TSTP Solution File: SYN078+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 04:59:46 EDT 2022
% Result : Theorem 2.16s 1.21s
% Output : Proof 2.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n015.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 : Mon Jul 11 12:24:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.55/0.60 ____ _
% 0.55/0.60 ___ / __ \_____(_)___ ________ __________
% 0.55/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.60
% 0.55/0.60 A Theorem Prover for First-Order Logic
% 0.55/0.60 (ePrincess v.1.0)
% 0.55/0.60
% 0.55/0.60 (c) Philipp Rümmer, 2009-2015
% 0.55/0.60 (c) Peter Backeman, 2014-2015
% 0.55/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.60 Bug reports to peter@backeman.se
% 0.55/0.60
% 0.55/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.60
% 0.55/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.20/0.90 Prover 0: Preprocessing ...
% 1.29/0.98 Prover 0: Warning: ignoring some quantifiers
% 1.29/0.99 Prover 0: Constructing countermodel ...
% 1.68/1.11 Prover 0: gave up
% 1.68/1.11 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.68/1.12 Prover 1: Preprocessing ...
% 1.68/1.17 Prover 1: Constructing countermodel ...
% 2.16/1.21 Prover 1: proved (93ms)
% 2.16/1.21
% 2.16/1.21 No countermodel exists, formula is valid
% 2.16/1.21 % SZS status Theorem for theBenchmark
% 2.16/1.21
% 2.16/1.21 Generating proof ... found it (size 25)
% 2.46/1.38
% 2.46/1.38 % SZS output start Proof for theBenchmark
% 2.46/1.38 Assumed formulas after preprocessing and simplification:
% 2.46/1.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (f(v7) = v6) | ~ (f(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_p(v7) = v6) | ~ (big_p(v7) = v5)) & ((v4 = v0 & v3 = 0 & ~ (v1 = 0) & f(v2) = v0 & big_p(v2) = 0 & big_p(v0) = v1 & ! [v5] : ! [v6] : ( ~ (f(v5) = v6) | ? [v7] : ? [v8] : (big_p(v6) = v8 & big_p(v5) = v7 & ( ~ (v7 = 0) | v8 = 0)))) | (v1 = 0 & ~ (v3 = 0) & f(v0) = v2 & big_p(v2) = v3 & big_p(v0) = 0 & ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (f(v7) = v5) | ~ (big_p(v5) = v6) | ? [v8] : ( ~ (v8 = 0) & big_p(v7) = v8)))))
% 2.61/1.42 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 2.61/1.42 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ((all_0_0_0 = all_0_4_4 & all_0_1_1 = 0 & ~ (all_0_3_3 = 0) & f(all_0_2_2) = all_0_4_4 & big_p(all_0_2_2) = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_p(v1) = v3 & big_p(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))) | (all_0_3_3 = 0 & ~ (all_0_1_1 = 0) & f(all_0_4_4) = all_0_2_2 & big_p(all_0_2_2) = all_0_1_1 & big_p(all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (f(v2) = v0) | ~ (big_p(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & big_p(v2) = v3))))
% 2.61/1.43 |
% 2.61/1.43 | Applying alpha-rule on (1) yields:
% 2.61/1.43 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 2.61/1.43 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 2.61/1.44 | (4) (all_0_0_0 = all_0_4_4 & all_0_1_1 = 0 & ~ (all_0_3_3 = 0) & f(all_0_2_2) = all_0_4_4 & big_p(all_0_2_2) = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_p(v1) = v3 & big_p(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))) | (all_0_3_3 = 0 & ~ (all_0_1_1 = 0) & f(all_0_4_4) = all_0_2_2 & big_p(all_0_2_2) = all_0_1_1 & big_p(all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (f(v2) = v0) | ~ (big_p(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & big_p(v2) = v3)))
% 2.61/1.44 |
% 2.61/1.44 +-Applying beta-rule and splitting (4), into two cases.
% 2.61/1.44 |-Branch one:
% 2.61/1.44 | (5) all_0_0_0 = all_0_4_4 & all_0_1_1 = 0 & ~ (all_0_3_3 = 0) & f(all_0_2_2) = all_0_4_4 & big_p(all_0_2_2) = 0 & big_p(all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_p(v1) = v3 & big_p(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 2.61/1.44 |
% 2.61/1.44 | Applying alpha-rule on (5) yields:
% 2.61/1.44 | (6) all_0_1_1 = 0
% 2.61/1.44 | (7) big_p(all_0_4_4) = all_0_3_3
% 2.61/1.44 | (8) all_0_0_0 = all_0_4_4
% 2.61/1.45 | (9) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : (big_p(v1) = v3 & big_p(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 2.61/1.45 | (10) big_p(all_0_2_2) = 0
% 2.61/1.45 | (11) f(all_0_2_2) = all_0_4_4
% 2.61/1.45 | (12) ~ (all_0_3_3 = 0)
% 2.61/1.45 |
% 2.61/1.45 | Instantiating formula (9) with all_0_4_4, all_0_2_2 and discharging atoms f(all_0_2_2) = all_0_4_4, yields:
% 2.61/1.45 | (13) ? [v0] : ? [v1] : (big_p(all_0_2_2) = v0 & big_p(all_0_4_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 2.61/1.45 |
% 2.61/1.45 | Instantiating (13) with all_12_0_5, all_12_1_6 yields:
% 2.61/1.45 | (14) big_p(all_0_2_2) = all_12_1_6 & big_p(all_0_4_4) = all_12_0_5 & ( ~ (all_12_1_6 = 0) | all_12_0_5 = 0)
% 2.61/1.46 |
% 2.61/1.46 | Applying alpha-rule on (14) yields:
% 2.61/1.46 | (15) big_p(all_0_2_2) = all_12_1_6
% 2.61/1.46 | (16) big_p(all_0_4_4) = all_12_0_5
% 2.61/1.46 | (17) ~ (all_12_1_6 = 0) | all_12_0_5 = 0
% 2.61/1.46 |
% 2.61/1.46 | Instantiating formula (3) with all_0_2_2, all_12_1_6, 0 and discharging atoms big_p(all_0_2_2) = all_12_1_6, big_p(all_0_2_2) = 0, yields:
% 2.61/1.46 | (18) all_12_1_6 = 0
% 2.61/1.46 |
% 2.61/1.46 | Instantiating formula (3) with all_0_4_4, all_12_0_5, all_0_3_3 and discharging atoms big_p(all_0_4_4) = all_12_0_5, big_p(all_0_4_4) = all_0_3_3, yields:
% 2.61/1.46 | (19) all_12_0_5 = all_0_3_3
% 2.61/1.46 |
% 2.61/1.46 +-Applying beta-rule and splitting (17), into two cases.
% 2.61/1.46 |-Branch one:
% 2.61/1.46 | (20) ~ (all_12_1_6 = 0)
% 2.61/1.46 |
% 2.61/1.46 | Equations (18) can reduce 20 to:
% 2.61/1.46 | (21) $false
% 2.61/1.46 |
% 2.83/1.46 |-The branch is then unsatisfiable
% 2.83/1.46 |-Branch two:
% 2.83/1.46 | (18) all_12_1_6 = 0
% 2.83/1.46 | (23) all_12_0_5 = 0
% 2.83/1.46 |
% 2.83/1.47 | Combining equations (23,19) yields a new equation:
% 2.83/1.47 | (24) all_0_3_3 = 0
% 2.83/1.47 |
% 2.83/1.47 | Equations (24) can reduce 12 to:
% 2.83/1.47 | (21) $false
% 2.83/1.47 |
% 2.83/1.47 |-The branch is then unsatisfiable
% 2.83/1.47 |-Branch two:
% 2.83/1.47 | (26) all_0_3_3 = 0 & ~ (all_0_1_1 = 0) & f(all_0_4_4) = all_0_2_2 & big_p(all_0_2_2) = all_0_1_1 & big_p(all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (f(v2) = v0) | ~ (big_p(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & big_p(v2) = v3))
% 2.83/1.47 |
% 2.83/1.47 | Applying alpha-rule on (26) yields:
% 2.83/1.47 | (27) ~ (all_0_1_1 = 0)
% 2.83/1.47 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (f(v2) = v0) | ~ (big_p(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & big_p(v2) = v3))
% 2.83/1.47 | (29) big_p(all_0_2_2) = all_0_1_1
% 2.83/1.47 | (30) f(all_0_4_4) = all_0_2_2
% 2.83/1.47 | (24) all_0_3_3 = 0
% 2.83/1.47 | (32) big_p(all_0_4_4) = 0
% 2.83/1.47 |
% 2.83/1.47 | Instantiating formula (28) with all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms f(all_0_4_4) = all_0_2_2, big_p(all_0_2_2) = all_0_1_1, yields:
% 2.83/1.47 | (33) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & big_p(all_0_4_4) = v0)
% 2.83/1.47 |
% 2.83/1.47 +-Applying beta-rule and splitting (33), into two cases.
% 2.83/1.47 |-Branch one:
% 2.83/1.47 | (6) all_0_1_1 = 0
% 2.83/1.47 |
% 2.83/1.47 | Equations (6) can reduce 27 to:
% 2.83/1.47 | (21) $false
% 2.83/1.47 |
% 2.83/1.47 |-The branch is then unsatisfiable
% 2.83/1.47 |-Branch two:
% 2.83/1.47 | (27) ~ (all_0_1_1 = 0)
% 2.83/1.47 | (37) ? [v0] : ( ~ (v0 = 0) & big_p(all_0_4_4) = v0)
% 2.83/1.47 |
% 2.83/1.47 | Instantiating (37) with all_18_0_7 yields:
% 2.83/1.47 | (38) ~ (all_18_0_7 = 0) & big_p(all_0_4_4) = all_18_0_7
% 2.83/1.47 |
% 2.83/1.47 | Applying alpha-rule on (38) yields:
% 2.83/1.47 | (39) ~ (all_18_0_7 = 0)
% 2.83/1.47 | (40) big_p(all_0_4_4) = all_18_0_7
% 2.85/1.47 |
% 2.85/1.47 | Instantiating formula (3) with all_0_4_4, all_18_0_7, 0 and discharging atoms big_p(all_0_4_4) = all_18_0_7, big_p(all_0_4_4) = 0, yields:
% 2.85/1.47 | (41) all_18_0_7 = 0
% 2.85/1.47 |
% 2.85/1.47 | Equations (41) can reduce 39 to:
% 2.85/1.47 | (21) $false
% 2.85/1.47 |
% 2.85/1.47 |-The branch is then unsatisfiable
% 2.85/1.47 % SZS output end Proof for theBenchmark
% 2.85/1.47
% 2.85/1.47 862ms
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