TSTP Solution File: SYN081+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN081+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 04:59:48 EDT 2022
% Result : Theorem 2.36s 1.28s
% Output : Proof 3.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN081+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n007.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 16:15:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 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 ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.22/0.88 Prover 0: Preprocessing ...
% 1.37/0.95 Prover 0: Constructing countermodel ...
% 1.37/0.99 Prover 0: gave up
% 1.37/0.99 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.37/1.01 Prover 1: Preprocessing ...
% 1.57/1.05 Prover 1: Constructing countermodel ...
% 1.57/1.06 Prover 1: gave up
% 1.57/1.06 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.57/1.07 Prover 2: Preprocessing ...
% 1.86/1.12 Prover 2: Warning: ignoring some quantifiers
% 1.86/1.13 Prover 2: Constructing countermodel ...
% 1.86/1.16 Prover 2: gave up
% 1.86/1.16 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.86/1.18 Prover 3: Preprocessing ...
% 2.15/1.19 Prover 3: Constructing countermodel ...
% 2.15/1.19 Prover 3: gave up
% 2.15/1.19 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.15/1.20 Prover 4: Preprocessing ...
% 2.25/1.23 Prover 4: Warning: ignoring some quantifiers
% 2.36/1.23 Prover 4: Constructing countermodel ...
% 2.36/1.28 Prover 4: proved (90ms)
% 2.36/1.28
% 2.36/1.28 No countermodel exists, formula is valid
% 2.36/1.28 % SZS status Theorem for theBenchmark
% 2.36/1.28
% 2.36/1.28 Generating proof ... Warning: ignoring some quantifiers
% 3.07/1.50 found it (size 50)
% 3.07/1.50
% 3.07/1.50 % SZS output start Proof for theBenchmark
% 3.07/1.50 Assumed formulas after preprocessing and simplification:
% 3.07/1.50 | (0) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1) | ? [v2] : (f(v0) = v2 & big_f(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_f(v1) = v3 & big_f(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_f(v1) = v3 & big_f(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_f(v1) = v2 & big_f(v0) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & f(v0) = v1 & big_f(v1) = v2)) & ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : (f(v0) = v1 & big_f(v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (f(v0) = v2 & big_f(v2) = v3 & big_f(v0) = v1 & ( ~ (v1 = 0) | v3 = 0))
% 3.19/1.52 | Applying alpha-rule on (0) yields:
% 3.19/1.52 | (1) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_f(v1) = v3 & big_f(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 3.19/1.53 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 3.19/1.53 | (3) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (f(v0) = v2 & big_f(v2) = v3 & big_f(v0) = v1 & ( ~ (v1 = 0) | v3 = 0))
% 3.19/1.53 | (4) ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : (f(v0) = v1 & big_f(v1) = 0))
% 3.19/1.53 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1) | ? [v2] : (f(v0) = v2 & big_f(v2) = 0))
% 3.19/1.53 | (6) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_f(v1) = v3 & big_f(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 3.19/1.53 | (7) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_f(v1) = v2 & big_f(v0) = v3 & (v3 = 0 | v2 = 0)))
% 3.19/1.53 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 3.28/1.53 | (9) ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & f(v0) = v1 & big_f(v1) = v2))
% 3.28/1.53 |
% 3.28/1.53 | Instantiating (3) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3 yields:
% 3.28/1.53 | (10) f(all_1_3_3) = all_1_1_1 & big_f(all_1_1_1) = all_1_0_0 & big_f(all_1_3_3) = all_1_2_2 & ( ~ (all_1_2_2 = 0) | all_1_0_0 = 0)
% 3.28/1.53 |
% 3.28/1.53 | Applying alpha-rule on (10) yields:
% 3.28/1.53 | (11) f(all_1_3_3) = all_1_1_1
% 3.28/1.53 | (12) big_f(all_1_1_1) = all_1_0_0
% 3.28/1.53 | (13) big_f(all_1_3_3) = all_1_2_2
% 3.28/1.53 | (14) ~ (all_1_2_2 = 0) | all_1_0_0 = 0
% 3.28/1.53 |
% 3.28/1.53 | Instantiating formula (1) with all_1_1_1, all_1_3_3 and discharging atoms f(all_1_3_3) = all_1_1_1, yields:
% 3.28/1.53 | (15) ? [v0] : ? [v1] : (big_f(all_1_1_1) = v1 & big_f(all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 3.28/1.53 |
% 3.28/1.53 | Instantiating formula (6) with all_1_1_1, all_1_3_3 and discharging atoms f(all_1_3_3) = all_1_1_1, yields:
% 3.28/1.53 | (16) ? [v0] : ? [v1] : (big_f(all_1_1_1) = v1 & big_f(all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 3.28/1.53 |
% 3.28/1.53 | Instantiating formula (7) with all_1_1_1, all_1_3_3 and discharging atoms f(all_1_3_3) = all_1_1_1, yields:
% 3.28/1.53 | (17) ? [v0] : ? [v1] : (big_f(all_1_1_1) = v0 & big_f(all_1_3_3) = v1 & (v1 = 0 | v0 = 0))
% 3.28/1.53 |
% 3.28/1.53 | Instantiating formula (5) with all_1_2_2, all_1_3_3 and discharging atoms big_f(all_1_3_3) = all_1_2_2, yields:
% 3.28/1.53 | (18) all_1_2_2 = 0 | ? [v0] : (f(all_1_3_3) = v0 & big_f(v0) = 0)
% 3.28/1.54 |
% 3.28/1.54 | Instantiating (17) with all_8_0_4, all_8_1_5 yields:
% 3.28/1.54 | (19) big_f(all_1_1_1) = all_8_1_5 & big_f(all_1_3_3) = all_8_0_4 & (all_8_0_4 = 0 | all_8_1_5 = 0)
% 3.28/1.54 |
% 3.28/1.54 | Applying alpha-rule on (19) yields:
% 3.28/1.54 | (20) big_f(all_1_1_1) = all_8_1_5
% 3.28/1.54 | (21) big_f(all_1_3_3) = all_8_0_4
% 3.28/1.54 | (22) all_8_0_4 = 0 | all_8_1_5 = 0
% 3.28/1.54 |
% 3.28/1.54 | Instantiating (16) with all_10_0_6, all_10_1_7 yields:
% 3.28/1.54 | (23) big_f(all_1_1_1) = all_10_0_6 & big_f(all_1_3_3) = all_10_1_7 & ( ~ (all_10_1_7 = 0) | all_10_0_6 = 0)
% 3.28/1.54 |
% 3.28/1.54 | Applying alpha-rule on (23) yields:
% 3.28/1.54 | (24) big_f(all_1_1_1) = all_10_0_6
% 3.28/1.54 | (25) big_f(all_1_3_3) = all_10_1_7
% 3.28/1.54 | (26) ~ (all_10_1_7 = 0) | all_10_0_6 = 0
% 3.28/1.54 |
% 3.28/1.54 | Instantiating (15) with all_12_0_8, all_12_1_9 yields:
% 3.28/1.54 | (27) big_f(all_1_1_1) = all_12_0_8 & big_f(all_1_3_3) = all_12_1_9 & ( ~ (all_12_0_8 = 0) | ~ (all_12_1_9 = 0))
% 3.28/1.54 |
% 3.28/1.54 | Applying alpha-rule on (27) yields:
% 3.28/1.54 | (28) big_f(all_1_1_1) = all_12_0_8
% 3.28/1.54 | (29) big_f(all_1_3_3) = all_12_1_9
% 3.28/1.54 | (30) ~ (all_12_0_8 = 0) | ~ (all_12_1_9 = 0)
% 3.28/1.54 |
% 3.28/1.54 | Instantiating formula (8) with all_1_1_1, all_10_0_6, all_1_0_0 and discharging atoms big_f(all_1_1_1) = all_10_0_6, big_f(all_1_1_1) = all_1_0_0, yields:
% 3.28/1.54 | (31) all_10_0_6 = all_1_0_0
% 3.28/1.54 |
% 3.28/1.54 | Instantiating formula (8) with all_1_1_1, all_10_0_6, all_12_0_8 and discharging atoms big_f(all_1_1_1) = all_12_0_8, big_f(all_1_1_1) = all_10_0_6, yields:
% 3.28/1.54 | (32) all_12_0_8 = all_10_0_6
% 3.28/1.54 |
% 3.28/1.54 | Instantiating formula (8) with all_1_1_1, all_8_1_5, all_12_0_8 and discharging atoms big_f(all_1_1_1) = all_12_0_8, big_f(all_1_1_1) = all_8_1_5, yields:
% 3.28/1.54 | (33) all_12_0_8 = all_8_1_5
% 3.28/1.54 |
% 3.28/1.54 | Instantiating formula (8) with all_1_3_3, all_12_1_9, all_1_2_2 and discharging atoms big_f(all_1_3_3) = all_12_1_9, big_f(all_1_3_3) = all_1_2_2, yields:
% 3.28/1.54 | (34) all_12_1_9 = all_1_2_2
% 3.28/1.54 |
% 3.28/1.54 | Instantiating formula (8) with all_1_3_3, all_10_1_7, all_12_1_9 and discharging atoms big_f(all_1_3_3) = all_12_1_9, big_f(all_1_3_3) = all_10_1_7, yields:
% 3.28/1.54 | (35) all_12_1_9 = all_10_1_7
% 3.28/1.54 |
% 3.28/1.54 | Combining equations (32,33) yields a new equation:
% 3.28/1.54 | (36) all_10_0_6 = all_8_1_5
% 3.28/1.54 |
% 3.28/1.54 | Simplifying 36 yields:
% 3.28/1.54 | (37) all_10_0_6 = all_8_1_5
% 3.28/1.54 |
% 3.28/1.54 | Combining equations (34,35) yields a new equation:
% 3.28/1.54 | (38) all_10_1_7 = all_1_2_2
% 3.28/1.54 |
% 3.28/1.54 | Combining equations (31,37) yields a new equation:
% 3.28/1.54 | (39) all_8_1_5 = all_1_0_0
% 3.28/1.54 |
% 3.28/1.54 | Combining equations (38,35) yields a new equation:
% 3.28/1.54 | (34) all_12_1_9 = all_1_2_2
% 3.28/1.54 |
% 3.28/1.54 | Combining equations (39,33) yields a new equation:
% 3.28/1.54 | (41) all_12_0_8 = all_1_0_0
% 3.28/1.54 |
% 3.28/1.54 +-Applying beta-rule and splitting (14), into two cases.
% 3.28/1.54 |-Branch one:
% 3.28/1.54 | (42) ~ (all_1_2_2 = 0)
% 3.28/1.54 |
% 3.28/1.54 +-Applying beta-rule and splitting (18), into two cases.
% 3.28/1.54 |-Branch one:
% 3.28/1.54 | (43) all_1_2_2 = 0
% 3.28/1.54 |
% 3.28/1.54 | Equations (43) can reduce 42 to:
% 3.28/1.54 | (44) $false
% 3.28/1.54 |
% 3.28/1.54 |-The branch is then unsatisfiable
% 3.28/1.54 |-Branch two:
% 3.28/1.54 | (42) ~ (all_1_2_2 = 0)
% 3.28/1.54 | (46) ? [v0] : (f(all_1_3_3) = v0 & big_f(v0) = 0)
% 3.28/1.54 |
% 3.28/1.54 | Instantiating (46) with all_29_0_10 yields:
% 3.28/1.54 | (47) f(all_1_3_3) = all_29_0_10 & big_f(all_29_0_10) = 0
% 3.28/1.54 |
% 3.28/1.54 | Applying alpha-rule on (47) yields:
% 3.28/1.54 | (48) f(all_1_3_3) = all_29_0_10
% 3.28/1.54 | (49) big_f(all_29_0_10) = 0
% 3.28/1.54 |
% 3.28/1.54 | Instantiating formula (2) with all_1_3_3, all_29_0_10, all_1_1_1 and discharging atoms f(all_1_3_3) = all_29_0_10, f(all_1_3_3) = all_1_1_1, yields:
% 3.28/1.54 | (50) all_29_0_10 = all_1_1_1
% 3.28/1.54 |
% 3.28/1.54 | From (50) and (49) follows:
% 3.28/1.54 | (51) big_f(all_1_1_1) = 0
% 3.28/1.54 |
% 3.28/1.54 | Instantiating formula (9) with all_1_1_1 and discharging atoms big_f(all_1_1_1) = 0, yields:
% 3.28/1.54 | (52) ? [v0] : ? [v1] : ( ~ (v1 = 0) & f(all_1_1_1) = v0 & big_f(v0) = v1)
% 3.28/1.55 |
% 3.28/1.55 | Instantiating formula (4) with all_1_1_1 and discharging atoms big_f(all_1_1_1) = 0, yields:
% 3.28/1.55 | (53) ? [v0] : (f(all_1_1_1) = v0 & big_f(v0) = 0)
% 3.28/1.55 |
% 3.28/1.55 | Instantiating (53) with all_44_0_11 yields:
% 3.28/1.55 | (54) f(all_1_1_1) = all_44_0_11 & big_f(all_44_0_11) = 0
% 3.28/1.55 |
% 3.28/1.55 | Applying alpha-rule on (54) yields:
% 3.28/1.55 | (55) f(all_1_1_1) = all_44_0_11
% 3.28/1.55 | (56) big_f(all_44_0_11) = 0
% 3.28/1.55 |
% 3.28/1.55 | Instantiating (52) with all_46_0_12, all_46_1_13 yields:
% 3.28/1.55 | (57) ~ (all_46_0_12 = 0) & f(all_1_1_1) = all_46_1_13 & big_f(all_46_1_13) = all_46_0_12
% 3.28/1.55 |
% 3.28/1.55 | Applying alpha-rule on (57) yields:
% 3.28/1.55 | (58) ~ (all_46_0_12 = 0)
% 3.28/1.55 | (59) f(all_1_1_1) = all_46_1_13
% 3.28/1.55 | (60) big_f(all_46_1_13) = all_46_0_12
% 3.28/1.55 |
% 3.28/1.55 | Instantiating formula (2) with all_1_1_1, all_44_0_11, all_46_1_13 and discharging atoms f(all_1_1_1) = all_46_1_13, f(all_1_1_1) = all_44_0_11, yields:
% 3.28/1.55 | (61) all_46_1_13 = all_44_0_11
% 3.28/1.55 |
% 3.28/1.55 | From (61) and (60) follows:
% 3.28/1.55 | (62) big_f(all_44_0_11) = all_46_0_12
% 3.28/1.55 |
% 3.28/1.55 | Instantiating formula (8) with all_44_0_11, all_46_0_12, 0 and discharging atoms big_f(all_44_0_11) = all_46_0_12, big_f(all_44_0_11) = 0, yields:
% 3.28/1.55 | (63) all_46_0_12 = 0
% 3.28/1.55 |
% 3.28/1.55 | Equations (63) can reduce 58 to:
% 3.28/1.55 | (44) $false
% 3.28/1.55 |
% 3.28/1.55 |-The branch is then unsatisfiable
% 3.28/1.55 |-Branch two:
% 3.28/1.55 | (43) all_1_2_2 = 0
% 3.28/1.55 | (66) all_1_0_0 = 0
% 3.28/1.55 |
% 3.28/1.55 | Combining equations (43,34) yields a new equation:
% 3.28/1.55 | (67) all_12_1_9 = 0
% 3.28/1.55 |
% 3.28/1.55 | Combining equations (66,41) yields a new equation:
% 3.28/1.55 | (68) all_12_0_8 = 0
% 3.28/1.55 |
% 3.28/1.55 +-Applying beta-rule and splitting (30), into two cases.
% 3.28/1.55 |-Branch one:
% 3.28/1.55 | (69) ~ (all_12_0_8 = 0)
% 3.28/1.55 |
% 3.28/1.55 | Equations (68) can reduce 69 to:
% 3.28/1.55 | (44) $false
% 3.28/1.55 |
% 3.28/1.55 |-The branch is then unsatisfiable
% 3.28/1.55 |-Branch two:
% 3.28/1.55 | (68) all_12_0_8 = 0
% 3.28/1.55 | (72) ~ (all_12_1_9 = 0)
% 3.28/1.55 |
% 3.28/1.55 | Equations (67) can reduce 72 to:
% 3.28/1.55 | (44) $false
% 3.28/1.55 |
% 3.28/1.55 |-The branch is then unsatisfiable
% 3.28/1.55 % SZS output end Proof for theBenchmark
% 3.28/1.55
% 3.28/1.55 957ms
%------------------------------------------------------------------------------