TSTP Solution File: SYN061+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN061+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 04:59:33 EDT 2022
% Result : Theorem 2.40s 1.22s
% Output : Proof 3.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SYN061+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.31 % Computer : n012.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jul 11 19:10:57 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.51 ____ _
% 0.16/0.51 ___ / __ \_____(_)___ ________ __________
% 0.16/0.51 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.16/0.51 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.16/0.51 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.16/0.51
% 0.16/0.51 A Theorem Prover for First-Order Logic
% 0.16/0.51 (ePrincess v.1.0)
% 0.16/0.51
% 0.16/0.51 (c) Philipp Rümmer, 2009-2015
% 0.16/0.51 (c) Peter Backeman, 2014-2015
% 0.16/0.51 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.16/0.51 Free software under GNU Lesser General Public License (LGPL).
% 0.16/0.51 Bug reports to peter@backeman.se
% 0.16/0.51
% 0.16/0.51 For more information, visit http://user.uu.se/~petba168/breu/
% 0.16/0.51
% 0.16/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.60 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.22/0.84 Prover 0: Preprocessing ...
% 1.26/0.89 Prover 0: Warning: ignoring some quantifiers
% 1.26/0.91 Prover 0: Constructing countermodel ...
% 1.62/1.00 Prover 0: gave up
% 1.62/1.00 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.62/1.01 Prover 1: Preprocessing ...
% 1.89/1.08 Prover 1: Constructing countermodel ...
% 1.99/1.10 Prover 1: gave up
% 1.99/1.10 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.99/1.11 Prover 2: Preprocessing ...
% 2.25/1.17 Prover 2: Warning: ignoring some quantifiers
% 2.25/1.17 Prover 2: Constructing countermodel ...
% 2.40/1.22 Prover 2: proved (122ms)
% 2.40/1.22
% 2.40/1.22 No countermodel exists, formula is valid
% 2.40/1.22 % SZS status Theorem for theBenchmark
% 2.40/1.23
% 2.40/1.23 Generating proof ... Warning: ignoring some quantifiers
% 2.89/1.40 found it (size 15)
% 2.89/1.40
% 2.89/1.40 % SZS output start Proof for theBenchmark
% 2.89/1.40 Assumed formulas after preprocessing and simplification:
% 2.89/1.40 | (0) ? [v0] : (big_i(v0) = 0 & big_f(v0) = 0 & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_j(v3) = v2) | ~ (big_j(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_i(v3) = v2) | ~ (big_i(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_g(v3) = v2) | ~ (big_g(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_f(v3) = v2) | ~ (big_f(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_h(v3) = v2) | ~ (big_h(v3) = v1)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (big_j(v1) = v2) | big_h(v1) = 0) & ! [v1] : ! [v2] : (v2 = 0 | ~ (big_h(v1) = v2) | big_j(v1) = 0) & ! [v1] : ! [v2] : ( ~ (big_g(v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ~ (v2 = 0) & big_h(v1) = v3) | ( ~ (v3 = 0) & big_f(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (big_h(v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ~ (v2 = 0) & big_g(v1) = v3) | ( ~ (v3 = 0) & big_f(v1) = v3))) & ! [v1] : ( ~ (big_j(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & big_i(v1) = v2)) & ! [v1] : ( ~ (big_i(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & big_j(v1) = v2)) & ! [v1] : ( ~ (big_f(v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & big_g(v1) = v2 & big_h(v1) = v3)) & ? [v1] : ? [v2] : big_j(v1) = v2 & ? [v1] : ? [v2] : big_i(v1) = v2 & ? [v1] : ? [v2] : big_g(v1) = v2 & ? [v1] : ? [v2] : big_f(v1) = v2 & ? [v1] : ? [v2] : big_h(v1) = v2)
% 2.89/1.43 | Instantiating (0) with all_0_0_0 yields:
% 2.89/1.43 | (1) big_i(all_0_0_0) = 0 & big_f(all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_j(v2) = v1) | ~ (big_j(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_i(v2) = v1) | ~ (big_i(v2) = v0)) & ! [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_h(v2) = v1) | ~ (big_h(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(v0) = v1) | big_h(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_h(v0) = v1) | big_j(v0) = 0) & ! [v0] : ! [v1] : ( ~ (big_g(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & ~ (v1 = 0) & big_h(v0) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (big_h(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2))) & ! [v0] : ( ~ (big_j(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_i(v0) = v1)) & ! [v0] : ( ~ (big_i(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_j(v0) = v1)) & ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v1 & big_h(v0) = v2)) & ? [v0] : ? [v1] : big_j(v0) = v1 & ? [v0] : ? [v1] : big_i(v0) = v1 & ? [v0] : ? [v1] : big_g(v0) = v1 & ? [v0] : ? [v1] : big_f(v0) = v1 & ? [v0] : ? [v1] : big_h(v0) = v1
% 3.13/1.44 |
% 3.13/1.44 | Applying alpha-rule on (1) yields:
% 3.13/1.44 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0))
% 3.13/1.44 | (3) big_i(all_0_0_0) = 0
% 3.13/1.44 | (4) ? [v0] : ? [v1] : big_j(v0) = v1
% 3.13/1.44 | (5) ! [v0] : ( ~ (big_i(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_j(v0) = v1))
% 3.13/1.44 | (6) ! [v0] : ( ~ (big_j(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_i(v0) = v1))
% 3.13/1.44 | (7) ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v1 & big_h(v0) = v2))
% 3.13/1.44 | (8) ? [v0] : ? [v1] : big_g(v0) = v1
% 3.13/1.44 | (9) ? [v0] : ? [v1] : big_h(v0) = v1
% 3.13/1.44 | (10) ! [v0] : ! [v1] : ( ~ (big_g(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & ~ (v1 = 0) & big_h(v0) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2)))
% 3.13/1.44 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_h(v2) = v1) | ~ (big_h(v2) = v0))
% 3.13/1.44 | (12) ? [v0] : ? [v1] : big_f(v0) = v1
% 3.13/1.44 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_i(v2) = v1) | ~ (big_i(v2) = v0))
% 3.13/1.44 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_h(v0) = v1) | big_j(v0) = 0)
% 3.13/1.44 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(v0) = v1) | big_h(v0) = 0)
% 3.13/1.44 | (16) ! [v0] : ! [v1] : ( ~ (big_h(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v2) | ( ~ (v2 = 0) & big_f(v0) = v2)))
% 3.13/1.44 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 3.13/1.44 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_j(v2) = v1) | ~ (big_j(v2) = v0))
% 3.13/1.44 | (19) ? [v0] : ? [v1] : big_i(v0) = v1
% 3.13/1.44 | (20) big_f(all_0_0_0) = 0
% 3.13/1.44 |
% 3.13/1.44 | Instantiating formula (5) with all_0_0_0 and discharging atoms big_i(all_0_0_0) = 0, yields:
% 3.13/1.45 | (21) ? [v0] : ( ~ (v0 = 0) & big_j(all_0_0_0) = v0)
% 3.13/1.45 |
% 3.13/1.45 | Instantiating formula (7) with all_0_0_0 and discharging atoms big_f(all_0_0_0) = 0, yields:
% 3.13/1.45 | (22) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & big_g(all_0_0_0) = v0 & big_h(all_0_0_0) = v1)
% 3.13/1.45 |
% 3.13/1.45 | Instantiating (22) with all_18_0_11, all_18_1_12 yields:
% 3.13/1.45 | (23) ~ (all_18_0_11 = 0) & ~ (all_18_1_12 = 0) & big_g(all_0_0_0) = all_18_1_12 & big_h(all_0_0_0) = all_18_0_11
% 3.13/1.45 |
% 3.13/1.45 | Applying alpha-rule on (23) yields:
% 3.13/1.45 | (24) ~ (all_18_0_11 = 0)
% 3.13/1.45 | (25) ~ (all_18_1_12 = 0)
% 3.13/1.45 | (26) big_g(all_0_0_0) = all_18_1_12
% 3.13/1.45 | (27) big_h(all_0_0_0) = all_18_0_11
% 3.13/1.45 |
% 3.13/1.45 | Instantiating (21) with all_20_0_13 yields:
% 3.13/1.45 | (28) ~ (all_20_0_13 = 0) & big_j(all_0_0_0) = all_20_0_13
% 3.13/1.45 |
% 3.13/1.45 | Applying alpha-rule on (28) yields:
% 3.13/1.45 | (29) ~ (all_20_0_13 = 0)
% 3.13/1.45 | (30) big_j(all_0_0_0) = all_20_0_13
% 3.13/1.45 |
% 3.13/1.45 | Instantiating formula (15) with all_20_0_13, all_0_0_0 and discharging atoms big_j(all_0_0_0) = all_20_0_13, yields:
% 3.13/1.45 | (31) all_20_0_13 = 0 | big_h(all_0_0_0) = 0
% 3.13/1.45 |
% 3.13/1.45 +-Applying beta-rule and splitting (31), into two cases.
% 3.13/1.45 |-Branch one:
% 3.13/1.45 | (32) big_h(all_0_0_0) = 0
% 3.13/1.45 |
% 3.13/1.45 | Instantiating formula (11) with all_0_0_0, 0, all_18_0_11 and discharging atoms big_h(all_0_0_0) = all_18_0_11, big_h(all_0_0_0) = 0, yields:
% 3.13/1.45 | (33) all_18_0_11 = 0
% 3.13/1.45 |
% 3.13/1.45 | Equations (33) can reduce 24 to:
% 3.13/1.45 | (34) $false
% 3.13/1.45 |
% 3.13/1.45 |-The branch is then unsatisfiable
% 3.13/1.45 |-Branch two:
% 3.13/1.45 | (35) ~ (big_h(all_0_0_0) = 0)
% 3.13/1.45 | (36) all_20_0_13 = 0
% 3.13/1.45 |
% 3.13/1.45 | Equations (36) can reduce 29 to:
% 3.13/1.45 | (34) $false
% 3.13/1.45 |
% 3.13/1.45 |-The branch is then unsatisfiable
% 3.13/1.45 % SZS output end Proof for theBenchmark
% 3.13/1.45
% 3.13/1.45 912ms
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