TSTP Solution File: SYN060+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN060+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 04:59:32 EDT 2022
% Result : Theorem 2.17s 1.18s
% Output : Proof 2.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN060+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n006.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 : Tue Jul 12 06:06:35 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.53/0.60 ____ _
% 0.53/0.60 ___ / __ \_____(_)___ ________ __________
% 0.53/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.60
% 0.53/0.60 A Theorem Prover for First-Order Logic
% 0.53/0.60 (ePrincess v.1.0)
% 0.53/0.60
% 0.53/0.60 (c) Philipp Rümmer, 2009-2015
% 0.53/0.60 (c) Peter Backeman, 2014-2015
% 0.53/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.60 Bug reports to peter@backeman.se
% 0.53/0.60
% 0.53/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.60
% 0.53/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.88 Prover 0: Preprocessing ...
% 1.49/0.94 Prover 0: Warning: ignoring some quantifiers
% 1.49/0.96 Prover 0: Constructing countermodel ...
% 1.71/1.07 Prover 0: gave up
% 1.71/1.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.90/1.09 Prover 1: Preprocessing ...
% 1.90/1.14 Prover 1: Constructing countermodel ...
% 2.17/1.18 Prover 1: proved (109ms)
% 2.17/1.18
% 2.17/1.18 No countermodel exists, formula is valid
% 2.17/1.18 % SZS status Theorem for theBenchmark
% 2.17/1.18
% 2.17/1.18 Generating proof ... found it (size 18)
% 2.60/1.33
% 2.60/1.33 % SZS output start Proof for theBenchmark
% 2.60/1.33 Assumed formulas after preprocessing and simplification:
% 2.60/1.33 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & big_i(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (big_i(v4) = v3) | ~ (big_i(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (big_h(v4) = v3) | ~ (big_h(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (big_f(v4) = v3) | ~ (big_f(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (big_g(v4) = v3) | ~ (big_g(v4) = v2)) & ! [v2] : ! [v3] : ( ~ (big_i(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (big_h(v2) = v6 & big_f(v2) = v5 & big_g(v2) = v4 & ((v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v2] : ( ~ (big_h(v2) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & big_f(v2) = v3 & big_g(v2) = v4)))
% 2.68/1.36 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 2.68/1.36 | (1) ~ (all_0_0_0 = 0) & big_i(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_i(v2) = v1) | ~ (big_i(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_h(v2) = v1) | ~ (big_h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (big_i(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (big_h(v0) = v4 & big_f(v0) = v3 & big_g(v0) = v2 & ((v4 = 0 & v3 = 0) | (v2 = 0 & v1 = 0)))) & ! [v0] : ( ~ (big_h(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & big_f(v0) = v1 & big_g(v0) = v2))
% 2.68/1.36 |
% 2.68/1.36 | Applying alpha-rule on (1) yields:
% 2.68/1.36 | (2) ~ (all_0_0_0 = 0)
% 2.68/1.36 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_i(v2) = v1) | ~ (big_i(v2) = v0))
% 2.68/1.37 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 2.68/1.37 | (5) ! [v0] : ! [v1] : ( ~ (big_i(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (big_h(v0) = v4 & big_f(v0) = v3 & big_g(v0) = v2 & ((v4 = 0 & v3 = 0) | (v2 = 0 & v1 = 0))))
% 2.68/1.37 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_h(v2) = v1) | ~ (big_h(v2) = v0))
% 2.68/1.37 | (7) big_i(all_0_1_1) = all_0_0_0
% 2.68/1.37 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0))
% 2.68/1.37 | (9) ! [v0] : ( ~ (big_h(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & big_f(v0) = v1 & big_g(v0) = v2))
% 2.68/1.37 |
% 2.68/1.37 | Instantiating formula (5) with all_0_0_0, all_0_1_1 and discharging atoms big_i(all_0_1_1) = all_0_0_0, yields:
% 2.68/1.37 | (10) ? [v0] : ? [v1] : ? [v2] : (big_h(all_0_1_1) = v2 & big_f(all_0_1_1) = v1 & big_g(all_0_1_1) = v0 & ((v2 = 0 & v1 = 0) | (v0 = 0 & all_0_0_0 = 0)))
% 2.68/1.37 |
% 2.68/1.37 | Instantiating (10) with all_8_0_2, all_8_1_3, all_8_2_4 yields:
% 2.68/1.37 | (11) big_h(all_0_1_1) = all_8_0_2 & big_f(all_0_1_1) = all_8_1_3 & big_g(all_0_1_1) = all_8_2_4 & ((all_8_0_2 = 0 & all_8_1_3 = 0) | (all_8_2_4 = 0 & all_0_0_0 = 0))
% 2.68/1.37 |
% 2.68/1.37 | Applying alpha-rule on (11) yields:
% 2.68/1.37 | (12) big_h(all_0_1_1) = all_8_0_2
% 2.68/1.37 | (13) big_f(all_0_1_1) = all_8_1_3
% 2.68/1.37 | (14) big_g(all_0_1_1) = all_8_2_4
% 2.68/1.37 | (15) (all_8_0_2 = 0 & all_8_1_3 = 0) | (all_8_2_4 = 0 & all_0_0_0 = 0)
% 2.68/1.37 |
% 2.68/1.37 +-Applying beta-rule and splitting (15), into two cases.
% 2.68/1.37 |-Branch one:
% 2.68/1.37 | (16) all_8_0_2 = 0 & all_8_1_3 = 0
% 2.68/1.37 |
% 2.68/1.37 | Applying alpha-rule on (16) yields:
% 2.68/1.37 | (17) all_8_0_2 = 0
% 2.68/1.37 | (18) all_8_1_3 = 0
% 2.68/1.37 |
% 2.68/1.38 | From (17) and (12) follows:
% 2.68/1.38 | (19) big_h(all_0_1_1) = 0
% 2.68/1.38 |
% 2.68/1.38 | From (18) and (13) follows:
% 2.68/1.38 | (20) big_f(all_0_1_1) = 0
% 2.68/1.38 |
% 2.68/1.38 | Instantiating formula (9) with all_0_1_1 and discharging atoms big_h(all_0_1_1) = 0, yields:
% 2.68/1.38 | (21) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & big_f(all_0_1_1) = v0 & big_g(all_0_1_1) = v1)
% 2.68/1.38 |
% 2.68/1.38 | Instantiating (21) with all_19_0_5, all_19_1_6 yields:
% 2.68/1.38 | (22) ~ (all_19_0_5 = 0) & ~ (all_19_1_6 = 0) & big_f(all_0_1_1) = all_19_1_6 & big_g(all_0_1_1) = all_19_0_5
% 2.68/1.38 |
% 2.68/1.38 | Applying alpha-rule on (22) yields:
% 2.68/1.38 | (23) ~ (all_19_0_5 = 0)
% 2.68/1.38 | (24) ~ (all_19_1_6 = 0)
% 2.68/1.38 | (25) big_f(all_0_1_1) = all_19_1_6
% 2.68/1.38 | (26) big_g(all_0_1_1) = all_19_0_5
% 2.68/1.38 |
% 2.68/1.38 | Instantiating formula (4) with all_0_1_1, all_19_1_6, 0 and discharging atoms big_f(all_0_1_1) = all_19_1_6, big_f(all_0_1_1) = 0, yields:
% 2.68/1.38 | (27) all_19_1_6 = 0
% 2.68/1.38 |
% 2.68/1.38 | Equations (27) can reduce 24 to:
% 2.68/1.38 | (28) $false
% 2.68/1.38 |
% 2.68/1.38 |-The branch is then unsatisfiable
% 2.68/1.38 |-Branch two:
% 2.68/1.38 | (29) all_8_2_4 = 0 & all_0_0_0 = 0
% 2.68/1.38 |
% 2.68/1.38 | Applying alpha-rule on (29) yields:
% 2.68/1.38 | (30) all_8_2_4 = 0
% 2.68/1.38 | (31) all_0_0_0 = 0
% 2.68/1.38 |
% 2.68/1.38 | Equations (31) can reduce 2 to:
% 2.68/1.38 | (28) $false
% 2.68/1.38 |
% 2.68/1.38 |-The branch is then unsatisfiable
% 2.68/1.38 % SZS output end Proof for theBenchmark
% 2.68/1.38
% 2.68/1.38 766ms
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