TSTP Solution File: SEU138+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU138+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 : Tue Jul 19 08:46:52 EDT 2022
% Result : Theorem 20.82s 6.11s
% Output : Proof 24.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU138+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sun Jun 19 07:31:18 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.57/0.62 ____ _
% 0.57/0.62 ___ / __ \_____(_)___ ________ __________
% 0.57/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.62
% 0.57/0.62 A Theorem Prover for First-Order Logic
% 0.57/0.63 (ePrincess v.1.0)
% 0.57/0.63
% 0.57/0.63 (c) Philipp Rümmer, 2009-2015
% 0.57/0.63 (c) Peter Backeman, 2014-2015
% 0.57/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.63 Bug reports to peter@backeman.se
% 0.57/0.63
% 0.57/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.63
% 0.57/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.46/0.96 Prover 0: Preprocessing ...
% 1.84/1.15 Prover 0: Warning: ignoring some quantifiers
% 1.84/1.17 Prover 0: Constructing countermodel ...
% 2.75/1.39 Prover 0: gave up
% 2.75/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.75/1.42 Prover 1: Preprocessing ...
% 3.21/1.50 Prover 1: Warning: ignoring some quantifiers
% 3.21/1.51 Prover 1: Constructing countermodel ...
% 3.47/1.61 Prover 1: gave up
% 3.47/1.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.81/1.62 Prover 2: Preprocessing ...
% 4.16/1.72 Prover 2: Warning: ignoring some quantifiers
% 4.16/1.72 Prover 2: Constructing countermodel ...
% 4.80/1.84 Prover 2: gave up
% 4.80/1.84 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.80/1.86 Prover 3: Preprocessing ...
% 4.80/1.89 Prover 3: Warning: ignoring some quantifiers
% 4.80/1.89 Prover 3: Constructing countermodel ...
% 5.15/1.97 Prover 3: gave up
% 5.15/1.97 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.47/1.98 Prover 4: Preprocessing ...
% 5.91/2.09 Prover 4: Warning: ignoring some quantifiers
% 6.01/2.09 Prover 4: Constructing countermodel ...
% 10.36/3.18 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.36/3.20 Prover 5: Preprocessing ...
% 10.75/3.28 Prover 5: Warning: ignoring some quantifiers
% 10.75/3.28 Prover 5: Constructing countermodel ...
% 11.41/3.38 Prover 5: gave up
% 11.41/3.38 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 11.41/3.39 Prover 6: Preprocessing ...
% 11.65/3.44 Prover 6: Warning: ignoring some quantifiers
% 11.73/3.44 Prover 6: Constructing countermodel ...
% 11.73/3.50 Prover 6: gave up
% 11.73/3.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 11.73/3.51 Prover 7: Preprocessing ...
% 12.07/3.54 Prover 7: Proving ...
% 20.82/6.11 Prover 7: proved (2605ms)
% 20.82/6.11 Prover 4: stopped
% 20.82/6.11
% 20.82/6.11 % SZS status Theorem for theBenchmark
% 20.82/6.11
% 20.82/6.11 Generating proof ... found it (size 53)
% 24.99/7.38
% 24.99/7.38 % SZS output start Proof for theBenchmark
% 24.99/7.38 Assumed formulas after preprocessing and simplification:
% 24.99/7.38 | (0) ? [v0] : (empty(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_difference(v4, v3) = v2) | ~ (set_difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_intersection2(v4, v3) = v2) | ~ (set_intersection2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v1) | in(v5, v2)) & (in(v5, v4) | (in(v5, v1) & ~ in(v5, v2)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v1) & ~ in(v4, v2))) & ! [v4] : ( ~ in(v4, v1) | in(v4, v3) | in(v4, v2)))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | set_intersection2(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v2) | ~ in(v5, v1)) & (in(v5, v4) | (in(v5, v2) & in(v5, v1)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v2) & in(v4, v1))) & ! [v4] : ( ~ in(v4, v2) | ~ in(v4, v1) | in(v4, v3)))) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_difference(v1, v0) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_intersection2(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ empty(v2) | ~ empty(v1)) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v2, v1) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v1, v0) = v2)) & ! [v1] : ! [v2] : ( ~ empty(v2) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ in(v3, v1) | in(v3, v2))) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (in(v3, v1) & ~ in(v3, v2))) & ! [v1] : (v1 = v0 | ~ empty(v1)) & ! [v1] : subset(v1, v1) & ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & set_difference(v1, v3) = v4 & set_difference(v1, v2) = v3 & set_intersection2(v1, v2) = v5) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1))
% 24.99/7.41 | Instantiating (0) with all_0_0_0 yields:
% 24.99/7.41 | (1) empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) & ! [v3] : ( ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_intersection2(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & set_difference(v0, v2) = v3 & set_difference(v0, v1) = v2 & set_intersection2(v0, v1) = v4) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0)
% 24.99/7.42 |
% 24.99/7.42 | Applying alpha-rule on (1) yields:
% 24.99/7.42 | (2) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 24.99/7.42 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 24.99/7.42 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 24.99/7.42 | (5) empty(all_0_0_0)
% 24.99/7.42 | (6) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 24.99/7.42 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1))))))
% 24.99/7.42 | (8) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_intersection2(v0, all_0_0_0) = v1))
% 24.99/7.42 | (9) ? [v0] : ~ empty(v0)
% 24.99/7.42 | (10) ! [v0] : subset(v0, v0)
% 24.99/7.42 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) & ! [v3] : ( ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))))
% 24.99/7.42 | (12) ? [v0] : empty(v0)
% 24.99/7.42 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 24.99/7.42 | (14) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & set_difference(v0, v2) = v3 & set_difference(v0, v1) = v2 & set_intersection2(v0, v1) = v4)
% 24.99/7.42 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1))
% 24.99/7.42 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 24.99/7.42 | (17) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1))
% 24.99/7.42 | (18) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1)))
% 24.99/7.42 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0))))))
% 24.99/7.42 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 24.99/7.42 | (21) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 24.99/7.42 | (22) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0))
% 24.99/7.42 | (23) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 24.99/7.42 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1))))
% 24.99/7.42 |
% 24.99/7.42 | Instantiating (14) with all_5_0_2, all_5_1_3, all_5_2_4, all_5_3_5, all_5_4_6 yields:
% 24.99/7.42 | (25) ~ (all_5_0_2 = all_5_1_3) & set_difference(all_5_4_6, all_5_2_4) = all_5_1_3 & set_difference(all_5_4_6, all_5_3_5) = all_5_2_4 & set_intersection2(all_5_4_6, all_5_3_5) = all_5_0_2
% 24.99/7.42 |
% 24.99/7.42 | Applying alpha-rule on (25) yields:
% 24.99/7.42 | (26) ~ (all_5_0_2 = all_5_1_3)
% 24.99/7.42 | (27) set_difference(all_5_4_6, all_5_2_4) = all_5_1_3
% 24.99/7.42 | (28) set_difference(all_5_4_6, all_5_3_5) = all_5_2_4
% 24.99/7.42 | (29) set_intersection2(all_5_4_6, all_5_3_5) = all_5_0_2
% 24.99/7.42 |
% 24.99/7.42 | Instantiating formula (7) with all_5_1_3, all_5_2_4, all_5_4_6 and discharging atoms set_difference(all_5_4_6, all_5_2_4) = all_5_1_3, yields:
% 24.99/7.43 | (30) ! [v0] : (v0 = all_5_1_3 | ? [v1] : (( ~ in(v1, v0) | ~ in(v1, all_5_4_6) | in(v1, all_5_2_4)) & (in(v1, v0) | (in(v1, all_5_4_6) & ~ in(v1, all_5_2_4)))))
% 24.99/7.43 |
% 24.99/7.43 | Instantiating formula (24) with all_5_2_4, all_5_3_5, all_5_4_6 and discharging atoms set_difference(all_5_4_6, all_5_3_5) = all_5_2_4, yields:
% 24.99/7.43 | (31) ! [v0] : ( ~ in(v0, all_5_2_4) | (in(v0, all_5_4_6) & ~ in(v0, all_5_3_5))) & ! [v0] : ( ~ in(v0, all_5_4_6) | in(v0, all_5_2_4) | in(v0, all_5_3_5))
% 24.99/7.43 |
% 24.99/7.43 | Applying alpha-rule on (31) yields:
% 24.99/7.43 | (32) ! [v0] : ( ~ in(v0, all_5_2_4) | (in(v0, all_5_4_6) & ~ in(v0, all_5_3_5)))
% 24.99/7.43 | (33) ! [v0] : ( ~ in(v0, all_5_4_6) | in(v0, all_5_2_4) | in(v0, all_5_3_5))
% 24.99/7.43 |
% 24.99/7.43 | Instantiating formula (13) with all_5_0_2, all_5_3_5, all_5_4_6 and discharging atoms set_intersection2(all_5_4_6, all_5_3_5) = all_5_0_2, yields:
% 24.99/7.43 | (34) set_intersection2(all_5_3_5, all_5_4_6) = all_5_0_2
% 24.99/7.43 |
% 24.99/7.43 | Instantiating formula (11) with all_5_0_2, all_5_4_6, all_5_3_5 and discharging atoms set_intersection2(all_5_3_5, all_5_4_6) = all_5_0_2, yields:
% 24.99/7.43 | (35) ! [v0] : ( ~ in(v0, all_5_0_2) | (in(v0, all_5_3_5) & in(v0, all_5_4_6))) & ! [v0] : ( ~ in(v0, all_5_3_5) | ~ in(v0, all_5_4_6) | in(v0, all_5_0_2))
% 24.99/7.43 |
% 24.99/7.43 | Applying alpha-rule on (35) yields:
% 24.99/7.43 | (36) ! [v0] : ( ~ in(v0, all_5_0_2) | (in(v0, all_5_3_5) & in(v0, all_5_4_6)))
% 24.99/7.43 | (37) ! [v0] : ( ~ in(v0, all_5_3_5) | ~ in(v0, all_5_4_6) | in(v0, all_5_0_2))
% 24.99/7.43 |
% 24.99/7.43 | Introducing new symbol ex_58_0_14 defined by:
% 24.99/7.43 | (38) ex_58_0_14 = all_5_0_2
% 24.99/7.43 |
% 24.99/7.43 | Instantiating formula (30) with ex_58_0_14 yields:
% 24.99/7.43 | (39) ex_58_0_14 = all_5_1_3 | ? [v0] : (( ~ in(v0, ex_58_0_14) | ~ in(v0, all_5_4_6) | in(v0, all_5_2_4)) & (in(v0, ex_58_0_14) | (in(v0, all_5_4_6) & ~ in(v0, all_5_2_4))))
% 24.99/7.43 |
% 24.99/7.43 +-Applying beta-rule and splitting (39), into two cases.
% 24.99/7.43 |-Branch one:
% 24.99/7.43 | (40) ex_58_0_14 = all_5_1_3
% 24.99/7.43 |
% 24.99/7.43 | Combining equations (38,40) yields a new equation:
% 24.99/7.43 | (41) all_5_0_2 = all_5_1_3
% 24.99/7.43 |
% 24.99/7.43 | Simplifying 41 yields:
% 24.99/7.43 | (42) all_5_0_2 = all_5_1_3
% 24.99/7.43 |
% 24.99/7.43 | Equations (42) can reduce 26 to:
% 24.99/7.43 | (43) $false
% 24.99/7.43 |
% 24.99/7.43 |-The branch is then unsatisfiable
% 24.99/7.43 |-Branch two:
% 24.99/7.43 | (44) ? [v0] : (( ~ in(v0, ex_58_0_14) | ~ in(v0, all_5_4_6) | in(v0, all_5_2_4)) & (in(v0, ex_58_0_14) | (in(v0, all_5_4_6) & ~ in(v0, all_5_2_4))))
% 24.99/7.43 |
% 24.99/7.43 | Instantiating (44) with all_61_0_15 yields:
% 24.99/7.43 | (45) ( ~ in(all_61_0_15, ex_58_0_14) | ~ in(all_61_0_15, all_5_4_6) | in(all_61_0_15, all_5_2_4)) & (in(all_61_0_15, ex_58_0_14) | (in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_2_4)))
% 24.99/7.43 |
% 24.99/7.43 | Applying alpha-rule on (45) yields:
% 24.99/7.43 | (46) ~ in(all_61_0_15, ex_58_0_14) | ~ in(all_61_0_15, all_5_4_6) | in(all_61_0_15, all_5_2_4)
% 24.99/7.43 | (47) in(all_61_0_15, ex_58_0_14) | (in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_2_4))
% 24.99/7.43 |
% 24.99/7.43 +-Applying beta-rule and splitting (46), into two cases.
% 24.99/7.43 |-Branch one:
% 24.99/7.43 | (48) ~ in(all_61_0_15, ex_58_0_14)
% 24.99/7.43 |
% 24.99/7.43 +-Applying beta-rule and splitting (47), into two cases.
% 24.99/7.43 |-Branch one:
% 24.99/7.43 | (49) in(all_61_0_15, ex_58_0_14)
% 24.99/7.43 |
% 24.99/7.43 | Using (49) and (48) yields:
% 24.99/7.43 | (50) $false
% 24.99/7.43 |
% 24.99/7.43 |-The branch is then unsatisfiable
% 24.99/7.43 |-Branch two:
% 24.99/7.43 | (51) in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_2_4)
% 24.99/7.43 |
% 24.99/7.43 | Applying alpha-rule on (51) yields:
% 24.99/7.43 | (52) in(all_61_0_15, all_5_4_6)
% 24.99/7.43 | (53) ~ in(all_61_0_15, all_5_2_4)
% 24.99/7.43 |
% 24.99/7.43 | Instantiating formula (37) with all_61_0_15 and discharging atoms in(all_61_0_15, all_5_4_6), yields:
% 24.99/7.43 | (54) ~ in(all_61_0_15, all_5_3_5) | in(all_61_0_15, all_5_0_2)
% 24.99/7.43 |
% 24.99/7.43 | Instantiating formula (33) with all_61_0_15 and discharging atoms in(all_61_0_15, all_5_4_6), ~ in(all_61_0_15, all_5_2_4), yields:
% 24.99/7.43 | (55) in(all_61_0_15, all_5_3_5)
% 24.99/7.43 |
% 24.99/7.43 +-Applying beta-rule and splitting (54), into two cases.
% 24.99/7.43 |-Branch one:
% 24.99/7.43 | (56) ~ in(all_61_0_15, all_5_3_5)
% 24.99/7.43 |
% 24.99/7.43 | Using (55) and (56) yields:
% 24.99/7.43 | (50) $false
% 24.99/7.43 |
% 24.99/7.43 |-The branch is then unsatisfiable
% 24.99/7.43 |-Branch two:
% 24.99/7.43 | (58) in(all_61_0_15, all_5_0_2)
% 24.99/7.43 |
% 24.99/7.43 | From (38) and (48) follows:
% 24.99/7.43 | (59) ~ in(all_61_0_15, all_5_0_2)
% 24.99/7.43 |
% 24.99/7.43 | Using (58) and (59) yields:
% 24.99/7.43 | (50) $false
% 24.99/7.43 |
% 24.99/7.43 |-The branch is then unsatisfiable
% 24.99/7.43 |-Branch two:
% 24.99/7.43 | (49) in(all_61_0_15, ex_58_0_14)
% 24.99/7.43 | (62) ~ in(all_61_0_15, all_5_4_6) | in(all_61_0_15, all_5_2_4)
% 24.99/7.44 |
% 24.99/7.44 | Instantiating formula (36) with all_61_0_15 yields:
% 24.99/7.44 | (63) ~ in(all_61_0_15, all_5_0_2) | (in(all_61_0_15, all_5_3_5) & in(all_61_0_15, all_5_4_6))
% 24.99/7.44 |
% 24.99/7.44 | Instantiating formula (32) with all_61_0_15 yields:
% 24.99/7.44 | (64) ~ in(all_61_0_15, all_5_2_4) | (in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_3_5))
% 24.99/7.44 |
% 24.99/7.44 +-Applying beta-rule and splitting (62), into two cases.
% 24.99/7.44 |-Branch one:
% 24.99/7.44 | (65) ~ in(all_61_0_15, all_5_4_6)
% 24.99/7.44 |
% 24.99/7.44 +-Applying beta-rule and splitting (63), into two cases.
% 24.99/7.44 |-Branch one:
% 24.99/7.44 | (59) ~ in(all_61_0_15, all_5_0_2)
% 24.99/7.44 |
% 24.99/7.44 | From (38) and (49) follows:
% 24.99/7.44 | (58) in(all_61_0_15, all_5_0_2)
% 24.99/7.44 |
% 24.99/7.44 | Using (58) and (59) yields:
% 24.99/7.44 | (50) $false
% 24.99/7.44 |
% 24.99/7.44 |-The branch is then unsatisfiable
% 24.99/7.44 |-Branch two:
% 24.99/7.44 | (69) in(all_61_0_15, all_5_3_5) & in(all_61_0_15, all_5_4_6)
% 24.99/7.44 |
% 24.99/7.44 | Applying alpha-rule on (69) yields:
% 24.99/7.44 | (55) in(all_61_0_15, all_5_3_5)
% 24.99/7.44 | (52) in(all_61_0_15, all_5_4_6)
% 24.99/7.44 |
% 24.99/7.44 | Using (52) and (65) yields:
% 24.99/7.44 | (50) $false
% 24.99/7.44 |
% 24.99/7.44 |-The branch is then unsatisfiable
% 24.99/7.44 |-Branch two:
% 24.99/7.44 | (73) in(all_61_0_15, all_5_2_4)
% 24.99/7.44 |
% 24.99/7.44 +-Applying beta-rule and splitting (64), into two cases.
% 24.99/7.44 |-Branch one:
% 24.99/7.44 | (53) ~ in(all_61_0_15, all_5_2_4)
% 24.99/7.44 |
% 24.99/7.44 | Using (73) and (53) yields:
% 24.99/7.44 | (50) $false
% 24.99/7.44 |
% 24.99/7.44 |-The branch is then unsatisfiable
% 24.99/7.44 |-Branch two:
% 24.99/7.44 | (76) in(all_61_0_15, all_5_4_6) & ~ in(all_61_0_15, all_5_3_5)
% 24.99/7.44 |
% 24.99/7.44 | Applying alpha-rule on (76) yields:
% 24.99/7.44 | (52) in(all_61_0_15, all_5_4_6)
% 24.99/7.44 | (56) ~ in(all_61_0_15, all_5_3_5)
% 24.99/7.44 |
% 24.99/7.44 +-Applying beta-rule and splitting (63), into two cases.
% 24.99/7.44 |-Branch one:
% 24.99/7.44 | (59) ~ in(all_61_0_15, all_5_0_2)
% 24.99/7.44 |
% 24.99/7.44 | From (38) and (49) follows:
% 24.99/7.44 | (58) in(all_61_0_15, all_5_0_2)
% 24.99/7.44 |
% 24.99/7.44 | Using (58) and (59) yields:
% 24.99/7.44 | (50) $false
% 24.99/7.44 |
% 24.99/7.44 |-The branch is then unsatisfiable
% 24.99/7.44 |-Branch two:
% 24.99/7.44 | (69) in(all_61_0_15, all_5_3_5) & in(all_61_0_15, all_5_4_6)
% 24.99/7.44 |
% 24.99/7.44 | Applying alpha-rule on (69) yields:
% 24.99/7.44 | (55) in(all_61_0_15, all_5_3_5)
% 24.99/7.44 | (52) in(all_61_0_15, all_5_4_6)
% 24.99/7.44 |
% 24.99/7.44 | Using (55) and (56) yields:
% 24.99/7.44 | (50) $false
% 24.99/7.44 |
% 24.99/7.44 |-The branch is then unsatisfiable
% 24.99/7.44 % SZS output end Proof for theBenchmark
% 24.99/7.44
% 24.99/7.44 6802ms
%------------------------------------------------------------------------------