TSTP Solution File: SYN074+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN074+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 04:59:43 EDT 2022
% Result : Theorem 5.22s 2.08s
% Output : Proof 7.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SYN074+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n029.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 19:26:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.56 ____ _
% 0.54/0.56 ___ / __ \_____(_)___ ________ __________
% 0.54/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.56
% 0.54/0.56 A Theorem Prover for First-Order Logic
% 0.54/0.57 (ePrincess v.1.0)
% 0.54/0.57
% 0.54/0.57 (c) Philipp Rümmer, 2009-2015
% 0.54/0.57 (c) Peter Backeman, 2014-2015
% 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.57 Bug reports to peter@backeman.se
% 0.54/0.57
% 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.57
% 0.54/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.61/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.22/0.84 Prover 0: Preprocessing ...
% 1.31/0.92 Prover 0: Warning: ignoring some quantifiers
% 1.31/0.93 Prover 0: Constructing countermodel ...
% 1.65/1.03 Prover 0: gave up
% 1.65/1.04 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.65/1.05 Prover 1: Preprocessing ...
% 1.86/1.13 Prover 1: Warning: ignoring some quantifiers
% 1.86/1.14 Prover 1: Constructing countermodel ...
% 2.12/1.16 Prover 1: gave up
% 2.12/1.16 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.12/1.18 Prover 2: Preprocessing ...
% 2.27/1.21 Prover 2: Warning: ignoring some quantifiers
% 2.27/1.21 Prover 2: Constructing countermodel ...
% 2.27/1.24 Prover 2: gave up
% 2.40/1.24 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.40/1.24 Prover 3: Preprocessing ...
% 2.44/1.26 Prover 3: Warning: ignoring some quantifiers
% 2.44/1.26 Prover 3: Constructing countermodel ...
% 2.44/1.29 Prover 3: gave up
% 2.44/1.29 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.44/1.29 Prover 4: Preprocessing ...
% 2.65/1.34 Prover 4: Warning: ignoring some quantifiers
% 2.65/1.34 Prover 4: Constructing countermodel ...
% 2.82/1.40 Prover 4: gave up
% 2.82/1.40 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.82/1.40 Prover 5: Preprocessing ...
% 2.82/1.42 Prover 5: Warning: ignoring some quantifiers
% 2.82/1.42 Prover 5: Constructing countermodel ...
% 2.82/1.44 Prover 5: gave up
% 2.82/1.44 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.07/1.45 Prover 6: Preprocessing ...
% 3.07/1.46 Prover 6: Warning: ignoring some quantifiers
% 3.07/1.47 Prover 6: Constructing countermodel ...
% 3.07/1.48 Prover 6: gave up
% 3.07/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.07/1.48 Prover 7: Preprocessing ...
% 3.19/1.49 Prover 7: Proving ...
% 5.22/2.08 Prover 7: proved (596ms)
% 5.22/2.08
% 5.22/2.08 % SZS status Theorem for theBenchmark
% 5.22/2.08
% 5.22/2.08 Generating proof ... found it (size 41)
% 7.16/2.85
% 7.16/2.85 % SZS output start Proof for theBenchmark
% 7.16/2.85 Assumed formulas after preprocessing and simplification:
% 7.16/2.85 | (0) ! [v0] : ? [v1] : (( ~ (v1 = v0) | ! [v2] : ? [v3] : (( ~ (v3 = v2) | ~ big_f(v0, v2)) & (v3 = v2 | big_f(v0, v3)))) & (v1 = v0 | ? [v2] : (big_f(v1, v2) & ! [v3] : (v3 = v2 | ~ big_f(v1, v3))))) & ? [v0] : ? [v1] : (big_f(v0, v1) & ! [v2] : ! [v3] : ( ~ big_f(v2, v3) | (v3 = v1 & v2 = v0)))
% 7.16/2.85 | Applying alpha-rule on (0) yields:
% 7.16/2.85 | (1) ! [v0] : ? [v1] : (( ~ (v1 = v0) | ! [v2] : ? [v3] : (( ~ (v3 = v2) | ~ big_f(v0, v2)) & (v3 = v2 | big_f(v0, v3)))) & (v1 = v0 | ? [v2] : (big_f(v1, v2) & ! [v3] : (v3 = v2 | ~ big_f(v1, v3)))))
% 7.16/2.86 | (2) ? [v0] : ? [v1] : (big_f(v0, v1) & ! [v2] : ! [v3] : ( ~ big_f(v2, v3) | (v3 = v1 & v2 = v0)))
% 7.16/2.86 |
% 7.16/2.86 | Instantiating (2) with all_0_0_0, all_0_1_1 yields:
% 7.16/2.86 | (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))
% 7.16/2.86 |
% 7.16/2.86 | Applying alpha-rule on (3) yields:
% 7.16/2.86 | (4) big_f(all_0_1_1, all_0_0_0)
% 7.16/2.86 | (5) ! [v0] : ! [v1] : ( ~ big_f(v0, v1) | (v1 = all_0_0_0 & v0 = all_0_1_1))
% 7.16/2.86 |
% 7.16/2.86 | Introducing new symbol ex_9_0_2 defined by:
% 7.16/2.86 | (6) ex_9_0_2 = all_0_1_1
% 7.16/2.86 |
% 7.16/2.86 | Instantiating formula (1) with ex_9_0_2 yields:
% 7.16/2.86 | (7) ? [v0] : (( ~ (v0 = ex_9_0_2) | ! [v1] : ? [v2] : (( ~ (v2 = v1) | ~ big_f(ex_9_0_2, v1)) & (v2 = v1 | big_f(ex_9_0_2, v2)))) & (v0 = ex_9_0_2 | ? [v1] : (big_f(v0, v1) & ! [v2] : (v2 = v1 | ~ big_f(v0, v2)))))
% 7.16/2.86 |
% 7.16/2.86 | Instantiating (7) with all_10_0_3 yields:
% 7.16/2.86 | (8) ( ~ (all_10_0_3 = ex_9_0_2) | ! [v0] : ? [v1] : (( ~ (v1 = v0) | ~ big_f(ex_9_0_2, v0)) & (v1 = v0 | big_f(ex_9_0_2, v1)))) & (all_10_0_3 = ex_9_0_2 | ? [v0] : (big_f(all_10_0_3, v0) & ! [v1] : (v1 = v0 | ~ big_f(all_10_0_3, v1))))
% 7.16/2.86 |
% 7.16/2.86 | Applying alpha-rule on (8) yields:
% 7.16/2.86 | (9) ~ (all_10_0_3 = ex_9_0_2) | ! [v0] : ? [v1] : (( ~ (v1 = v0) | ~ big_f(ex_9_0_2, v0)) & (v1 = v0 | big_f(ex_9_0_2, v1)))
% 7.16/2.86 | (10) all_10_0_3 = ex_9_0_2 | ? [v0] : (big_f(all_10_0_3, v0) & ! [v1] : (v1 = v0 | ~ big_f(all_10_0_3, v1)))
% 7.16/2.86 |
% 7.16/2.86 +-Applying beta-rule and splitting (10), into two cases.
% 7.16/2.86 |-Branch one:
% 7.16/2.86 | (11) all_10_0_3 = ex_9_0_2
% 7.16/2.86 |
% 7.16/2.86 +-Applying beta-rule and splitting (9), into two cases.
% 7.16/2.86 |-Branch one:
% 7.16/2.86 | (12) ~ (all_10_0_3 = ex_9_0_2)
% 7.16/2.86 |
% 7.16/2.86 | Equations (11) can reduce 12 to:
% 7.16/2.86 | (13) $false
% 7.16/2.86 |
% 7.16/2.86 |-The branch is then unsatisfiable
% 7.16/2.86 |-Branch two:
% 7.16/2.86 | (14) ! [v0] : ? [v1] : (( ~ (v1 = v0) | ~ big_f(ex_9_0_2, v0)) & (v1 = v0 | big_f(ex_9_0_2, v1)))
% 7.16/2.86 |
% 7.16/2.86 | Introducing new symbol ex_37_0_8 defined by:
% 7.16/2.86 | (15) ex_37_0_8 = all_0_0_0
% 7.16/2.86 |
% 7.16/2.86 | Instantiating formula (14) with ex_37_0_8 yields:
% 7.16/2.86 | (16) ? [v0] : (( ~ (v0 = ex_37_0_8) | ~ big_f(ex_9_0_2, ex_37_0_8)) & (v0 = ex_37_0_8 | big_f(ex_9_0_2, v0)))
% 7.16/2.86 |
% 7.16/2.86 | Instantiating (16) with all_38_0_9 yields:
% 7.16/2.86 | (17) ( ~ (all_38_0_9 = ex_37_0_8) | ~ big_f(ex_9_0_2, ex_37_0_8)) & (all_38_0_9 = ex_37_0_8 | big_f(ex_9_0_2, all_38_0_9))
% 7.16/2.86 |
% 7.16/2.86 | Applying alpha-rule on (17) yields:
% 7.16/2.86 | (18) ~ (all_38_0_9 = ex_37_0_8) | ~ big_f(ex_9_0_2, ex_37_0_8)
% 7.16/2.86 | (19) all_38_0_9 = ex_37_0_8 | big_f(ex_9_0_2, all_38_0_9)
% 7.16/2.86 |
% 7.16/2.86 +-Applying beta-rule and splitting (19), into two cases.
% 7.16/2.86 |-Branch one:
% 7.16/2.86 | (20) big_f(ex_9_0_2, all_38_0_9)
% 7.16/2.86 |
% 7.16/2.86 | Instantiating formula (5) with all_38_0_9, ex_9_0_2 and discharging atoms big_f(ex_9_0_2, all_38_0_9), yields:
% 7.16/2.86 | (21) all_38_0_9 = all_0_0_0 & ex_9_0_2 = all_0_1_1
% 7.16/2.86 |
% 7.16/2.86 | Applying alpha-rule on (21) yields:
% 7.16/2.86 | (22) all_38_0_9 = all_0_0_0
% 7.16/2.86 | (6) ex_9_0_2 = all_0_1_1
% 7.16/2.86 |
% 7.16/2.86 +-Applying beta-rule and splitting (18), into two cases.
% 7.16/2.86 |-Branch one:
% 7.16/2.86 | (24) ~ big_f(ex_9_0_2, ex_37_0_8)
% 7.16/2.86 |
% 7.16/2.86 | From (6) and (24) follows:
% 7.16/2.86 | (25) ~ big_f(all_0_1_1, ex_37_0_8)
% 7.16/2.86 |
% 7.16/2.86 | From (15) and (25) follows:
% 7.16/2.86 | (26) ~ big_f(all_0_1_1, all_0_0_0)
% 7.16/2.86 |
% 7.16/2.86 | Using (4) and (26) yields:
% 7.16/2.86 | (27) $false
% 7.16/2.86 |
% 7.16/2.86 |-The branch is then unsatisfiable
% 7.16/2.86 |-Branch two:
% 7.16/2.86 | (28) ~ (all_38_0_9 = ex_37_0_8)
% 7.16/2.86 |
% 7.16/2.86 | Equations (22) can reduce 28 to:
% 7.16/2.86 | (29) ~ (ex_37_0_8 = all_0_0_0)
% 7.16/2.86 |
% 7.16/2.86 | Simplifying 29 yields:
% 7.16/2.86 | (30) ~ (ex_37_0_8 = all_0_0_0)
% 7.16/2.86 |
% 7.16/2.86 | Equations (15) can reduce 30 to:
% 7.16/2.86 | (13) $false
% 7.16/2.86 |
% 7.16/2.86 |-The branch is then unsatisfiable
% 7.16/2.86 |-Branch two:
% 7.16/2.86 | (32) all_38_0_9 = ex_37_0_8
% 7.16/2.86 |
% 7.16/2.86 +-Applying beta-rule and splitting (18), into two cases.
% 7.16/2.86 |-Branch one:
% 7.16/2.86 | (24) ~ big_f(ex_9_0_2, ex_37_0_8)
% 7.16/2.86 |
% 7.16/2.86 | From (6)(15) and (24) follows:
% 7.16/2.86 | (26) ~ big_f(all_0_1_1, all_0_0_0)
% 7.16/2.87 |
% 7.16/2.87 | Using (4) and (26) yields:
% 7.16/2.87 | (27) $false
% 7.16/2.87 |
% 7.16/2.87 |-The branch is then unsatisfiable
% 7.16/2.87 |-Branch two:
% 7.16/2.87 | (28) ~ (all_38_0_9 = ex_37_0_8)
% 7.16/2.87 |
% 7.16/2.87 | Equations (32) can reduce 28 to:
% 7.16/2.87 | (13) $false
% 7.16/2.87 |
% 7.16/2.87 |-The branch is then unsatisfiable
% 7.16/2.87 |-Branch two:
% 7.16/2.87 | (12) ~ (all_10_0_3 = ex_9_0_2)
% 7.16/2.87 | (39) ? [v0] : (big_f(all_10_0_3, v0) & ! [v1] : (v1 = v0 | ~ big_f(all_10_0_3, v1)))
% 7.16/2.87 |
% 7.16/2.87 | Instantiating (39) with all_13_0_4 yields:
% 7.16/2.87 | (40) big_f(all_10_0_3, all_13_0_4) & ! [v0] : (v0 = all_13_0_4 | ~ big_f(all_10_0_3, v0))
% 7.16/2.87 |
% 7.16/2.87 | Applying alpha-rule on (40) yields:
% 7.16/2.87 | (41) big_f(all_10_0_3, all_13_0_4)
% 7.16/2.87 | (42) ! [v0] : (v0 = all_13_0_4 | ~ big_f(all_10_0_3, v0))
% 7.16/2.87 |
% 7.16/2.87 | Instantiating formula (5) with all_13_0_4, all_10_0_3 and discharging atoms big_f(all_10_0_3, all_13_0_4), yields:
% 7.16/2.87 | (43) all_13_0_4 = all_0_0_0 & all_10_0_3 = all_0_1_1
% 7.16/2.87 |
% 7.16/2.87 | Applying alpha-rule on (43) yields:
% 7.16/2.87 | (44) all_13_0_4 = all_0_0_0
% 7.16/2.87 | (45) all_10_0_3 = all_0_1_1
% 7.16/2.87 |
% 7.16/2.87 | Equations (45) can reduce 12 to:
% 7.16/2.87 | (46) ~ (ex_9_0_2 = all_0_1_1)
% 7.16/2.87 |
% 7.16/2.87 | Simplifying 46 yields:
% 7.16/2.87 | (47) ~ (ex_9_0_2 = all_0_1_1)
% 7.16/2.87 |
% 7.16/2.87 | Equations (6) can reduce 47 to:
% 7.16/2.87 | (13) $false
% 7.16/2.87 |
% 7.16/2.87 |-The branch is then unsatisfiable
% 7.16/2.87 % SZS output end Proof for theBenchmark
% 7.16/2.87
% 7.16/2.87 2293ms
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