TSTP Solution File: SYN728+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN728+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 05:04:45 EDT 2022
% Result : Theorem 56.70s 31.74s
% Output : Proof 58.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN728+1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 12 07:31:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.92 Prover 0: Preprocessing ...
% 1.57/1.01 Prover 0: Warning: ignoring some quantifiers
% 1.57/1.02 Prover 0: Constructing countermodel ...
% 1.76/1.15 Prover 0: gave up
% 1.76/1.15 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.76/1.17 Prover 1: Preprocessing ...
% 2.27/1.22 Prover 1: Constructing countermodel ...
% 2.34/1.26 Prover 1: gave up
% 2.34/1.26 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.34/1.27 Prover 2: Preprocessing ...
% 2.34/1.31 Prover 2: Warning: ignoring some quantifiers
% 2.34/1.31 Prover 2: Constructing countermodel ...
% 2.84/1.39 Prover 2: gave up
% 2.84/1.39 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.84/1.40 Prover 3: Preprocessing ...
% 2.84/1.42 Prover 3: Warning: ignoring some quantifiers
% 2.84/1.42 Prover 3: Constructing countermodel ...
% 2.84/1.44 Prover 3: gave up
% 2.84/1.44 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.84/1.45 Prover 4: Preprocessing ...
% 3.13/1.48 Prover 4: Warning: ignoring some quantifiers
% 3.13/1.49 Prover 4: Constructing countermodel ...
% 4.59/1.84 Prover 4: gave up
% 4.59/1.84 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.59/1.85 Prover 5: Preprocessing ...
% 4.59/1.86 Prover 5: Warning: ignoring some quantifiers
% 4.59/1.86 Prover 5: Constructing countermodel ...
% 5.05/1.94 Prover 5: gave up
% 5.05/1.94 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.05/1.95 Prover 6: Preprocessing ...
% 5.05/1.96 Prover 6: Warning: ignoring some quantifiers
% 5.05/1.96 Prover 6: Constructing countermodel ...
% 5.05/1.99 Prover 6: gave up
% 5.05/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.05/1.99 Prover 7: Preprocessing ...
% 5.47/2.00 Prover 7: Proving ...
% 24.90/12.80 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 25.00/12.81 Prover 8: Preprocessing ...
% 25.00/12.83 Prover 8: Proving ...
% 55.47/31.34 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal
% 55.47/31.35 Prover 9: Preprocessing ...
% 55.47/31.36 Prover 9: Proving ...
% 56.45/31.65 Prover 9: proved (307ms)
% 56.45/31.65 Prover 7: stopped
% 56.70/31.74 Prover 8: stopped
% 56.70/31.74
% 56.70/31.74 % SZS status Theorem for theBenchmark
% 56.70/31.74
% 56.70/31.74 Generating proof ... found it (size 39)
% 57.77/32.09
% 57.77/32.09 % SZS output start Proof for theBenchmark
% 57.77/32.09 Assumed formulas after preprocessing and simplification:
% 57.77/32.09 | (0) ? [v0] : ? [v1] : (g(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (f(v5, v4) = v3) | ~ (f(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (g(v4) = v3) | ~ (g(v4) = v2)) & ! [v2] : ( ~ q(v2) | ? [v3] : (g(v2) = v3 & ~ m(v3))) & ! [v2] : ? [v3] : ? [v4] : (f(v2, v3) = v4 & (p(v2, v3) | (q(v4) & m(v2)))) & ( ~ p(v0, v0) | ! [v2] : ~ p(v1, v2)) & ( ! [v2] : ! [v3] : ~ p(v2, v3) | ! [v2] : p(v2, v2)))
% 57.77/32.11 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 57.77/32.11 | (1) g(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (f(v3, v2) = v1) | ~ (f(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) & ! [v0] : ( ~ q(v0) | ? [v1] : (g(v0) = v1 & ~ m(v1))) & ! [v0] : ? [v1] : ? [v2] : (f(v0, v1) = v2 & (p(v0, v1) | (q(v2) & m(v0)))) & ( ~ p(all_0_1_1, all_0_1_1) | ! [v0] : ~ p(all_0_0_0, v0)) & ( ! [v0] : ! [v1] : ~ p(v0, v1) | ! [v0] : p(v0, v0))
% 57.77/32.11 |
% 57.77/32.11 | Applying alpha-rule on (1) yields:
% 57.77/32.11 | (2) ! [v0] : ! [v1] : ~ p(v0, v1) | ! [v0] : p(v0, v0)
% 58.08/32.11 | (3) ! [v0] : ? [v1] : ? [v2] : (f(v0, v1) = v2 & (p(v0, v1) | (q(v2) & m(v0))))
% 58.08/32.11 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (f(v3, v2) = v1) | ~ (f(v3, v2) = v0))
% 58.08/32.11 | (5) ! [v0] : ( ~ q(v0) | ? [v1] : (g(v0) = v1 & ~ m(v1)))
% 58.08/32.11 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0))
% 58.08/32.11 | (7) ~ p(all_0_1_1, all_0_1_1) | ! [v0] : ~ p(all_0_0_0, v0)
% 58.08/32.11 | (8) g(all_0_1_1) = all_0_0_0
% 58.08/32.11 |
% 58.08/32.11 +-Applying beta-rule and splitting (7), into two cases.
% 58.08/32.11 |-Branch one:
% 58.08/32.11 | (9) ~ p(all_0_1_1, all_0_1_1)
% 58.08/32.11 |
% 58.08/32.11 +-Applying beta-rule and splitting (2), into two cases.
% 58.08/32.11 |-Branch one:
% 58.08/32.11 | (10) ! [v0] : ! [v1] : ~ p(v0, v1)
% 58.08/32.11 |
% 58.08/32.11 | Instantiating formula (3) with ex_19_0_2 yields:
% 58.08/32.11 | (11) ? [v0] : ? [v1] : (f(ex_19_0_2, v0) = v1 & (p(ex_19_0_2, v0) | (q(v1) & m(ex_19_0_2))))
% 58.08/32.11 |
% 58.08/32.11 | Instantiating (11) with all_20_0_3, all_20_1_4 yields:
% 58.08/32.11 | (12) f(ex_19_0_2, all_20_1_4) = all_20_0_3 & (p(ex_19_0_2, all_20_1_4) | (q(all_20_0_3) & m(ex_19_0_2)))
% 58.08/32.11 |
% 58.08/32.12 | Applying alpha-rule on (12) yields:
% 58.08/32.12 | (13) f(ex_19_0_2, all_20_1_4) = all_20_0_3
% 58.08/32.12 | (14) p(ex_19_0_2, all_20_1_4) | (q(all_20_0_3) & m(ex_19_0_2))
% 58.08/32.12 |
% 58.08/32.12 +-Applying beta-rule and splitting (14), into two cases.
% 58.08/32.12 |-Branch one:
% 58.08/32.12 | (15) p(ex_19_0_2, all_20_1_4)
% 58.08/32.12 |
% 58.08/32.12 | Instantiating formula (10) with all_20_1_4, ex_19_0_2 and discharging atoms p(ex_19_0_2, all_20_1_4), yields:
% 58.08/32.12 | (16) $false
% 58.08/32.12 |
% 58.08/32.12 |-The branch is then unsatisfiable
% 58.08/32.12 |-Branch two:
% 58.08/32.12 | (17) q(all_20_0_3) & m(ex_19_0_2)
% 58.08/32.12 |
% 58.08/32.12 | Applying alpha-rule on (17) yields:
% 58.08/32.12 | (18) q(all_20_0_3)
% 58.08/32.12 | (19) m(ex_19_0_2)
% 58.08/32.12 |
% 58.08/32.12 | Instantiating formula (5) with all_20_0_3 and discharging atoms q(all_20_0_3), yields:
% 58.08/32.12 | (20) ? [v0] : (g(all_20_0_3) = v0 & ~ m(v0))
% 58.08/32.12 |
% 58.08/32.12 | Instantiating (20) with all_34_0_5 yields:
% 58.08/32.12 | (21) g(all_20_0_3) = all_34_0_5 & ~ m(all_34_0_5)
% 58.08/32.12 |
% 58.08/32.12 | Applying alpha-rule on (21) yields:
% 58.08/32.12 | (22) g(all_20_0_3) = all_34_0_5
% 58.08/32.12 | (23) ~ m(all_34_0_5)
% 58.08/32.12 |
% 58.08/32.12 | Introducing new symbol ex_42_0_6 defined by:
% 58.08/32.12 | (24) ex_42_0_6 = all_34_0_5
% 58.08/32.12 |
% 58.08/32.12 | Instantiating formula (3) with ex_42_0_6 yields:
% 58.08/32.12 | (25) ? [v0] : ? [v1] : (f(ex_42_0_6, v0) = v1 & (p(ex_42_0_6, v0) | (q(v1) & m(ex_42_0_6))))
% 58.08/32.12 |
% 58.08/32.12 | Instantiating (25) with all_43_0_7, all_43_1_8 yields:
% 58.08/32.12 | (26) f(ex_42_0_6, all_43_1_8) = all_43_0_7 & (p(ex_42_0_6, all_43_1_8) | (q(all_43_0_7) & m(ex_42_0_6)))
% 58.08/32.12 |
% 58.08/32.12 | Applying alpha-rule on (26) yields:
% 58.08/32.12 | (27) f(ex_42_0_6, all_43_1_8) = all_43_0_7
% 58.08/32.12 | (28) p(ex_42_0_6, all_43_1_8) | (q(all_43_0_7) & m(ex_42_0_6))
% 58.08/32.12 |
% 58.08/32.12 +-Applying beta-rule and splitting (28), into two cases.
% 58.08/32.12 |-Branch one:
% 58.08/32.12 | (29) p(ex_42_0_6, all_43_1_8)
% 58.08/32.12 |
% 58.08/32.12 | Instantiating formula (10) with all_43_1_8, ex_42_0_6 and discharging atoms p(ex_42_0_6, all_43_1_8), yields:
% 58.08/32.12 | (16) $false
% 58.08/32.12 |
% 58.08/32.12 |-The branch is then unsatisfiable
% 58.08/32.12 |-Branch two:
% 58.08/32.12 | (31) q(all_43_0_7) & m(ex_42_0_6)
% 58.08/32.12 |
% 58.08/32.12 | Applying alpha-rule on (31) yields:
% 58.08/32.12 | (32) q(all_43_0_7)
% 58.08/32.12 | (33) m(ex_42_0_6)
% 58.08/32.12 |
% 58.08/32.12 | From (24) and (33) follows:
% 58.08/32.12 | (34) m(all_34_0_5)
% 58.08/32.12 |
% 58.08/32.12 | Using (34) and (23) yields:
% 58.08/32.12 | (16) $false
% 58.08/32.12 |
% 58.08/32.12 |-The branch is then unsatisfiable
% 58.08/32.12 |-Branch two:
% 58.08/32.12 | (36) ! [v0] : p(v0, v0)
% 58.08/32.12 |
% 58.08/32.12 | Introducing new symbol ex_33_0_12 defined by:
% 58.08/32.12 | (37) ex_33_0_12 = all_0_1_1
% 58.08/32.12 |
% 58.08/32.12 | Instantiating formula (36) with ex_33_0_12 yields:
% 58.08/32.12 | (38) p(ex_33_0_12, ex_33_0_12)
% 58.08/32.12 |
% 58.08/32.12 | From (37)(37) and (38) follows:
% 58.08/32.12 | (39) p(all_0_1_1, all_0_1_1)
% 58.08/32.12 |
% 58.08/32.12 | Using (39) and (9) yields:
% 58.08/32.12 | (16) $false
% 58.08/32.12 |
% 58.08/32.12 |-The branch is then unsatisfiable
% 58.08/32.12 |-Branch two:
% 58.08/32.12 | (39) p(all_0_1_1, all_0_1_1)
% 58.08/32.12 | (42) ! [v0] : ~ p(all_0_0_0, v0)
% 58.08/32.12 |
% 58.08/32.12 +-Applying beta-rule and splitting (2), into two cases.
% 58.08/32.12 |-Branch one:
% 58.08/32.12 | (10) ! [v0] : ! [v1] : ~ p(v0, v1)
% 58.08/32.12 |
% 58.08/32.12 | Instantiating formula (10) with all_0_1_1, all_0_1_1 and discharging atoms p(all_0_1_1, all_0_1_1), yields:
% 58.08/32.12 | (16) $false
% 58.08/32.12 |
% 58.08/32.12 |-The branch is then unsatisfiable
% 58.08/32.12 |-Branch two:
% 58.08/32.12 | (36) ! [v0] : p(v0, v0)
% 58.08/32.12 |
% 58.08/32.12 | Introducing new symbol ex_41_0_19 defined by:
% 58.08/32.12 | (46) ex_41_0_19 = all_0_0_0
% 58.08/32.12 |
% 58.08/32.12 | Instantiating formula (36) with ex_41_0_19 yields:
% 58.08/32.12 | (47) p(ex_41_0_19, ex_41_0_19)
% 58.08/32.12 |
% 58.08/32.12 | Instantiating formula (42) with all_0_0_0 yields:
% 58.08/32.12 | (48) ~ p(all_0_0_0, all_0_0_0)
% 58.08/32.12 |
% 58.08/32.12 | From (46)(46) and (47) follows:
% 58.08/32.12 | (49) p(all_0_0_0, all_0_0_0)
% 58.08/32.12 |
% 58.08/32.12 | Using (49) and (48) yields:
% 58.08/32.12 | (16) $false
% 58.08/32.12 |
% 58.08/32.12 |-The branch is then unsatisfiable
% 58.08/32.12 % SZS output end Proof for theBenchmark
% 58.08/32.12
% 58.08/32.12 31525ms
%------------------------------------------------------------------------------