TSTP Solution File: SYN941+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN941+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 05:05:59 EDT 2022
% Result : Theorem 2.87s 1.42s
% Output : Proof 3.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN941+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jul 12 05:58:40 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.65/0.64 ____ _
% 0.65/0.64 ___ / __ \_____(_)___ ________ __________
% 0.65/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.65/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.65/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.65/0.64
% 0.65/0.64 A Theorem Prover for First-Order Logic
% 0.65/0.64 (ePrincess v.1.0)
% 0.65/0.64
% 0.65/0.64 (c) Philipp Rümmer, 2009-2015
% 0.65/0.64 (c) Peter Backeman, 2014-2015
% 0.65/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.65/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.65/0.64 Bug reports to peter@backeman.se
% 0.65/0.64
% 0.65/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.65/0.64
% 0.65/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.80/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.93 Prover 0: Preprocessing ...
% 1.40/1.00 Prover 0: Warning: ignoring some quantifiers
% 1.57/1.01 Prover 0: Constructing countermodel ...
% 1.75/1.15 Prover 0: gave up
% 1.75/1.15 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.75/1.17 Prover 1: Preprocessing ...
% 2.28/1.22 Prover 1: Constructing countermodel ...
% 2.35/1.29 Prover 1: gave up
% 2.35/1.29 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.35/1.30 Prover 2: Preprocessing ...
% 2.66/1.37 Prover 2: Warning: ignoring some quantifiers
% 2.66/1.37 Prover 2: Constructing countermodel ...
% 2.87/1.42 Prover 2: proved (128ms)
% 2.87/1.42
% 2.87/1.42 No countermodel exists, formula is valid
% 2.87/1.42 % SZS status Theorem for theBenchmark
% 2.87/1.42
% 2.87/1.42 Generating proof ... Warning: ignoring some quantifiers
% 3.34/1.60 found it (size 24)
% 3.34/1.60
% 3.34/1.60 % SZS output start Proof for theBenchmark
% 3.34/1.60 Assumed formulas after preprocessing and simplification:
% 3.34/1.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (f(v0) = v2 & q(v2) = 0 & r(v1) = v4 & r(v0) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (f(v6) = v7) | ~ (p(v7) = v8) | ~ (p(v5) = v9) | ? [v10] : ( ~ (v10 = 0) & q(v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (f(v6) = v7) | ~ (q(v5) = 0) | ~ (p(v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (f(v6) = v7) | ~ (q(v5) = 0) | ~ (p(v7) = v8) | ? [v9] : ((v9 = 0 & r(v6) = 0 & ( ~ (v4 = 0) | ~ (v3 = 0))) | ( ~ (v9 = 0) & p(v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (f(v6) = v7) | ~ (p(v7) = v8) | ~ (p(v5) = 0) | ? [v9] : ((v9 = 0 & r(v6) = 0 & ( ~ (v4 = 0) | ~ (v3 = 0))) | ( ~ (v9 = 0) & q(v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (p(v5) = v7) | ~ (r(v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & f(v6) = v9 & p(v9) = 0 & ( ~ (v7 = 0) | (v8 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0))))) | ( ~ (v9 = 0) & q(v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (f(v7) = v6) | ~ (f(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (q(v7) = v6) | ~ (q(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (p(v7) = v6) | ~ (p(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (r(v7) = v6) | ~ (r(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (q(v5) = 0) | ~ (r(v6) = v7) | ? [v8] : ? [v9] : (f(v6) = v8 & p(v8) = 0 & ((v7 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0))) | ( ~ (v9 = 0) & p(v5) = v9)))) & ? [v5] : ? [v6] : f(v5) = v6 & ? [v5] : ? [v6] : q(v5) = v6 & ? [v5] : ? [v6] : p(v5) = v6 & ? [v5] : ? [v6] : r(v5) = v6)
% 3.61/1.64 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.61/1.64 | (1) f(all_0_4_4) = all_0_2_2 & q(all_0_2_2) = 0 & r(all_0_3_3) = all_0_0_0 & r(all_0_4_4) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (f(v1) = v2) | ~ (p(v2) = v3) | ~ (p(v0) = v4) | ? [v5] : ( ~ (v5 = 0) & q(v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (f(v1) = v2) | ~ (q(v0) = 0) | ~ (p(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (f(v1) = v2) | ~ (q(v0) = 0) | ~ (p(v2) = v3) | ? [v4] : ((v4 = 0 & r(v1) = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))) | ( ~ (v4 = 0) & p(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (f(v1) = v2) | ~ (p(v2) = v3) | ~ (p(v0) = 0) | ? [v4] : ((v4 = 0 & r(v1) = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))) | ( ~ (v4 = 0) & q(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (p(v0) = v2) | ~ (r(v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & f(v1) = v4 & p(v4) = 0 & ( ~ (v2 = 0) | (v3 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))))) | ( ~ (v4 = 0) & q(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r(v2) = v1) | ~ (r(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (q(v0) = 0) | ~ (r(v1) = v2) | ? [v3] : ? [v4] : (f(v1) = v3 & p(v3) = 0 & ((v2 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))) | ( ~ (v4 = 0) & p(v0) = v4)))) & ? [v0] : ? [v1] : f(v0) = v1 & ? [v0] : ? [v1] : q(v0) = v1 & ? [v0] : ? [v1] : p(v0) = v1 & ? [v0] : ? [v1] : r(v0) = v1
% 3.61/1.65 |
% 3.61/1.65 | Applying alpha-rule on (1) yields:
% 3.61/1.65 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 3.61/1.65 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (f(v1) = v2) | ~ (q(v0) = 0) | ~ (p(v2) = v3))
% 3.61/1.65 | (4) ? [v0] : ? [v1] : r(v0) = v1
% 3.61/1.65 | (5) ? [v0] : ? [v1] : f(v0) = v1
% 3.61/1.65 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0))
% 3.61/1.65 | (7) r(all_0_3_3) = all_0_0_0
% 3.61/1.65 | (8) r(all_0_4_4) = all_0_1_1
% 3.61/1.65 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (f(v1) = v2) | ~ (p(v2) = v3) | ~ (p(v0) = v4) | ? [v5] : ( ~ (v5 = 0) & q(v0) = v5))
% 3.61/1.65 | (10) f(all_0_4_4) = all_0_2_2
% 3.61/1.65 | (11) ? [v0] : ? [v1] : p(v0) = v1
% 3.61/1.65 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 3.61/1.65 | (13) ? [v0] : ? [v1] : q(v0) = v1
% 3.61/1.65 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (f(v1) = v2) | ~ (p(v2) = v3) | ~ (p(v0) = 0) | ? [v4] : ((v4 = 0 & r(v1) = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))) | ( ~ (v4 = 0) & q(v0) = v4)))
% 3.61/1.65 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (f(v1) = v2) | ~ (q(v0) = 0) | ~ (p(v2) = v3) | ? [v4] : ((v4 = 0 & r(v1) = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))) | ( ~ (v4 = 0) & p(v0) = v4)))
% 3.61/1.65 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r(v2) = v1) | ~ (r(v2) = v0))
% 3.61/1.65 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (p(v0) = v2) | ~ (r(v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & f(v1) = v4 & p(v4) = 0 & ( ~ (v2 = 0) | (v3 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))))) | ( ~ (v4 = 0) & q(v0) = v4)))
% 3.61/1.65 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (q(v0) = 0) | ~ (r(v1) = v2) | ? [v3] : ? [v4] : (f(v1) = v3 & p(v3) = 0 & ((v2 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))) | ( ~ (v4 = 0) & p(v0) = v4))))
% 3.61/1.65 | (19) q(all_0_2_2) = 0
% 3.61/1.65 |
% 3.61/1.65 | Instantiating formula (18) with all_0_0_0, all_0_3_3, all_0_2_2 and discharging atoms q(all_0_2_2) = 0, r(all_0_3_3) = all_0_0_0, yields:
% 3.61/1.66 | (20) ? [v0] : ? [v1] : (f(all_0_3_3) = v0 & p(v0) = 0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | ( ~ (v1 = 0) & p(all_0_2_2) = v1)))
% 3.61/1.66 |
% 3.61/1.66 | Instantiating formula (18) with all_0_1_1, all_0_4_4, all_0_2_2 and discharging atoms q(all_0_2_2) = 0, r(all_0_4_4) = all_0_1_1, yields:
% 3.61/1.66 | (21) ? [v0] : ? [v1] : (f(all_0_4_4) = v0 & p(v0) = 0 & ((all_0_1_1 = 0 & ~ (all_0_0_0 = 0)) | ( ~ (v1 = 0) & p(all_0_2_2) = v1)))
% 3.61/1.66 |
% 3.61/1.66 | Instantiating (21) with all_16_0_13, all_16_1_14 yields:
% 3.61/1.66 | (22) f(all_0_4_4) = all_16_1_14 & p(all_16_1_14) = 0 & ((all_0_1_1 = 0 & ~ (all_0_0_0 = 0)) | ( ~ (all_16_0_13 = 0) & p(all_0_2_2) = all_16_0_13))
% 3.61/1.66 |
% 3.61/1.66 | Applying alpha-rule on (22) yields:
% 3.61/1.66 | (23) f(all_0_4_4) = all_16_1_14
% 3.61/1.66 | (24) p(all_16_1_14) = 0
% 3.61/1.66 | (25) (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)) | ( ~ (all_16_0_13 = 0) & p(all_0_2_2) = all_16_0_13)
% 3.61/1.66 |
% 3.61/1.66 | Instantiating (20) with all_18_0_15, all_18_1_16 yields:
% 3.61/1.66 | (26) f(all_0_3_3) = all_18_1_16 & p(all_18_1_16) = 0 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | ( ~ (all_18_0_15 = 0) & p(all_0_2_2) = all_18_0_15))
% 3.61/1.66 |
% 3.61/1.66 | Applying alpha-rule on (26) yields:
% 3.61/1.66 | (27) f(all_0_3_3) = all_18_1_16
% 3.61/1.66 | (28) p(all_18_1_16) = 0
% 3.61/1.66 | (29) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | ( ~ (all_18_0_15 = 0) & p(all_0_2_2) = all_18_0_15)
% 3.61/1.66 |
% 3.61/1.66 | Instantiating formula (12) with all_0_4_4, all_16_1_14, all_0_2_2 and discharging atoms f(all_0_4_4) = all_16_1_14, f(all_0_4_4) = all_0_2_2, yields:
% 3.61/1.66 | (30) all_16_1_14 = all_0_2_2
% 3.61/1.66 |
% 3.61/1.66 | From (30) and (24) follows:
% 3.61/1.66 | (31) p(all_0_2_2) = 0
% 3.61/1.66 |
% 3.61/1.66 +-Applying beta-rule and splitting (25), into two cases.
% 3.61/1.66 |-Branch one:
% 3.61/1.66 | (32) all_0_1_1 = 0 & ~ (all_0_0_0 = 0)
% 3.61/1.66 |
% 3.61/1.66 | Applying alpha-rule on (32) yields:
% 3.61/1.66 | (33) all_0_1_1 = 0
% 3.61/1.66 | (34) ~ (all_0_0_0 = 0)
% 3.61/1.66 |
% 3.61/1.66 +-Applying beta-rule and splitting (29), into two cases.
% 3.61/1.66 |-Branch one:
% 3.61/1.66 | (35) all_0_0_0 = 0 & ~ (all_0_1_1 = 0)
% 3.61/1.66 |
% 3.61/1.66 | Applying alpha-rule on (35) yields:
% 3.61/1.66 | (36) all_0_0_0 = 0
% 3.61/1.66 | (37) ~ (all_0_1_1 = 0)
% 3.61/1.66 |
% 3.61/1.66 | Equations (33) can reduce 37 to:
% 3.61/1.66 | (38) $false
% 3.61/1.66 |
% 3.61/1.66 |-The branch is then unsatisfiable
% 3.61/1.66 |-Branch two:
% 3.61/1.66 | (39) ~ (all_18_0_15 = 0) & p(all_0_2_2) = all_18_0_15
% 3.61/1.66 |
% 3.61/1.66 | Applying alpha-rule on (39) yields:
% 3.61/1.66 | (40) ~ (all_18_0_15 = 0)
% 3.61/1.66 | (41) p(all_0_2_2) = all_18_0_15
% 3.61/1.66 |
% 3.61/1.66 | Instantiating formula (2) with all_0_2_2, 0, all_18_0_15 and discharging atoms p(all_0_2_2) = all_18_0_15, p(all_0_2_2) = 0, yields:
% 3.61/1.66 | (42) all_18_0_15 = 0
% 3.61/1.66 |
% 3.61/1.66 | Equations (42) can reduce 40 to:
% 3.61/1.66 | (38) $false
% 3.61/1.66 |
% 3.61/1.66 |-The branch is then unsatisfiable
% 3.61/1.66 |-Branch two:
% 3.61/1.66 | (44) ~ (all_16_0_13 = 0) & p(all_0_2_2) = all_16_0_13
% 3.61/1.66 |
% 3.61/1.66 | Applying alpha-rule on (44) yields:
% 3.61/1.66 | (45) ~ (all_16_0_13 = 0)
% 3.61/1.66 | (46) p(all_0_2_2) = all_16_0_13
% 3.61/1.66 |
% 3.61/1.66 | Instantiating formula (2) with all_0_2_2, 0, all_16_0_13 and discharging atoms p(all_0_2_2) = all_16_0_13, p(all_0_2_2) = 0, yields:
% 3.61/1.67 | (47) all_16_0_13 = 0
% 3.61/1.67 |
% 3.61/1.67 | Equations (47) can reduce 45 to:
% 3.61/1.67 | (38) $false
% 3.61/1.67 |
% 3.61/1.67 |-The branch is then unsatisfiable
% 3.61/1.67 % SZS output end Proof for theBenchmark
% 3.61/1.67
% 3.61/1.67 1010ms
%------------------------------------------------------------------------------