TSTP Solution File: SYN058+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN058+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 04:59:30 EDT 2022
% Result : Theorem 2.23s 1.21s
% Output : Proof 3.04s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN058+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jul 12 04:59:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.53/0.61 ____ _
% 0.53/0.61 ___ / __ \_____(_)___ ________ __________
% 0.53/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.61
% 0.53/0.61 A Theorem Prover for First-Order Logic
% 0.53/0.61 (ePrincess v.1.0)
% 0.53/0.61
% 0.53/0.61 (c) Philipp Rümmer, 2009-2015
% 0.53/0.61 (c) Peter Backeman, 2014-2015
% 0.53/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.61 Bug reports to peter@backeman.se
% 0.53/0.61
% 0.53/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.61
% 0.53/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.35/0.90 Prover 0: Preprocessing ...
% 1.50/0.95 Prover 0: Warning: ignoring some quantifiers
% 1.56/0.97 Prover 0: Constructing countermodel ...
% 1.67/1.07 Prover 0: gave up
% 1.82/1.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.82/1.09 Prover 1: Preprocessing ...
% 2.14/1.16 Prover 1: Constructing countermodel ...
% 2.23/1.21 Prover 1: proved (138ms)
% 2.23/1.21
% 2.23/1.21 No countermodel exists, formula is valid
% 2.23/1.21 % SZS status Theorem for theBenchmark
% 2.23/1.21
% 2.23/1.21 Generating proof ... found it (size 20)
% 2.74/1.39
% 2.74/1.39 % SZS output start Proof for theBenchmark
% 2.74/1.39 Assumed formulas after preprocessing and simplification:
% 2.74/1.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v1 = 0) & big_g(v0) = v1 & big_f(v0) = 0 & big_p(v0) = 0 & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (big_p(v5) = 0) | ~ (big_q(v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_g(v7) = v6) | ~ (big_g(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_f(v7) = v6) | ~ (big_f(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_s(v7) = v6) | ~ (big_s(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_r(v7) = v6) | ~ (big_r(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_p(v7) = v6) | ~ (big_p(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_q(v7) = v6) | ~ (big_q(v7) = v5)) & ( ! [v5] : ! [v6] : (v6 = 0 | ~ (big_g(v5) = v6) | ? [v7] : ( ~ (v7 = 0) & big_f(v5) = v7)) | ! [v5] : ~ (big_s(v5) = 0)) & ((v4 = 0 & v3 = 0 & big_s(v2) = 0 & big_q(v2) = 0) | ( ~ (v4 = 0) & ~ (v3 = 0) & big_r(v2) = v4 & big_q(v2) = v3)))
% 2.74/1.42 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 2.74/1.42 | (1) ~ (all_0_3_3 = 0) & big_g(all_0_4_4) = all_0_3_3 & big_f(all_0_4_4) = 0 & big_p(all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_p(v0) = 0) | ~ (big_q(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_s(v2) = v1) | ~ (big_s(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_r(v2) = v1) | ~ (big_r(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_q(v2) = v1) | ~ (big_q(v2) = v0)) & ( ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_f(v0) = v2)) | ! [v0] : ~ (big_s(v0) = 0)) & ((all_0_0_0 = 0 & all_0_1_1 = 0 & big_s(all_0_2_2) = 0 & big_q(all_0_2_2) = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & big_r(all_0_2_2) = all_0_0_0 & big_q(all_0_2_2) = all_0_1_1))
% 2.74/1.43 |
% 2.74/1.43 | Applying alpha-rule on (1) yields:
% 2.74/1.43 | (2) big_f(all_0_4_4) = 0
% 2.74/1.43 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_s(v2) = v1) | ~ (big_s(v2) = v0))
% 2.74/1.43 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_q(v2) = v1) | ~ (big_q(v2) = v0))
% 2.74/1.43 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_r(v2) = v1) | ~ (big_r(v2) = v0))
% 2.74/1.43 | (6) ~ (all_0_3_3 = 0)
% 2.74/1.43 | (7) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_f(v0) = v2)) | ! [v0] : ~ (big_s(v0) = 0)
% 2.74/1.43 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0))
% 2.74/1.43 | (9) (all_0_0_0 = 0 & all_0_1_1 = 0 & big_s(all_0_2_2) = 0 & big_q(all_0_2_2) = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & big_r(all_0_2_2) = all_0_0_0 & big_q(all_0_2_2) = all_0_1_1)
% 2.74/1.43 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 2.74/1.43 | (11) big_g(all_0_4_4) = all_0_3_3
% 2.74/1.43 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_p(v0) = 0) | ~ (big_q(v1) = v2))
% 2.74/1.43 | (13) big_p(all_0_4_4) = 0
% 2.74/1.43 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 2.74/1.43 |
% 2.74/1.43 +-Applying beta-rule and splitting (9), into two cases.
% 2.74/1.43 |-Branch one:
% 2.74/1.43 | (15) all_0_0_0 = 0 & all_0_1_1 = 0 & big_s(all_0_2_2) = 0 & big_q(all_0_2_2) = 0
% 2.74/1.43 |
% 2.74/1.43 | Applying alpha-rule on (15) yields:
% 2.74/1.43 | (16) all_0_0_0 = 0
% 2.74/1.43 | (17) all_0_1_1 = 0
% 2.74/1.43 | (18) big_s(all_0_2_2) = 0
% 2.74/1.43 | (19) big_q(all_0_2_2) = 0
% 2.74/1.43 |
% 2.74/1.43 +-Applying beta-rule and splitting (7), into two cases.
% 2.74/1.43 |-Branch one:
% 2.74/1.43 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_g(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_f(v0) = v2))
% 2.74/1.44 |
% 2.74/1.44 | Instantiating formula (20) with all_0_3_3, all_0_4_4 and discharging atoms big_g(all_0_4_4) = all_0_3_3, yields:
% 2.74/1.44 | (21) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & big_f(all_0_4_4) = v0)
% 3.04/1.44 |
% 3.04/1.44 +-Applying beta-rule and splitting (21), into two cases.
% 3.04/1.44 |-Branch one:
% 3.04/1.44 | (22) all_0_3_3 = 0
% 3.04/1.44 |
% 3.04/1.44 | Equations (22) can reduce 6 to:
% 3.04/1.44 | (23) $false
% 3.04/1.44 |
% 3.04/1.44 |-The branch is then unsatisfiable
% 3.04/1.44 |-Branch two:
% 3.04/1.44 | (6) ~ (all_0_3_3 = 0)
% 3.04/1.44 | (25) ? [v0] : ( ~ (v0 = 0) & big_f(all_0_4_4) = v0)
% 3.04/1.44 |
% 3.04/1.44 | Instantiating (25) with all_21_0_5 yields:
% 3.04/1.44 | (26) ~ (all_21_0_5 = 0) & big_f(all_0_4_4) = all_21_0_5
% 3.04/1.44 |
% 3.04/1.44 | Applying alpha-rule on (26) yields:
% 3.04/1.44 | (27) ~ (all_21_0_5 = 0)
% 3.04/1.44 | (28) big_f(all_0_4_4) = all_21_0_5
% 3.04/1.44 |
% 3.04/1.44 | Instantiating formula (10) with all_0_4_4, all_21_0_5, 0 and discharging atoms big_f(all_0_4_4) = all_21_0_5, big_f(all_0_4_4) = 0, yields:
% 3.04/1.44 | (29) all_21_0_5 = 0
% 3.04/1.44 |
% 3.04/1.44 | Equations (29) can reduce 27 to:
% 3.04/1.44 | (23) $false
% 3.04/1.44 |
% 3.04/1.44 |-The branch is then unsatisfiable
% 3.04/1.44 |-Branch two:
% 3.04/1.44 | (31) ! [v0] : ~ (big_s(v0) = 0)
% 3.04/1.44 |
% 3.04/1.44 | Instantiating formula (31) with all_0_2_2 and discharging atoms big_s(all_0_2_2) = 0, yields:
% 3.04/1.44 | (32) $false
% 3.04/1.44 |
% 3.04/1.44 |-The branch is then unsatisfiable
% 3.04/1.44 |-Branch two:
% 3.04/1.44 | (33) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & big_r(all_0_2_2) = all_0_0_0 & big_q(all_0_2_2) = all_0_1_1
% 3.04/1.44 |
% 3.04/1.44 | Applying alpha-rule on (33) yields:
% 3.04/1.44 | (34) ~ (all_0_0_0 = 0)
% 3.04/1.44 | (35) ~ (all_0_1_1 = 0)
% 3.04/1.44 | (36) big_r(all_0_2_2) = all_0_0_0
% 3.04/1.44 | (37) big_q(all_0_2_2) = all_0_1_1
% 3.04/1.44 |
% 3.04/1.44 | Instantiating formula (12) with all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms big_p(all_0_4_4) = 0, big_q(all_0_2_2) = all_0_1_1, yields:
% 3.04/1.44 | (17) all_0_1_1 = 0
% 3.04/1.44 |
% 3.04/1.44 | Equations (17) can reduce 35 to:
% 3.04/1.44 | (23) $false
% 3.04/1.44 |
% 3.04/1.44 |-The branch is then unsatisfiable
% 3.04/1.44 % SZS output end Proof for theBenchmark
% 3.04/1.44
% 3.04/1.44 824ms
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