TSTP Solution File: SYN980+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN980+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 05:06:15 EDT 2022
% Result : Theorem 2.27s 1.23s
% Output : Proof 3.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN980+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 14:15:43 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.66/0.63 ____ _
% 0.66/0.63 ___ / __ \_____(_)___ ________ __________
% 0.66/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.66/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.66/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.66/0.63
% 0.66/0.63 A Theorem Prover for First-Order Logic
% 0.66/0.63 (ePrincess v.1.0)
% 0.66/0.63
% 0.66/0.63 (c) Philipp Rümmer, 2009-2015
% 0.66/0.63 (c) Peter Backeman, 2014-2015
% 0.66/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.66/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.66/0.63 Bug reports to peter@backeman.se
% 0.66/0.63
% 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.63
% 0.66/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.79/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.24/0.90 Prover 0: Preprocessing ...
% 1.41/0.97 Prover 0: Warning: ignoring some quantifiers
% 1.51/0.99 Prover 0: Constructing countermodel ...
% 1.85/1.11 Prover 0: gave up
% 1.85/1.11 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.85/1.13 Prover 1: Preprocessing ...
% 2.12/1.17 Prover 1: Constructing countermodel ...
% 2.27/1.23 Prover 1: proved (118ms)
% 2.27/1.23
% 2.27/1.23 No countermodel exists, formula is valid
% 2.27/1.23 % SZS status Theorem for theBenchmark
% 2.27/1.23
% 2.27/1.23 Generating proof ... found it (size 41)
% 2.69/1.42
% 2.69/1.42 % SZS output start Proof for theBenchmark
% 2.69/1.42 Assumed formulas after preprocessing and simplification:
% 2.69/1.42 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (q(v2, v0) = v3 & f(v0) = v2 & r(v0) = v1 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (q(v7, v6) = v5) | ~ (q(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (p(v7, v6) = v5) | ~ (p(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v1 = 0 | ~ (f(v4) = v5) | ~ (p(v5, v4) = v6)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (f(v4) = v5) | ~ (p(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & r(v4) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (f(v6) = v5) | ~ (f(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (r(v6) = v5) | ~ (r(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v3 = 0 | ~ (q(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & p(v4, v5) = v7)) & ! [v4] : ! [v5] : ( ~ (q(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & p(v4, v5) = v6)))
% 2.95/1.45 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.95/1.45 | (1) q(all_0_1_1, all_0_3_3) = all_0_0_0 & f(all_0_3_3) = all_0_1_1 & r(all_0_3_3) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (q(v3, v2) = v1) | ~ (q(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (p(v3, v2) = v1) | ~ (p(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | all_0_2_2 = 0 | ~ (f(v0) = v1) | ~ (p(v1, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (f(v0) = v1) | ~ (p(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & r(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r(v2) = v1) | ~ (r(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (all_0_0_0 = 0 | ~ (q(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & p(v0, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (q(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & p(v0, v1) = v2))
% 2.95/1.46 |
% 2.95/1.46 | Applying alpha-rule on (1) yields:
% 2.95/1.46 | (2) ! [v0] : ! [v1] : ( ~ (q(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & p(v0, v1) = v2))
% 2.95/1.46 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (p(v3, v2) = v1) | ~ (p(v3, v2) = v0))
% 2.95/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (q(v3, v2) = v1) | ~ (q(v3, v2) = v0))
% 2.95/1.46 | (5) f(all_0_3_3) = all_0_1_1
% 2.95/1.46 | (6) ! [v0] : ! [v1] : ! [v2] : (all_0_0_0 = 0 | ~ (q(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & p(v0, v1) = v3))
% 2.95/1.46 | (7) q(all_0_1_1, all_0_3_3) = all_0_0_0
% 2.95/1.46 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 2.95/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r(v2) = v1) | ~ (r(v2) = v0))
% 2.95/1.46 | (10) r(all_0_3_3) = all_0_2_2
% 2.95/1.46 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (f(v0) = v1) | ~ (p(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & r(v0) = v3))
% 2.95/1.46 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | all_0_2_2 = 0 | ~ (f(v0) = v1) | ~ (p(v1, v0) = v2))
% 2.95/1.46 |
% 2.95/1.46 | Instantiating formula (2) with all_0_3_3, all_0_1_1 yields:
% 2.95/1.46 | (13) ~ (q(all_0_1_1, all_0_3_3) = 0) | ? [v0] : ( ~ (v0 = 0) & p(all_0_1_1, all_0_3_3) = v0)
% 2.95/1.46 |
% 2.95/1.46 | Instantiating formula (6) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms q(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 2.95/1.46 | (14) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & p(all_0_1_1, all_0_3_3) = v0)
% 2.95/1.46 |
% 2.95/1.46 +-Applying beta-rule and splitting (13), into two cases.
% 2.95/1.46 |-Branch one:
% 2.95/1.46 | (15) ~ (q(all_0_1_1, all_0_3_3) = 0)
% 2.95/1.46 |
% 2.95/1.47 | Using (7) and (15) yields:
% 2.95/1.47 | (16) ~ (all_0_0_0 = 0)
% 2.95/1.47 |
% 2.95/1.47 +-Applying beta-rule and splitting (14), into two cases.
% 2.95/1.47 |-Branch one:
% 2.95/1.47 | (17) all_0_0_0 = 0
% 2.95/1.47 |
% 2.95/1.47 | Equations (17) can reduce 16 to:
% 2.95/1.47 | (18) $false
% 2.95/1.47 |
% 2.95/1.47 |-The branch is then unsatisfiable
% 2.95/1.47 |-Branch two:
% 2.95/1.47 | (16) ~ (all_0_0_0 = 0)
% 2.95/1.47 | (20) ? [v0] : ( ~ (v0 = 0) & p(all_0_1_1, all_0_3_3) = v0)
% 2.95/1.47 |
% 2.95/1.47 | Instantiating (20) with all_18_0_4 yields:
% 2.95/1.47 | (21) ~ (all_18_0_4 = 0) & p(all_0_1_1, all_0_3_3) = all_18_0_4
% 2.95/1.47 |
% 2.95/1.47 | Applying alpha-rule on (21) yields:
% 2.95/1.47 | (22) ~ (all_18_0_4 = 0)
% 2.95/1.47 | (23) p(all_0_1_1, all_0_3_3) = all_18_0_4
% 3.08/1.47 |
% 3.08/1.47 | Instantiating formula (12) with all_18_0_4, all_0_1_1, all_0_3_3 and discharging atoms f(all_0_3_3) = all_0_1_1, p(all_0_1_1, all_0_3_3) = all_18_0_4, yields:
% 3.08/1.47 | (24) all_18_0_4 = 0 | all_0_2_2 = 0
% 3.08/1.47 |
% 3.08/1.47 | Instantiating formula (11) with all_18_0_4, all_0_1_1, all_0_3_3 and discharging atoms f(all_0_3_3) = all_0_1_1, p(all_0_1_1, all_0_3_3) = all_18_0_4, yields:
% 3.08/1.47 | (25) all_18_0_4 = 0 | ? [v0] : ( ~ (v0 = 0) & r(all_0_3_3) = v0)
% 3.08/1.47 |
% 3.08/1.47 +-Applying beta-rule and splitting (24), into two cases.
% 3.08/1.47 |-Branch one:
% 3.08/1.47 | (26) all_18_0_4 = 0
% 3.08/1.47 |
% 3.08/1.47 | Equations (26) can reduce 22 to:
% 3.08/1.47 | (18) $false
% 3.08/1.47 |
% 3.08/1.47 |-The branch is then unsatisfiable
% 3.08/1.47 |-Branch two:
% 3.08/1.47 | (22) ~ (all_18_0_4 = 0)
% 3.08/1.47 | (29) all_0_2_2 = 0
% 3.08/1.47 |
% 3.08/1.47 | From (29) and (10) follows:
% 3.08/1.47 | (30) r(all_0_3_3) = 0
% 3.08/1.47 |
% 3.08/1.47 +-Applying beta-rule and splitting (25), into two cases.
% 3.08/1.47 |-Branch one:
% 3.08/1.47 | (26) all_18_0_4 = 0
% 3.08/1.47 |
% 3.08/1.47 | Equations (26) can reduce 22 to:
% 3.08/1.47 | (18) $false
% 3.08/1.47 |
% 3.08/1.47 |-The branch is then unsatisfiable
% 3.08/1.47 |-Branch two:
% 3.08/1.47 | (22) ~ (all_18_0_4 = 0)
% 3.08/1.47 | (34) ? [v0] : ( ~ (v0 = 0) & r(all_0_3_3) = v0)
% 3.08/1.47 |
% 3.08/1.47 | Instantiating (34) with all_31_0_5 yields:
% 3.08/1.47 | (35) ~ (all_31_0_5 = 0) & r(all_0_3_3) = all_31_0_5
% 3.08/1.47 |
% 3.08/1.47 | Applying alpha-rule on (35) yields:
% 3.08/1.47 | (36) ~ (all_31_0_5 = 0)
% 3.08/1.47 | (37) r(all_0_3_3) = all_31_0_5
% 3.08/1.47 |
% 3.08/1.47 | Instantiating formula (9) with all_0_3_3, 0, all_31_0_5 and discharging atoms r(all_0_3_3) = all_31_0_5, r(all_0_3_3) = 0, yields:
% 3.08/1.47 | (38) all_31_0_5 = 0
% 3.08/1.47 |
% 3.08/1.47 | Equations (38) can reduce 36 to:
% 3.08/1.47 | (18) $false
% 3.08/1.47 |
% 3.08/1.47 |-The branch is then unsatisfiable
% 3.08/1.47 |-Branch two:
% 3.08/1.47 | (40) q(all_0_1_1, all_0_3_3) = 0
% 3.08/1.47 | (20) ? [v0] : ( ~ (v0 = 0) & p(all_0_1_1, all_0_3_3) = v0)
% 3.08/1.47 |
% 3.08/1.47 | Instantiating (20) with all_10_0_6 yields:
% 3.08/1.47 | (42) ~ (all_10_0_6 = 0) & p(all_0_1_1, all_0_3_3) = all_10_0_6
% 3.08/1.47 |
% 3.08/1.47 | Applying alpha-rule on (42) yields:
% 3.08/1.47 | (43) ~ (all_10_0_6 = 0)
% 3.08/1.47 | (44) p(all_0_1_1, all_0_3_3) = all_10_0_6
% 3.08/1.47 |
% 3.08/1.47 | Instantiating formula (12) with all_10_0_6, all_0_1_1, all_0_3_3 and discharging atoms f(all_0_3_3) = all_0_1_1, p(all_0_1_1, all_0_3_3) = all_10_0_6, yields:
% 3.08/1.47 | (45) all_10_0_6 = 0 | all_0_2_2 = 0
% 3.08/1.47 |
% 3.08/1.47 +-Applying beta-rule and splitting (45), into two cases.
% 3.08/1.47 |-Branch one:
% 3.08/1.47 | (46) all_10_0_6 = 0
% 3.08/1.47 |
% 3.08/1.47 | Equations (46) can reduce 43 to:
% 3.08/1.47 | (18) $false
% 3.08/1.47 |
% 3.08/1.47 |-The branch is then unsatisfiable
% 3.08/1.47 |-Branch two:
% 3.08/1.47 | (43) ~ (all_10_0_6 = 0)
% 3.08/1.47 | (29) all_0_2_2 = 0
% 3.08/1.47 |
% 3.08/1.47 | From (29) and (10) follows:
% 3.08/1.47 | (30) r(all_0_3_3) = 0
% 3.08/1.48 |
% 3.08/1.48 | Instantiating formula (11) with all_10_0_6, all_0_1_1, all_0_3_3 and discharging atoms f(all_0_3_3) = all_0_1_1, p(all_0_1_1, all_0_3_3) = all_10_0_6, yields:
% 3.08/1.48 | (51) all_10_0_6 = 0 | ? [v0] : ( ~ (v0 = 0) & r(all_0_3_3) = v0)
% 3.08/1.48 |
% 3.08/1.48 +-Applying beta-rule and splitting (51), into two cases.
% 3.08/1.48 |-Branch one:
% 3.08/1.48 | (46) all_10_0_6 = 0
% 3.08/1.48 |
% 3.08/1.48 | Equations (46) can reduce 43 to:
% 3.08/1.48 | (18) $false
% 3.08/1.48 |
% 3.08/1.48 |-The branch is then unsatisfiable
% 3.08/1.48 |-Branch two:
% 3.08/1.48 | (43) ~ (all_10_0_6 = 0)
% 3.08/1.48 | (34) ? [v0] : ( ~ (v0 = 0) & r(all_0_3_3) = v0)
% 3.08/1.48 |
% 3.08/1.48 | Instantiating (34) with all_27_0_7 yields:
% 3.08/1.48 | (56) ~ (all_27_0_7 = 0) & r(all_0_3_3) = all_27_0_7
% 3.08/1.48 |
% 3.08/1.48 | Applying alpha-rule on (56) yields:
% 3.08/1.48 | (57) ~ (all_27_0_7 = 0)
% 3.08/1.48 | (58) r(all_0_3_3) = all_27_0_7
% 3.08/1.48 |
% 3.08/1.48 | Instantiating formula (9) with all_0_3_3, all_27_0_7, 0 and discharging atoms r(all_0_3_3) = all_27_0_7, r(all_0_3_3) = 0, yields:
% 3.08/1.48 | (59) all_27_0_7 = 0
% 3.08/1.48 |
% 3.08/1.48 | Equations (59) can reduce 57 to:
% 3.08/1.48 | (18) $false
% 3.08/1.48 |
% 3.08/1.48 |-The branch is then unsatisfiable
% 3.08/1.48 % SZS output end Proof for theBenchmark
% 3.08/1.48
% 3.08/1.48 833ms
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