using (44) and (45) yields:
% 12.88/4.50 | (18) $false
% 12.88/4.50 |
% 12.88/4.50 |-The branch is then unsatisfiable
% 12.88/4.50 % SZS output end Proof for theBenchmark
% 12.88/4.50
% 12.88/4.50 3919ms
%------------------------------------------------------------------------------