TSTP Solution File: SYN551+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n003.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 05:03:42 EDT 2022
% Result : Theorem 61.46s 48.58s
% Output : Proof 96.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n003.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jul 11 13:20:15 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.56 ____ _
% 0.17/0.56 ___ / __ \_____(_)___ ________ __________
% 0.17/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.17/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.17/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.17/0.56
% 0.17/0.56 A Theorem Prover for First-Order Logic
% 0.17/0.56 (ePrincess v.1.0)
% 0.17/0.56
% 0.17/0.56 (c) Philipp Rümmer, 2009-2015
% 0.17/0.56 (c) Peter Backeman, 2014-2015
% 0.17/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.17/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.17/0.57 Bug reports to peter@backeman.se
% 0.17/0.57
% 0.17/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.17/0.57
% 0.17/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.17/0.92 Prover 0: Preprocessing ...
% 1.36/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.36/1.05 Prover 0: Constructing countermodel ...
% 1.96/1.23 Prover 0: gave up
% 1.96/1.23 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.05/1.24 Prover 1: Preprocessing ...
% 2.05/1.30 Prover 1: Warning: ignoring some quantifiers
% 2.05/1.30 Prover 1: Constructing countermodel ...
% 2.26/1.34 Prover 1: gave up
% 2.26/1.35 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.26/1.35 Prover 2: Preprocessing ...
% 2.26/1.38 Prover 2: Warning: ignoring some quantifiers
% 2.26/1.38 Prover 2: Constructing countermodel ...
% 2.47/1.42 Prover 2: gave up
% 2.47/1.42 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.47/1.42 Prover 3: Preprocessing ...
% 2.47/1.45 Prover 3: Warning: ignoring some quantifiers
% 2.47/1.45 Prover 3: Constructing countermodel ...
% 2.78/1.50 Prover 3: gave up
% 2.78/1.50 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.90/1.51 Prover 4: Preprocessing ...
% 2.99/1.55 Prover 4: Warning: ignoring some quantifiers
% 2.99/1.55 Prover 4: Constructing countermodel ...
% 2.99/1.58 Prover 4: gave up
% 2.99/1.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.99/1.59 Prover 5: Preprocessing ...
% 2.99/1.62 Prover 5: Warning: ignoring some quantifiers
% 2.99/1.62 Prover 5: Constructing countermodel ...
% 3.24/1.65 Prover 5: gave up
% 3.24/1.65 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.24/1.66 Prover 6: Preprocessing ...
% 3.40/1.69 Prover 6: Warning: ignoring some quantifiers
% 3.40/1.69 Prover 6: Constructing countermodel ...
% 3.40/1.73 Prover 6: gave up
% 3.40/1.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.40/1.73 Prover 7: Preprocessing ...
% 3.40/1.76 Prover 7: Proving ...
% 18.56/12.67 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 18.56/12.67 Prover 8: Preprocessing ...
% 18.69/12.70 Prover 8: Proving ...
% 40.26/31.23 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal
% 40.26/31.24 Prover 9: Preprocessing ...
% 40.26/31.26 Prover 9: Proving ...
% 61.46/48.57 Prover 9: proved (16935ms)
% 61.46/48.57 Prover 8: stopped
% 61.46/48.57 Prover 7: stopped
% 61.46/48.58
% 61.46/48.58 % SZS status Theorem for theBenchmark
% 61.46/48.58
% 61.46/48.58 Generating proof ... found it (size 119)
% 95.78/76.95
% 95.78/76.95 % SZS output start Proof for theBenchmark
% 95.78/76.96 Assumed formulas after preprocessing and simplification:
% 95.78/76.96 | (0) ? [v0] : ( ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (g(v3) = v2) | ~ (g(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (f(v3) = v2) | ~ (f(v3) = v1)) & (( ! [v1] : ? [v2] : ? [v3] : (g(v2) = v3 & f(v1) = v2 & ( ~ (v3 = v1) | v1 = v0) & ( ~ (v1 = v0) | v3 = v0)) & ! [v1] : ? [v2] : ? [v3] : ? [v4] : (g(v2) = v3 & f(v3) = v4 & ( ~ (v4 = v1) | ~ (v2 = v1)) & (v4 = v2 | v2 = v1))) | ( ! [v1] : ? [v2] : ? [v3] : (g(v1) = v2 & f(v2) = v3 & ( ~ (v3 = v1) | v1 = v0) & ( ~ (v1 = v0) | v3 = v0)) & ! [v1] : ? [v2] : ? [v3] : ? [v4] : (g(v3) = v4 & f(v2) = v3 & ( ~ (v4 = v1) | ~ (v2 = v1)) & (v4 = v2 | v2 = v1)))))
% 95.78/76.98 | Instantiating (0) with all_0_0_0 yields:
% 95.78/76.98 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & (( ! [v0] : ? [v1] : ? [v2] : (g(v1) = v2 & f(v0) = v1 & ( ~ (v2 = v0) | v0 = all_0_0_0) & ( ~ (v0 = all_0_0_0) | v2 = all_0_0_0)) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : (g(v1) = v2 & f(v2) = v3 & ( ~ (v3 = v0) | ~ (v1 = v0)) & (v3 = v1 | v1 = v0))) | ( ! [v0] : ? [v1] : ? [v2] : (g(v0) = v1 & f(v1) = v2 & ( ~ (v2 = v0) | v0 = all_0_0_0) & ( ~ (v0 = all_0_0_0) | v2 = all_0_0_0)) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : (g(v2) = v3 & f(v1) = v2 & ( ~ (v3 = v0) | ~ (v1 = v0)) & (v3 = v1 | v1 = v0))))
% 95.78/76.98 |
% 95.78/76.98 | Applying alpha-rule on (1) yields:
% 95.78/76.98 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0))
% 95.78/76.98 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 95.78/76.98 | (4) ( ! [v0] : ? [v1] : ? [v2] : (g(v1) = v2 & f(v0) = v1 & ( ~ (v2 = v0) | v0 = all_0_0_0) & ( ~ (v0 = all_0_0_0) | v2 = all_0_0_0)) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : (g(v1) = v2 & f(v2) = v3 & ( ~ (v3 = v0) | ~ (v1 = v0)) & (v3 = v1 | v1 = v0))) | ( ! [v0] : ? [v1] : ? [v2] : (g(v0) = v1 & f(v1) = v2 & ( ~ (v2 = v0) | v0 = all_0_0_0) & ( ~ (v0 = all_0_0_0) | v2 = all_0_0_0)) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : (g(v2) = v3 & f(v1) = v2 & ( ~ (v3 = v0) | ~ (v1 = v0)) & (v3 = v1 | v1 = v0)))
% 95.78/76.98 |
% 95.78/76.98 +-Applying beta-rule and splitting (4), into two cases.
% 95.78/76.98 |-Branch one:
% 95.78/76.98 | (5) ! [v0] : ? [v1] : ? [v2] : (g(v1) = v2 & f(v0) = v1 & ( ~ (v2 = v0) | v0 = all_0_0_0) & ( ~ (v0 = all_0_0_0) | v2 = all_0_0_0)) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : (g(v1) = v2 & f(v2) = v3 & ( ~ (v3 = v0) | ~ (v1 = v0)) & (v3 = v1 | v1 = v0))
% 95.78/76.98 |
% 95.78/76.98 | Applying alpha-rule on (5) yields:
% 95.78/76.98 | (6) ! [v0] : ? [v1] : ? [v2] : (g(v1) = v2 & f(v0) = v1 & ( ~ (v2 = v0) | v0 = all_0_0_0) & ( ~ (v0 = all_0_0_0) | v2 = all_0_0_0))
% 95.78/76.98 | (7) ! [v0] : ? [v1] : ? [v2] : ? [v3] : (g(v1) = v2 & f(v2) = v3 & ( ~ (v3 = v0) | ~ (v1 = v0)) & (v3 = v1 | v1 = v0))
% 95.78/76.98 |
% 95.78/76.98 | Introducing new symbol ex_28_0_5 defined by:
% 95.78/76.98 | (8) ex_28_0_5 = all_0_0_0
% 95.78/76.98 |
% 95.78/76.98 | Instantiating formula (6) with ex_28_0_5 yields:
% 95.78/76.98 | (9) ? [v0] : ? [v1] : (g(v0) = v1 & f(ex_28_0_5) = v0 & ( ~ (v1 = ex_28_0_5) | ex_28_0_5 = all_0_0_0) & ( ~ (ex_28_0_5 = all_0_0_0) | v1 = all_0_0_0))
% 95.78/76.98 |
% 95.78/76.98 | Instantiating (9) with all_29_0_6, all_29_1_7 yields:
% 95.78/76.98 | (10) g(all_29_1_7) = all_29_0_6 & f(ex_28_0_5) = all_29_1_7 & ( ~ (all_29_0_6 = ex_28_0_5) | ex_28_0_5 = all_0_0_0) & ( ~ (ex_28_0_5 = all_0_0_0) | all_29_0_6 = all_0_0_0)
% 95.78/76.98 |
% 95.78/76.98 | Applying alpha-rule on (10) yields:
% 95.78/76.98 | (11) g(all_29_1_7) = all_29_0_6
% 95.78/76.98 | (12) f(ex_28_0_5) = all_29_1_7
% 95.78/76.98 | (13) ~ (all_29_0_6 = ex_28_0_5) | ex_28_0_5 = all_0_0_0
% 95.78/76.98 | (14) ~ (ex_28_0_5 = all_0_0_0) | all_29_0_6 = all_0_0_0
% 95.78/76.98 |
% 95.78/76.98 +-Applying beta-rule and splitting (13), into two cases.
% 95.78/76.98 |-Branch one:
% 95.78/76.98 | (15) ~ (all_29_0_6 = ex_28_0_5)
% 95.78/76.98 |
% 95.78/76.98 +-Applying beta-rule and splitting (14), into two cases.
% 95.78/76.98 |-Branch one:
% 95.78/76.98 | (16) all_29_0_6 = all_0_0_0
% 95.78/76.99 |
% 95.78/76.99 | Equations (16) can reduce 15 to:
% 95.78/76.99 | (17) ~ (ex_28_0_5 = all_0_0_0)
% 95.78/76.99 |
% 95.78/76.99 | Simplifying 17 yields:
% 95.78/76.99 | (18) ~ (ex_28_0_5 = all_0_0_0)
% 95.78/76.99 |
% 95.78/76.99 | Equations (8) can reduce 18 to:
% 95.78/76.99 | (19) $false
% 95.78/76.99 |
% 95.78/76.99 |-The branch is then unsatisfiable
% 95.78/76.99 |-Branch two:
% 95.78/76.99 | (18) ~ (ex_28_0_5 = all_0_0_0)
% 95.78/76.99 |
% 95.78/76.99 | Equations (8) can reduce 18 to:
% 95.78/76.99 | (19) $false
% 95.78/76.99 |
% 95.78/76.99 |-The branch is then unsatisfiable
% 95.78/76.99 |-Branch two:
% 95.78/76.99 | (22) all_29_0_6 = ex_28_0_5
% 95.78/76.99 | (8) ex_28_0_5 = all_0_0_0
% 95.78/76.99 |
% 95.78/76.99 | Combining equations (8,22) yields a new equation:
% 95.78/76.99 | (16) all_29_0_6 = all_0_0_0
% 95.78/76.99 |
% 95.78/76.99 | From (16) and (11) follows:
% 95.78/76.99 | (25) g(all_29_1_7) = all_0_0_0
% 95.78/76.99 |
% 95.78/76.99 | From (8) and (12) follows:
% 95.78/76.99 | (26) f(all_0_0_0) = all_29_1_7
% 95.78/76.99 |
% 95.78/76.99 | Introducing new symbol ex_44_0_8 defined by:
% 95.78/76.99 | (27) ex_44_0_8 = all_29_1_7
% 95.78/76.99 |
% 95.78/76.99 | Instantiating formula (7) with ex_44_0_8 yields:
% 95.78/76.99 | (28) ? [v0] : ? [v1] : ? [v2] : (g(v0) = v1 & f(v1) = v2 & ( ~ (v2 = ex_44_0_8) | ~ (v0 = ex_44_0_8)) & (v2 = v0 | v0 = ex_44_0_8))
% 95.78/76.99 |
% 95.78/76.99 | Instantiating (28) with all_45_0_9, all_45_1_10, all_45_2_11 yields:
% 95.78/76.99 | (29) g(all_45_2_11) = all_45_1_10 & f(all_45_1_10) = all_45_0_9 & ( ~ (all_45_0_9 = ex_44_0_8) | ~ (all_45_2_11 = ex_44_0_8)) & (all_45_0_9 = all_45_2_11 | all_45_2_11 = ex_44_0_8)
% 95.78/76.99 |
% 95.78/76.99 | Applying alpha-rule on (29) yields:
% 95.78/76.99 | (30) g(all_45_2_11) = all_45_1_10
% 95.78/76.99 | (31) f(all_45_1_10) = all_45_0_9
% 95.78/76.99 | (32) ~ (all_45_0_9 = ex_44_0_8) | ~ (all_45_2_11 = ex_44_0_8)
% 95.78/76.99 | (33) all_45_0_9 = all_45_2_11 | all_45_2_11 = ex_44_0_8
% 95.78/76.99 |
% 95.78/76.99 +-Applying beta-rule and splitting (32), into two cases.
% 95.78/76.99 |-Branch one:
% 95.78/76.99 | (34) ~ (all_45_0_9 = ex_44_0_8)
% 95.78/76.99 |
% 95.78/76.99 +-Applying beta-rule and splitting (33), into two cases.
% 95.78/76.99 |-Branch one:
% 95.78/76.99 | (35) all_45_0_9 = all_45_2_11
% 95.78/76.99 |
% 95.78/76.99 | Equations (35) can reduce 34 to:
% 95.78/76.99 | (36) ~ (all_45_2_11 = ex_44_0_8)
% 95.78/76.99 |
% 95.78/76.99 | From (35) and (31) follows:
% 95.78/76.99 | (37) f(all_45_1_10) = all_45_2_11
% 95.78/76.99 |
% 95.78/76.99 | Introducing new symbol ex_66_0_16 defined by:
% 96.23/76.99 | (38) ex_66_0_16 = all_45_1_10
% 96.23/76.99 |
% 96.23/76.99 | Instantiating formula (6) with ex_66_0_16 yields:
% 96.23/76.99 | (39) ? [v0] : ? [v1] : (g(v0) = v1 & f(ex_66_0_16) = v0 & ( ~ (v1 = ex_66_0_16) | ex_66_0_16 = all_0_0_0) & ( ~ (ex_66_0_16 = all_0_0_0) | v1 = all_0_0_0))
% 96.23/76.99 |
% 96.23/76.99 | Instantiating (39) with all_67_0_17, all_67_1_18 yields:
% 96.23/76.99 | (40) g(all_67_1_18) = all_67_0_17 & f(ex_66_0_16) = all_67_1_18 & ( ~ (all_67_0_17 = ex_66_0_16) | ex_66_0_16 = all_0_0_0) & ( ~ (ex_66_0_16 = all_0_0_0) | all_67_0_17 = all_0_0_0)
% 96.23/76.99 |
% 96.23/76.99 | Applying alpha-rule on (40) yields:
% 96.23/76.99 | (41) g(all_67_1_18) = all_67_0_17
% 96.23/76.99 | (42) f(ex_66_0_16) = all_67_1_18
% 96.23/76.99 | (43) ~ (all_67_0_17 = ex_66_0_16) | ex_66_0_16 = all_0_0_0
% 96.23/76.99 | (44) ~ (ex_66_0_16 = all_0_0_0) | all_67_0_17 = all_0_0_0
% 96.23/76.99 |
% 96.23/76.99 +-Applying beta-rule and splitting (43), into two cases.
% 96.23/76.99 |-Branch one:
% 96.23/76.99 | (45) ~ (all_67_0_17 = ex_66_0_16)
% 96.23/76.99 |
% 96.23/76.99 | Equations (38) can reduce 45 to:
% 96.23/76.99 | (46) ~ (all_67_0_17 = all_45_1_10)
% 96.23/76.99 |
% 96.23/76.99 | From (38) and (42) follows:
% 96.24/76.99 | (47) f(all_45_1_10) = all_67_1_18
% 96.24/76.99 |
% 96.24/76.99 | Instantiating formula (3) with all_45_1_10, all_45_2_11, all_67_1_18 and discharging atoms f(all_45_1_10) = all_67_1_18, f(all_45_1_10) = all_45_2_11, yields:
% 96.24/76.99 | (48) all_67_1_18 = all_45_2_11
% 96.24/76.99 |
% 96.24/76.99 | From (48) and (41) follows:
% 96.24/76.99 | (49) g(all_45_2_11) = all_67_0_17
% 96.24/76.99 |
% 96.24/76.99 | Instantiating formula (2) with all_45_2_11, all_67_0_17, all_45_1_10 and discharging atoms g(all_45_2_11) = all_67_0_17, g(all_45_2_11) = all_45_1_10, yields:
% 96.24/76.99 | (50) all_67_0_17 = all_45_1_10
% 96.24/76.99 |
% 96.24/76.99 | Equations (50) can reduce 46 to:
% 96.24/76.99 | (19) $false
% 96.24/76.99 |
% 96.24/76.99 |-The branch is then unsatisfiable
% 96.24/76.99 |-Branch two:
% 96.24/76.99 | (52) ex_66_0_16 = all_0_0_0
% 96.24/76.99 |
% 96.24/76.99 | Combining equations (38,52) yields a new equation:
% 96.24/76.99 | (53) all_45_1_10 = all_0_0_0
% 96.24/76.99 |
% 96.24/76.99 | Simplifying 53 yields:
% 96.24/76.99 | (54) all_45_1_10 = all_0_0_0
% 96.24/76.99 |
% 96.24/76.99 | Equations (27) can reduce 36 to:
% 96.24/76.99 | (55) ~ (all_45_2_11 = all_29_1_7)
% 96.24/76.99 |
% 96.24/76.99 | From (54) and (37) follows:
% 96.24/76.99 | (56) f(all_0_0_0) = all_45_2_11
% 96.24/76.99 |
% 96.24/76.99 | Instantiating formula (3) with all_0_0_0, all_29_1_7, all_45_2_11 and discharging atoms f(all_0_0_0) = all_45_2_11, f(all_0_0_0) = all_29_1_7, yields:
% 96.24/76.99 | (57) all_45_2_11 = all_29_1_7
% 96.24/76.99 |
% 96.24/76.99 | Equations (57) can reduce 55 to:
% 96.24/76.99 | (19) $false
% 96.24/76.99 |
% 96.24/76.99 |-The branch is then unsatisfiable
% 96.24/76.99 |-Branch two:
% 96.24/76.99 | (59) all_45_2_11 = ex_44_0_8
% 96.24/76.99 |
% 96.24/76.99 | From (59) and (30) follows:
% 96.24/76.99 | (60) g(ex_44_0_8) = all_45_1_10
% 96.24/76.99 |
% 96.24/76.99 | Equations (27) can reduce 34 to:
% 96.24/76.99 | (61) ~ (all_45_0_9 = all_29_1_7)
% 96.24/77.00 |
% 96.24/77.00 | From (27) and (60) follows:
% 96.24/77.00 | (62) g(all_29_1_7) = all_45_1_10
% 96.24/77.00 |
% 96.24/77.00 | Instantiating formula (2) with all_29_1_7, all_0_0_0, all_45_1_10 and discharging atoms g(all_29_1_7) = all_45_1_10, g(all_29_1_7) = all_0_0_0, yields:
% 96.24/77.00 | (54) all_45_1_10 = all_0_0_0
% 96.24/77.00 |
% 96.24/77.00 | From (54) and (31) follows:
% 96.24/77.00 | (64) f(all_0_0_0) = all_45_0_9
% 96.24/77.00 |
% 96.24/77.00 | Instantiating formula (3) with all_0_0_0, all_45_0_9, all_29_1_7 and discharging atoms f(all_0_0_0) = all_45_0_9, f(all_0_0_0) = all_29_1_7, yields:
% 96.24/77.00 | (65) all_45_0_9 = all_29_1_7
% 96.24/77.00 |
% 96.24/77.00 | Equations (65) can reduce 61 to:
% 96.24/77.00 | (19) $false
% 96.24/77.00 |
% 96.24/77.00 |-The branch is then unsatisfiable
% 96.24/77.00 |-Branch two:
% 96.24/77.00 | (67) all_45_0_9 = ex_44_0_8
% 96.24/77.00 | (36) ~ (all_45_2_11 = ex_44_0_8)
% 96.24/77.00 |
% 96.24/77.00 +-Applying beta-rule and splitting (33), into two cases.
% 96.24/77.00 |-Branch one:
% 96.24/77.00 | (35) all_45_0_9 = all_45_2_11
% 96.24/77.00 |
% 96.24/77.00 | Combining equations (35,67) yields a new equation:
% 96.24/77.00 | (70) all_45_2_11 = ex_44_0_8
% 96.24/77.00 |
% 96.24/77.00 | Simplifying 70 yields:
% 96.24/77.00 | (59) all_45_2_11 = ex_44_0_8
% 96.24/77.00 |
% 96.24/77.00 | Equations (59) can reduce 36 to:
% 96.24/77.00 | (19) $false
% 96.24/77.00 |
% 96.24/77.00 |-The branch is then unsatisfiable
% 96.24/77.00 |-Branch two:
% 96.24/77.00 | (59) all_45_2_11 = ex_44_0_8
% 96.24/77.00 |
% 96.24/77.00 | Equations (59) can reduce 36 to:
% 96.24/77.00 | (19) $false
% 96.24/77.00 |
% 96.24/77.00 |-The branch is then unsatisfiable
% 96.24/77.00 |-Branch two:
% 96.24/77.00 | (75) ! [v0] : ? [v1] : ? [v2] : (g(v0) = v1 & f(v1) = v2 & ( ~ (v2 = v0) | v0 = all_0_0_0) & ( ~ (v0 = all_0_0_0) | v2 = all_0_0_0)) & ! [v0] : ? [v1] : ? [v2] : ? [v3] : (g(v2) = v3 & f(v1) = v2 & ( ~ (v3 = v0) | ~ (v1 = v0)) & (v3 = v1 | v1 = v0))
% 96.24/77.00 |
% 96.24/77.00 | Applying alpha-rule on (75) yields:
% 96.24/77.00 | (76) ! [v0] : ? [v1] : ? [v2] : (g(v0) = v1 & f(v1) = v2 & ( ~ (v2 = v0) | v0 = all_0_0_0) & ( ~ (v0 = all_0_0_0) | v2 = all_0_0_0))
% 96.28/77.00 | (77) ! [v0] : ? [v1] : ? [v2] : ? [v3] : (g(v2) = v3 & f(v1) = v2 & ( ~ (v3 = v0) | ~ (v1 = v0)) & (v3 = v1 | v1 = v0))
% 96.28/77.00 |
% 96.28/77.00 | Introducing new symbol ex_28_0_66 defined by:
% 96.28/77.00 | (78) ex_28_0_66 = all_0_0_0
% 96.28/77.00 |
% 96.28/77.00 | Instantiating formula (76) with ex_28_0_66 yields:
% 96.28/77.00 | (79) ? [v0] : ? [v1] : (g(ex_28_0_66) = v0 & f(v0) = v1 & ( ~ (v1 = ex_28_0_66) | ex_28_0_66 = all_0_0_0) & ( ~ (ex_28_0_66 = all_0_0_0) | v1 = all_0_0_0))
% 96.28/77.00 |
% 96.28/77.00 | Instantiating (79) with all_29_0_67, all_29_1_68 yields:
% 96.28/77.00 | (80) g(ex_28_0_66) = all_29_1_68 & f(all_29_1_68) = all_29_0_67 & ( ~ (all_29_0_67 = ex_28_0_66) | ex_28_0_66 = all_0_0_0) & ( ~ (ex_28_0_66 = all_0_0_0) | all_29_0_67 = all_0_0_0)
% 96.28/77.00 |
% 96.28/77.00 | Applying alpha-rule on (80) yields:
% 96.28/77.00 | (81) g(ex_28_0_66) = all_29_1_68
% 96.28/77.00 | (82) f(all_29_1_68) = all_29_0_67
% 96.28/77.00 | (83) ~ (all_29_0_67 = ex_28_0_66) | ex_28_0_66 = all_0_0_0
% 96.28/77.00 | (84) ~ (ex_28_0_66 = all_0_0_0) | all_29_0_67 = all_0_0_0
% 96.28/77.00 |
% 96.28/77.00 +-Applying beta-rule and splitting (83), into two cases.
% 96.28/77.00 |-Branch one:
% 96.28/77.00 | (85) ~ (all_29_0_67 = ex_28_0_66)
% 96.28/77.00 |
% 96.28/77.00 +-Applying beta-rule and splitting (84), into two cases.
% 96.28/77.00 |-Branch one:
% 96.28/77.00 | (86) all_29_0_67 = all_0_0_0
% 96.28/77.00 |
% 96.28/77.00 | Equations (86) can reduce 85 to:
% 96.28/77.00 | (87) ~ (ex_28_0_66 = all_0_0_0)
% 96.28/77.00 |
% 96.28/77.00 | Simplifying 87 yields:
% 96.28/77.00 | (88) ~ (ex_28_0_66 = all_0_0_0)
% 96.28/77.00 |
% 96.28/77.00 | Equations (78) can reduce 88 to:
% 96.28/77.00 | (19) $false
% 96.28/77.00 |
% 96.28/77.00 |-The branch is then unsatisfiable
% 96.28/77.00 |-Branch two:
% 96.28/77.00 | (88) ~ (ex_28_0_66 = all_0_0_0)
% 96.28/77.00 |
% 96.28/77.00 | Equations (78) can reduce 88 to:
% 96.28/77.00 | (19) $false
% 96.28/77.00 |
% 96.28/77.00 |-The branch is then unsatisfiable
% 96.28/77.00 |-Branch two:
% 96.28/77.00 | (92) all_29_0_67 = ex_28_0_66
% 96.28/77.00 | (78) ex_28_0_66 = all_0_0_0
% 96.28/77.00 |
% 96.28/77.00 | Combining equations (78,92) yields a new equation:
% 96.28/77.00 | (86) all_29_0_67 = all_0_0_0
% 96.28/77.00 |
% 96.28/77.00 | From (78) and (81) follows:
% 96.28/77.00 | (95) g(all_0_0_0) = all_29_1_68
% 96.28/77.00 |
% 96.28/77.00 | From (86) and (82) follows:
% 96.30/77.00 | (96) f(all_29_1_68) = all_0_0_0
% 96.30/77.00 |
% 96.30/77.00 | Introducing new symbol ex_44_0_73 defined by:
% 96.30/77.00 | (97) ex_44_0_73 = all_29_1_68
% 96.30/77.00 |
% 96.30/77.00 | Instantiating formula (77) with ex_44_0_73 yields:
% 96.30/77.00 | (98) ? [v0] : ? [v1] : ? [v2] : (g(v1) = v2 & f(v0) = v1 & ( ~ (v2 = ex_44_0_73) | ~ (v0 = ex_44_0_73)) & (v2 = v0 | v0 = ex_44_0_73))
% 96.30/77.00 |
% 96.30/77.00 | Instantiating (98) with all_45_0_74, all_45_1_75, all_45_2_76 yields:
% 96.30/77.00 | (99) g(all_45_1_75) = all_45_0_74 & f(all_45_2_76) = all_45_1_75 & ( ~ (all_45_0_74 = ex_44_0_73) | ~ (all_45_2_76 = ex_44_0_73)) & (all_45_0_74 = all_45_2_76 | all_45_2_76 = ex_44_0_73)
% 96.30/77.01 |
% 96.30/77.01 | Applying alpha-rule on (99) yields:
% 96.30/77.01 | (100) g(all_45_1_75) = all_45_0_74
% 96.30/77.01 | (101) f(all_45_2_76) = all_45_1_75
% 96.30/77.01 | (102) ~ (all_45_0_74 = ex_44_0_73) | ~ (all_45_2_76 = ex_44_0_73)
% 96.30/77.01 | (103) all_45_0_74 = all_45_2_76 | all_45_2_76 = ex_44_0_73
% 96.30/77.01 |
% 96.30/77.01 +-Applying beta-rule and splitting (102), into two cases.
% 96.30/77.01 |-Branch one:
% 96.30/77.01 | (104) ~ (all_45_0_74 = ex_44_0_73)
% 96.30/77.01 |
% 96.30/77.01 +-Applying beta-rule and splitting (103), into two cases.
% 96.30/77.01 |-Branch one:
% 96.30/77.01 | (105) all_45_0_74 = all_45_2_76
% 96.30/77.01 |
% 96.30/77.01 | Equations (105) can reduce 104 to:
% 96.30/77.01 | (106) ~ (all_45_2_76 = ex_44_0_73)
% 96.30/77.01 |
% 96.30/77.01 | From (105) and (100) follows:
% 96.30/77.01 | (107) g(all_45_1_75) = all_45_2_76
% 96.30/77.01 |
% 96.30/77.01 | Introducing new symbol ex_66_0_80 defined by:
% 96.30/77.01 | (108) ex_66_0_80 = all_45_1_75
% 96.30/77.01 |
% 96.30/77.01 | Instantiating formula (76) with ex_66_0_80 yields:
% 96.30/77.01 | (109) ? [v0] : ? [v1] : (g(ex_66_0_80) = v0 & f(v0) = v1 & ( ~ (v1 = ex_66_0_80) | ex_66_0_80 = all_0_0_0) & ( ~ (ex_66_0_80 = all_0_0_0) | v1 = all_0_0_0))
% 96.30/77.01 |
% 96.30/77.01 | Instantiating (109) with all_67_0_81, all_67_1_82 yields:
% 96.30/77.01 | (110) g(ex_66_0_80) = all_67_1_82 & f(all_67_1_82) = all_67_0_81 & ( ~ (all_67_0_81 = ex_66_0_80) | ex_66_0_80 = all_0_0_0) & ( ~ (ex_66_0_80 = all_0_0_0) | all_67_0_81 = all_0_0_0)
% 96.30/77.01 |
% 96.30/77.01 | Applying alpha-rule on (110) yields:
% 96.30/77.01 | (111) g(ex_66_0_80) = all_67_1_82
% 96.30/77.01 | (112) f(all_67_1_82) = all_67_0_81
% 96.30/77.01 | (113) ~ (all_67_0_81 = ex_66_0_80) | ex_66_0_80 = all_0_0_0
% 96.30/77.01 | (114) ~ (ex_66_0_80 = all_0_0_0) | all_67_0_81 = all_0_0_0
% 96.30/77.01 |
% 96.30/77.01 +-Applying beta-rule and splitting (113), into two cases.
% 96.30/77.01 |-Branch one:
% 96.30/77.01 | (115) ~ (all_67_0_81 = ex_66_0_80)
% 96.30/77.01 |
% 96.30/77.01 | Equations (108) can reduce 115 to:
% 96.30/77.01 | (116) ~ (all_67_0_81 = all_45_1_75)
% 96.30/77.01 |
% 96.30/77.01 | From (108) and (111) follows:
% 96.30/77.01 | (117) g(all_45_1_75) = all_67_1_82
% 96.30/77.01 |
% 96.30/77.01 | Instantiating formula (2) with all_45_1_75, all_45_2_76, all_67_1_82 and discharging atoms g(all_45_1_75) = all_67_1_82, g(all_45_1_75) = all_45_2_76, yields:
% 96.30/77.01 | (118) all_67_1_82 = all_45_2_76
% 96.30/77.01 |
% 96.30/77.01 | From (118) and (112) follows:
% 96.30/77.01 | (119) f(all_45_2_76) = all_67_0_81
% 96.30/77.01 |
% 96.30/77.01 | Instantiating formula (3) with all_45_2_76, all_67_0_81, all_45_1_75 and discharging atoms f(all_45_2_76) = all_67_0_81, f(all_45_2_76) = all_45_1_75, yields:
% 96.30/77.01 | (120) all_67_0_81 = all_45_1_75
% 96.30/77.01 |
% 96.30/77.01 | Equations (120) can reduce 116 to:
% 96.30/77.01 | (19) $false
% 96.30/77.01 |
% 96.30/77.01 |-The branch is then unsatisfiable
% 96.30/77.01 |-Branch two:
% 96.30/77.01 | (122) ex_66_0_80 = all_0_0_0
% 96.30/77.01 |
% 96.30/77.01 | Combining equations (108,122) yields a new equation:
% 96.30/77.01 | (123) all_45_1_75 = all_0_0_0
% 96.30/77.01 |
% 96.30/77.01 | Simplifying 123 yields:
% 96.30/77.01 | (124) all_45_1_75 = all_0_0_0
% 96.30/77.01 |
% 96.30/77.01 | Equations (97) can reduce 106 to:
% 96.30/77.01 | (125) ~ (all_45_2_76 = all_29_1_68)
% 96.30/77.01 |
% 96.30/77.01 | From (124) and (107) follows:
% 96.30/77.01 | (126) g(all_0_0_0) = all_45_2_76
% 96.30/77.01 |
% 96.30/77.01 | Instantiating formula (2) with all_0_0_0, all_29_1_68, all_45_2_76 and discharging atoms g(all_0_0_0) = all_45_2_76, g(all_0_0_0) = all_29_1_68, yields:
% 96.30/77.01 | (127) all_45_2_76 = all_29_1_68
% 96.30/77.01 |
% 96.30/77.01 | Equations (127) can reduce 125 to:
% 96.30/77.01 | (19) $false
% 96.30/77.01 |
% 96.30/77.01 |-The branch is then unsatisfiable
% 96.30/77.01 |-Branch two:
% 96.30/77.01 | (129) all_45_2_76 = ex_44_0_73
% 96.30/77.01 |
% 96.30/77.01 | From (129) and (101) follows:
% 96.30/77.01 | (130) f(ex_44_0_73) = all_45_1_75
% 96.30/77.01 |
% 96.30/77.01 | Equations (97) can reduce 104 to:
% 96.30/77.01 | (131) ~ (all_45_0_74 = all_29_1_68)
% 96.30/77.01 |
% 96.30/77.01 | From (97) and (130) follows:
% 96.30/77.01 | (132) f(all_29_1_68) = all_45_1_75
% 96.30/77.01 |
% 96.30/77.01 | Instantiating formula (3) with all_29_1_68, all_0_0_0, all_45_1_75 and discharging atoms f(all_29_1_68) = all_45_1_75, f(all_29_1_68) = all_0_0_0, yields:
% 96.30/77.01 | (124) all_45_1_75 = all_0_0_0
% 96.30/77.01 |
% 96.30/77.01 | From (124) and (100) follows:
% 96.30/77.01 | (134) g(all_0_0_0) = all_45_0_74
% 96.30/77.01 |
% 96.30/77.01 | Instantiating formula (2) with all_0_0_0, all_45_0_74, all_29_1_68 and discharging atoms g(all_0_0_0) = all_45_0_74, g(all_0_0_0) = all_29_1_68, yields:
% 96.30/77.01 | (135) all_45_0_74 = all_29_1_68
% 96.30/77.01 |
% 96.30/77.02 | Equations (135) can reduce 131 to:
% 96.30/77.02 | (19) $false
% 96.30/77.02 |
% 96.30/77.02 |-The branch is then unsatisfiable
% 96.30/77.02 |-Branch two:
% 96.30/77.02 | (137) all_45_0_74 = ex_44_0_73
% 96.30/77.02 | (106) ~ (all_45_2_76 = ex_44_0_73)
% 96.30/77.02 |
% 96.30/77.02 +-Applying beta-rule and splitting (103), into two cases.
% 96.30/77.02 |-Branch one:
% 96.30/77.02 | (105) all_45_0_74 = all_45_2_76
% 96.30/77.02 |
% 96.30/77.02 | Combining equations (105,137) yields a new equation:
% 96.30/77.02 | (140) all_45_2_76 = ex_44_0_73
% 96.30/77.02 |
% 96.30/77.02 | Simplifying 140 yields:
% 96.30/77.02 | (129) all_45_2_76 = ex_44_0_73
% 96.30/77.02 |
% 96.30/77.02 | Equations (129) can reduce 106 to:
% 96.30/77.02 | (19) $false
% 96.30/77.02 |
% 96.30/77.02 |-The branch is then unsatisfiable
% 96.30/77.02 |-Branch two:
% 96.30/77.02 | (129) all_45_2_76 = ex_44_0_73
% 96.30/77.02 |
% 96.30/77.02 | Equations (129) can reduce 106 to:
% 96.30/77.02 | (19) $false
% 96.30/77.02 |
% 96.30/77.02 |-The branch is then unsatisfiable
% 96.30/77.02 % SZS output end Proof for theBenchmark
% 96.30/77.02
% 96.30/77.02 76439ms
%------------------------------------------------------------------------------