TSTP Solution File: SYN075+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN075+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 04:59:44 EDT 2022
% Result : Theorem 5.70s 2.26s
% Output : Proof 7.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN075+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n024.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 : Tue Jul 12 05:35:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.54/0.60 ____ _
% 0.54/0.60 ___ / __ \_____(_)___ ________ __________
% 0.54/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.60
% 0.54/0.60 A Theorem Prover for First-Order Logic
% 0.54/0.60 (ePrincess v.1.0)
% 0.54/0.60
% 0.54/0.60 (c) Philipp Rümmer, 2009-2015
% 0.54/0.60 (c) Peter Backeman, 2014-2015
% 0.54/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.60 Bug reports to peter@backeman.se
% 0.54/0.60
% 0.54/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.60
% 0.54/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.24/0.92 Prover 0: Preprocessing ...
% 1.42/1.00 Prover 0: Warning: ignoring some quantifiers
% 1.56/1.02 Prover 0: Constructing countermodel ...
% 1.90/1.18 Prover 0: gave up
% 1.90/1.18 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.02/1.19 Prover 1: Preprocessing ...
% 2.24/1.25 Prover 1: Warning: ignoring some quantifiers
% 2.24/1.25 Prover 1: Constructing countermodel ...
% 2.24/1.27 Prover 1: gave up
% 2.24/1.27 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.24/1.28 Prover 2: Preprocessing ...
% 2.50/1.33 Prover 2: Warning: ignoring some quantifiers
% 2.50/1.34 Prover 2: Constructing countermodel ...
% 2.60/1.38 Prover 2: gave up
% 2.60/1.38 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.60/1.39 Prover 3: Preprocessing ...
% 2.60/1.41 Prover 3: Warning: ignoring some quantifiers
% 2.60/1.41 Prover 3: Constructing countermodel ...
% 2.60/1.44 Prover 3: gave up
% 2.60/1.44 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.60/1.45 Prover 4: Preprocessing ...
% 2.97/1.49 Prover 4: Warning: ignoring some quantifiers
% 2.97/1.49 Prover 4: Constructing countermodel ...
% 3.16/1.56 Prover 4: gave up
% 3.16/1.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.16/1.56 Prover 5: Preprocessing ...
% 3.16/1.58 Prover 5: Warning: ignoring some quantifiers
% 3.16/1.58 Prover 5: Constructing countermodel ...
% 3.16/1.61 Prover 5: gave up
% 3.16/1.61 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.16/1.61 Prover 6: Preprocessing ...
% 3.37/1.63 Prover 6: Warning: ignoring some quantifiers
% 3.37/1.63 Prover 6: Constructing countermodel ...
% 3.37/1.64 Prover 6: gave up
% 3.37/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.37/1.65 Prover 7: Preprocessing ...
% 3.37/1.66 Prover 7: Proving ...
% 5.70/2.26 Prover 7: proved (619ms)
% 5.70/2.26
% 5.70/2.26 % SZS status Theorem for theBenchmark
% 5.70/2.26
% 5.70/2.26 Generating proof ... found it (size 41)
% 7.69/3.01
% 7.69/3.01 % SZS output start Proof for theBenchmark
% 7.69/3.01 Assumed formulas after preprocessing and simplification:
% 7.69/3.01 | (0) ! [v0] : ? [v1] : (( ~ (v1 = v0) | ! [v2] : ? [v3] : (( ~ (v3 = v2) | ~ big_f(v2, v0)) & (v3 = v2 | big_f(v3, v0)))) & (v1 = v0 | ? [v2] : (big_f(v2, v1) & ! [v3] : (v3 = v2 | ~ big_f(v3, v1))))) & ? [v0] : ? [v1] : (big_f(v0, v1) & ! [v2] : ! [v3] : ( ~ big_f(v2, v3) | (v3 = v1 & v2 = v0)))
% 7.69/3.01 | Applying alpha-rule on (0) yields:
% 7.69/3.01 | (1) ! [v0] : ? [v1] : (( ~ (v1 = v0) | ! [v2] : ? [v3] : (( ~ (v3 = v2) | ~ big_f(v2, v0)) & (v3 = v2 | big_f(v3, v0)))) & (v1 = v0 | ? [v2] : (big_f(v2, v1) & ! [v3] : (v3 = v2 | ~ big_f(v3, v1)))))
% 7.69/3.02 | (2) ? [v0] : ? [v1] : (big_f(v0, v1) & ! [v2] : ! [v3] : ( ~ big_f(v2, v3) | (v3 = v1 & v2 = v0)))
% 7.69/3.02 |
% 7.69/3.02 | Instantiating (2) with all_0_0_0, all_0_1_1 yields:
% 7.69/3.02 | (3) big_f(all_0_1_1, all_0_0_0) & ! [v0] : ! [v1] : ( ~ big_f(v0, v1) | (v1 = all_0_0_0 & v0 = all_0_1_1))
% 7.69/3.02 |
% 7.69/3.02 | Applying alpha-rule on (3) yields:
% 7.69/3.02 | (4) big_f(all_0_1_1, all_0_0_0)
% 7.69/3.02 | (5) ! [v0] : ! [v1] : ( ~ big_f(v0, v1) | (v1 = all_0_0_0 & v0 = all_0_1_1))
% 7.69/3.02 |
% 7.69/3.02 | Introducing new symbol ex_9_0_2 defined by:
% 7.69/3.02 | (6) ex_9_0_2 = all_0_0_0
% 7.69/3.02 |
% 7.69/3.02 | Instantiating formula (1) with ex_9_0_2 yields:
% 7.69/3.02 | (7) ? [v0] : (( ~ (v0 = ex_9_0_2) | ! [v1] : ? [v2] : (( ~ (v2 = v1) | ~ big_f(v1, ex_9_0_2)) & (v2 = v1 | big_f(v2, ex_9_0_2)))) & (v0 = ex_9_0_2 | ? [v1] : (big_f(v1, v0) & ! [v2] : (v2 = v1 | ~ big_f(v2, v0)))))
% 7.69/3.02 |
% 7.69/3.02 | Instantiating (7) with all_10_0_3 yields:
% 7.69/3.02 | (8) ( ~ (all_10_0_3 = ex_9_0_2) | ! [v0] : ? [v1] : (( ~ (v1 = v0) | ~ big_f(v0, ex_9_0_2)) & (v1 = v0 | big_f(v1, ex_9_0_2)))) & (all_10_0_3 = ex_9_0_2 | ? [v0] : (big_f(v0, all_10_0_3) & ! [v1] : (v1 = v0 | ~ big_f(v1, all_10_0_3))))
% 7.69/3.02 |
% 7.69/3.02 | Applying alpha-rule on (8) yields:
% 7.69/3.02 | (9) ~ (all_10_0_3 = ex_9_0_2) | ! [v0] : ? [v1] : (( ~ (v1 = v0) | ~ big_f(v0, ex_9_0_2)) & (v1 = v0 | big_f(v1, ex_9_0_2)))
% 7.69/3.02 | (10) all_10_0_3 = ex_9_0_2 | ? [v0] : (big_f(v0, all_10_0_3) & ! [v1] : (v1 = v0 | ~ big_f(v1, all_10_0_3)))
% 7.69/3.02 |
% 7.69/3.02 +-Applying beta-rule and splitting (10), into two cases.
% 7.69/3.02 |-Branch one:
% 7.69/3.02 | (11) all_10_0_3 = ex_9_0_2
% 7.69/3.02 |
% 7.69/3.02 +-Applying beta-rule and splitting (9), into two cases.
% 7.69/3.02 |-Branch one:
% 7.69/3.02 | (12) ~ (all_10_0_3 = ex_9_0_2)
% 7.69/3.02 |
% 7.69/3.02 | Equations (11) can reduce 12 to:
% 7.69/3.02 | (13) $false
% 7.69/3.02 |
% 7.69/3.02 |-The branch is then unsatisfiable
% 7.69/3.02 |-Branch two:
% 7.69/3.02 | (14) ! [v0] : ? [v1] : (( ~ (v1 = v0) | ~ big_f(v0, ex_9_0_2)) & (v1 = v0 | big_f(v1, ex_9_0_2)))
% 7.69/3.02 |
% 7.69/3.02 | Introducing new symbol ex_37_0_8 defined by:
% 7.69/3.02 | (15) ex_37_0_8 = all_0_1_1
% 7.69/3.02 |
% 7.69/3.02 | Instantiating formula (14) with ex_37_0_8 yields:
% 7.69/3.02 | (16) ? [v0] : (( ~ (v0 = ex_37_0_8) | ~ big_f(ex_37_0_8, ex_9_0_2)) & (v0 = ex_37_0_8 | big_f(v0, ex_9_0_2)))
% 7.69/3.02 |
% 7.69/3.02 | Instantiating (16) with all_38_0_9 yields:
% 7.69/3.02 | (17) ( ~ (all_38_0_9 = ex_37_0_8) | ~ big_f(ex_37_0_8, ex_9_0_2)) & (all_38_0_9 = ex_37_0_8 | big_f(all_38_0_9, ex_9_0_2))
% 7.69/3.02 |
% 7.69/3.02 | Applying alpha-rule on (17) yields:
% 7.69/3.02 | (18) ~ (all_38_0_9 = ex_37_0_8) | ~ big_f(ex_37_0_8, ex_9_0_2)
% 7.69/3.02 | (19) all_38_0_9 = ex_37_0_8 | big_f(all_38_0_9, ex_9_0_2)
% 7.69/3.02 |
% 7.69/3.02 +-Applying beta-rule and splitting (19), into two cases.
% 7.69/3.02 |-Branch one:
% 7.69/3.02 | (20) big_f(all_38_0_9, ex_9_0_2)
% 7.69/3.02 |
% 7.69/3.02 | Instantiating formula (5) with ex_9_0_2, all_38_0_9 and discharging atoms big_f(all_38_0_9, ex_9_0_2), yields:
% 7.69/3.02 | (21) all_38_0_9 = all_0_1_1 & ex_9_0_2 = all_0_0_0
% 7.69/3.02 |
% 7.69/3.02 | Applying alpha-rule on (21) yields:
% 7.69/3.02 | (22) all_38_0_9 = all_0_1_1
% 7.69/3.02 | (6) ex_9_0_2 = all_0_0_0
% 7.69/3.02 |
% 7.69/3.02 +-Applying beta-rule and splitting (18), into two cases.
% 7.69/3.02 |-Branch one:
% 7.69/3.02 | (24) ~ big_f(ex_37_0_8, ex_9_0_2)
% 7.69/3.02 |
% 7.69/3.02 | From (6) and (24) follows:
% 7.69/3.03 | (25) ~ big_f(ex_37_0_8, all_0_0_0)
% 7.69/3.03 |
% 7.69/3.03 | From (15) and (25) follows:
% 7.69/3.03 | (26) ~ big_f(all_0_1_1, all_0_0_0)
% 7.69/3.03 |
% 7.69/3.03 | Using (4) and (26) yields:
% 7.69/3.03 | (27) $false
% 7.69/3.03 |
% 7.69/3.03 |-The branch is then unsatisfiable
% 7.69/3.03 |-Branch two:
% 7.69/3.03 | (28) ~ (all_38_0_9 = ex_37_0_8)
% 7.69/3.03 |
% 7.69/3.03 | Equations (22) can reduce 28 to:
% 7.69/3.03 | (29) ~ (ex_37_0_8 = all_0_1_1)
% 7.69/3.03 |
% 7.69/3.03 | Simplifying 29 yields:
% 7.69/3.03 | (30) ~ (ex_37_0_8 = all_0_1_1)
% 7.69/3.03 |
% 7.69/3.03 | Equations (15) can reduce 30 to:
% 7.69/3.03 | (13) $false
% 7.69/3.03 |
% 7.69/3.03 |-The branch is then unsatisfiable
% 7.69/3.03 |-Branch two:
% 7.69/3.03 | (32) all_38_0_9 = ex_37_0_8
% 7.69/3.03 |
% 7.69/3.03 +-Applying beta-rule and splitting (18), into two cases.
% 7.69/3.03 |-Branch one:
% 7.69/3.03 | (24) ~ big_f(ex_37_0_8, ex_9_0_2)
% 7.69/3.03 |
% 7.69/3.03 | From (15)(6) and (24) follows:
% 7.69/3.03 | (26) ~ big_f(all_0_1_1, all_0_0_0)
% 7.69/3.03 |
% 7.69/3.03 | Using (4) and (26) yields:
% 7.69/3.03 | (27) $false
% 7.69/3.03 |
% 7.69/3.03 |-The branch is then unsatisfiable
% 7.69/3.03 |-Branch two:
% 7.69/3.03 | (28) ~ (all_38_0_9 = ex_37_0_8)
% 7.69/3.03 |
% 7.69/3.03 | Equations (32) can reduce 28 to:
% 7.69/3.03 | (13) $false
% 7.69/3.03 |
% 7.69/3.03 |-The branch is then unsatisfiable
% 7.69/3.03 |-Branch two:
% 7.69/3.03 | (12) ~ (all_10_0_3 = ex_9_0_2)
% 7.69/3.03 | (39) ? [v0] : (big_f(v0, all_10_0_3) & ! [v1] : (v1 = v0 | ~ big_f(v1, all_10_0_3)))
% 7.69/3.03 |
% 7.69/3.03 | Instantiating (39) with all_13_0_4 yields:
% 7.69/3.03 | (40) big_f(all_13_0_4, all_10_0_3) & ! [v0] : (v0 = all_13_0_4 | ~ big_f(v0, all_10_0_3))
% 7.69/3.03 |
% 7.69/3.03 | Applying alpha-rule on (40) yields:
% 7.69/3.03 | (41) big_f(all_13_0_4, all_10_0_3)
% 7.69/3.03 | (42) ! [v0] : (v0 = all_13_0_4 | ~ big_f(v0, all_10_0_3))
% 7.69/3.03 |
% 7.69/3.03 | Instantiating formula (5) with all_10_0_3, all_13_0_4 and discharging atoms big_f(all_13_0_4, all_10_0_3), yields:
% 7.69/3.03 | (43) all_13_0_4 = all_0_1_1 & all_10_0_3 = all_0_0_0
% 7.69/3.03 |
% 7.69/3.03 | Applying alpha-rule on (43) yields:
% 7.69/3.03 | (44) all_13_0_4 = all_0_1_1
% 7.69/3.03 | (45) all_10_0_3 = all_0_0_0
% 7.69/3.03 |
% 7.69/3.03 | Equations (45) can reduce 12 to:
% 7.69/3.03 | (46) ~ (ex_9_0_2 = all_0_0_0)
% 7.69/3.03 |
% 7.69/3.03 | Simplifying 46 yields:
% 7.69/3.03 | (47) ~ (ex_9_0_2 = all_0_0_0)
% 7.69/3.03 |
% 7.69/3.03 | Equations (6) can reduce 47 to:
% 7.69/3.03 | (13) $false
% 7.69/3.03 |
% 7.69/3.03 |-The branch is then unsatisfiable
% 7.69/3.03 % SZS output end Proof for theBenchmark
% 7.69/3.03
% 7.69/3.03 2420ms
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