TSTP Solution File: SYN355+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN355+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 05:01:44 EDT 2022
% Result : Theorem 2.24s 1.28s
% Output : Proof 2.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN355+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n029.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 : Tue Jul 12 07:49:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.55/0.62 ____ _
% 0.55/0.62 ___ / __ \_____(_)___ ________ __________
% 0.55/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.62
% 0.55/0.62 A Theorem Prover for First-Order Logic
% 0.55/0.62 (ePrincess v.1.0)
% 0.55/0.62
% 0.55/0.62 (c) Philipp Rümmer, 2009-2015
% 0.55/0.62 (c) Peter Backeman, 2014-2015
% 0.65/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.65/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.65/0.62 Bug reports to peter@backeman.se
% 0.65/0.62
% 0.65/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.65/0.63
% 0.65/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.96 Prover 0: Preprocessing ...
% 1.30/1.00 Prover 0: Warning: ignoring some quantifiers
% 1.46/1.02 Prover 0: Constructing countermodel ...
% 1.63/1.10 Prover 0: gave up
% 1.63/1.10 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.63/1.12 Prover 1: Preprocessing ...
% 2.04/1.17 Prover 1: Constructing countermodel ...
% 2.14/1.21 Prover 1: gave up
% 2.14/1.21 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.14/1.22 Prover 2: Preprocessing ...
% 2.24/1.25 Prover 2: Warning: ignoring some quantifiers
% 2.24/1.25 Prover 2: Constructing countermodel ...
% 2.24/1.28 Prover 2: proved (73ms)
% 2.24/1.28
% 2.24/1.28 No countermodel exists, formula is valid
% 2.24/1.28 % SZS status Theorem for theBenchmark
% 2.24/1.28
% 2.24/1.28 Generating proof ... Warning: ignoring some quantifiers
% 2.71/1.44 found it (size 15)
% 2.71/1.44
% 2.71/1.45 % SZS output start Proof for theBenchmark
% 2.71/1.45 Assumed formulas after preprocessing and simplification:
% 2.71/1.45 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & big_q(v0) = v2 & big_p(v0) = v1 & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (big_q(v5) = v4) | ~ (big_q(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (big_p(v5) = v4) | ~ (big_p(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (big_r(v5) = v4) | ~ (big_r(v5) = v3)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (big_q(v3) = v4) | big_r(v3) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (big_p(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & big_r(v3) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (big_r(v3) = v4) | big_q(v3) = 0) & ! [v3] : ( ~ (big_r(v3) = 0) | big_p(v3) = 0) & ? [v3] : ? [v4] : big_q(v3) = v4 & ? [v3] : ? [v4] : big_p(v3) = v4 & ? [v3] : ? [v4] : big_r(v3) = v4)
% 2.92/1.48 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.92/1.48 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & big_q(all_0_2_2) = all_0_0_0 & big_p(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_q(v2) = v1) | ~ (big_q(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_r(v2) = v1) | ~ (big_r(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_q(v0) = v1) | big_r(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_r(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_r(v0) = v1) | big_q(v0) = 0) & ! [v0] : ( ~ (big_r(v0) = 0) | big_p(v0) = 0) & ? [v0] : ? [v1] : big_q(v0) = v1 & ? [v0] : ? [v1] : big_p(v0) = v1 & ? [v0] : ? [v1] : big_r(v0) = v1
% 2.92/1.48 |
% 2.92/1.48 | Applying alpha-rule on (1) yields:
% 2.92/1.48 | (2) big_p(all_0_2_2) = all_0_1_1
% 2.92/1.48 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_r(v2) = v1) | ~ (big_r(v2) = v0))
% 2.92/1.48 | (4) ? [v0] : ? [v1] : big_q(v0) = v1
% 2.92/1.48 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_r(v0) = v2))
% 2.92/1.48 | (6) big_q(all_0_2_2) = all_0_0_0
% 2.92/1.48 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 2.92/1.48 | (8) ! [v0] : ( ~ (big_r(v0) = 0) | big_p(v0) = 0)
% 2.92/1.48 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_r(v0) = v1) | big_q(v0) = 0)
% 2.92/1.48 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_q(v0) = v1) | big_r(v0) = 0)
% 2.92/1.48 | (11) ? [v0] : ? [v1] : big_r(v0) = v1
% 2.92/1.48 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_q(v2) = v1) | ~ (big_q(v2) = v0))
% 2.92/1.49 | (13) ? [v0] : ? [v1] : big_p(v0) = v1
% 2.92/1.49 | (14) ~ (all_0_0_0 = 0)
% 2.92/1.49 | (15) ~ (all_0_1_1 = 0)
% 2.92/1.49 |
% 2.92/1.49 | Instantiating formula (10) with all_0_0_0, all_0_2_2 and discharging atoms big_q(all_0_2_2) = all_0_0_0, yields:
% 2.92/1.49 | (16) all_0_0_0 = 0 | big_r(all_0_2_2) = 0
% 2.92/1.49 |
% 2.92/1.49 | Instantiating formula (5) with all_0_1_1, all_0_2_2 and discharging atoms big_p(all_0_2_2) = all_0_1_1, yields:
% 2.92/1.49 | (17) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & big_r(all_0_2_2) = v0)
% 2.92/1.49 |
% 2.92/1.49 +-Applying beta-rule and splitting (16), into two cases.
% 2.92/1.49 |-Branch one:
% 2.92/1.49 | (18) big_r(all_0_2_2) = 0
% 2.92/1.49 |
% 2.92/1.49 +-Applying beta-rule and splitting (17), into two cases.
% 2.92/1.49 |-Branch one:
% 2.92/1.49 | (19) all_0_1_1 = 0
% 2.92/1.49 |
% 2.92/1.49 | Equations (19) can reduce 15 to:
% 2.92/1.49 | (20) $false
% 2.92/1.49 |
% 2.92/1.49 |-The branch is then unsatisfiable
% 2.92/1.49 |-Branch two:
% 2.92/1.49 | (15) ~ (all_0_1_1 = 0)
% 2.92/1.49 | (22) ? [v0] : ( ~ (v0 = 0) & big_r(all_0_2_2) = v0)
% 2.92/1.49 |
% 2.92/1.49 | Instantiating (22) with all_20_0_9 yields:
% 2.92/1.49 | (23) ~ (all_20_0_9 = 0) & big_r(all_0_2_2) = all_20_0_9
% 2.92/1.49 |
% 2.92/1.49 | Applying alpha-rule on (23) yields:
% 2.92/1.49 | (24) ~ (all_20_0_9 = 0)
% 2.92/1.49 | (25) big_r(all_0_2_2) = all_20_0_9
% 2.92/1.49 |
% 2.92/1.49 | Instantiating formula (3) with all_0_2_2, 0, all_20_0_9 and discharging atoms big_r(all_0_2_2) = all_20_0_9, big_r(all_0_2_2) = 0, yields:
% 2.92/1.49 | (26) all_20_0_9 = 0
% 2.92/1.49 |
% 2.92/1.49 | Equations (26) can reduce 24 to:
% 2.92/1.49 | (20) $false
% 2.92/1.49 |
% 2.92/1.49 |-The branch is then unsatisfiable
% 2.92/1.49 |-Branch two:
% 2.92/1.49 | (28) ~ (big_r(all_0_2_2) = 0)
% 2.92/1.49 | (29) all_0_0_0 = 0
% 2.92/1.49 |
% 2.92/1.49 | Equations (29) can reduce 14 to:
% 2.92/1.49 | (20) $false
% 2.92/1.49 |
% 2.92/1.49 |-The branch is then unsatisfiable
% 2.92/1.49 % SZS output end Proof for theBenchmark
% 2.92/1.49
% 2.92/1.49 851ms
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