TSTP Solution File: SET955+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 00:23:25 EDT 2022
% Result : Theorem 67.49s 30.07s
% Output : Proof 75.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 22:00:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.57 ____ _
% 0.51/0.57 ___ / __ \_____(_)___ ________ __________
% 0.51/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.57
% 0.51/0.57 A Theorem Prover for First-Order Logic
% 0.51/0.57 (ePrincess v.1.0)
% 0.51/0.57
% 0.51/0.57 (c) Philipp Rümmer, 2009-2015
% 0.51/0.57 (c) Peter Backeman, 2014-2015
% 0.51/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.57 Bug reports to peter@backeman.se
% 0.51/0.57
% 0.51/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.57
% 0.51/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.31/0.87 Prover 0: Preprocessing ...
% 1.78/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.78/1.07 Prover 0: Constructing countermodel ...
% 20.59/5.91 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.59/5.93 Prover 1: Preprocessing ...
% 20.96/5.99 Prover 1: Warning: ignoring some quantifiers
% 20.96/5.99 Prover 1: Constructing countermodel ...
% 21.45/6.11 Prover 1: gave up
% 21.45/6.11 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 21.45/6.12 Prover 2: Preprocessing ...
% 21.90/6.16 Prover 2: Warning: ignoring some quantifiers
% 21.90/6.17 Prover 2: Constructing countermodel ...
% 28.64/7.85 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 28.98/7.87 Prover 3: Preprocessing ...
% 29.11/7.91 Prover 3: Warning: ignoring some quantifiers
% 29.11/7.91 Prover 3: Constructing countermodel ...
% 29.46/7.99 Prover 3: gave up
% 29.46/7.99 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 29.46/8.00 Prover 4: Preprocessing ...
% 29.81/8.05 Prover 4: Warning: ignoring some quantifiers
% 29.81/8.05 Prover 4: Constructing countermodel ...
% 36.58/10.31 Prover 0: stopped
% 36.96/10.51 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 36.96/10.53 Prover 5: Preprocessing ...
% 37.16/10.57 Prover 5: Warning: ignoring some quantifiers
% 37.16/10.58 Prover 5: Constructing countermodel ...
% 54.64/24.03 Prover 5: stopped
% 54.80/24.23 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 54.80/24.24 Prover 6: Preprocessing ...
% 54.96/24.28 Prover 6: Warning: ignoring some quantifiers
% 54.96/24.28 Prover 6: Constructing countermodel ...
% 59.44/27.96 Prover 6: gave up
% 59.44/27.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 59.61/27.97 Prover 7: Preprocessing ...
% 59.61/27.99 Prover 7: Proving ...
% 67.49/30.07 Prover 7: proved (2105ms)
% 67.49/30.07 Prover 2: stopped
% 67.49/30.07 Prover 4: stopped
% 67.49/30.07
% 67.49/30.07 % SZS status Theorem for theBenchmark
% 67.49/30.07
% 67.49/30.07 Generating proof ... found it (size 54)
% 75.14/32.94
% 75.14/32.94 % SZS output start Proof for theBenchmark
% 75.14/32.94 Assumed formulas after preprocessing and simplification:
% 75.14/32.94 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ! [v5] : ! [v6] : ( ~ in(v6, v1) | ~ in(v5, v0) | ? [v7] : ( ~ (v7 = v4) & ordered_pair(v5, v6) = v7))) & (in(v4, v3) | ? [v5] : ? [v6] : (ordered_pair(v5, v6) = v4 & in(v6, v1) & in(v5, v0)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ! [v3] : (in(v3, v2) | ! [v4] : ! [v5] : ( ~ in(v5, v1) | ~ in(v4, v0) | ? [v6] : ( ~ (v6 = v3) & ordered_pair(v4, v5) = v6))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & cartesian_product2(v2, v3) = v5 & cartesian_product2(v0, v1) = v4 & ! [v6] : ! [v7] : ! [v8] : ( ~ (ordered_pair(v6, v7) = v8) | ~ in(v8, v5) | in(v8, v4)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (ordered_pair(v6, v7) = v8) | ~ in(v8, v4) | in(v8, v5))) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0)
% 75.39/32.96 | Applying alpha-rule on (0) yields:
% 75.39/32.96 | (1) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 75.39/32.96 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 75.39/32.96 | (3) ? [v0] : ~ empty(v0)
% 75.39/32.96 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 75.39/32.96 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ! [v5] : ! [v6] : ( ~ in(v6, v1) | ~ in(v5, v0) | ? [v7] : ( ~ (v7 = v4) & ordered_pair(v5, v6) = v7))) & (in(v4, v3) | ? [v5] : ? [v6] : (ordered_pair(v5, v6) = v4 & in(v6, v1) & in(v5, v0))))))
% 75.39/32.96 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 75.39/32.96 | (7) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 75.39/32.96 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ! [v3] : (in(v3, v2) | ! [v4] : ! [v5] : ( ~ in(v5, v1) | ~ in(v4, v0) | ? [v6] : ( ~ (v6 = v3) & ordered_pair(v4, v5) = v6)))))
% 75.39/32.96 | (9) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & cartesian_product2(v2, v3) = v5 & cartesian_product2(v0, v1) = v4 & ! [v6] : ! [v7] : ! [v8] : ( ~ (ordered_pair(v6, v7) = v8) | ~ in(v8, v5) | in(v8, v4)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (ordered_pair(v6, v7) = v8) | ~ in(v8, v4) | in(v8, v5)))
% 75.39/32.97 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 75.39/32.97 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 75.39/32.97 | (12) ? [v0] : empty(v0)
% 75.39/32.97 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 75.39/32.97 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 75.39/32.97 |
% 75.39/32.97 | Instantiating (9) with all_3_0_1, all_3_1_2, all_3_2_3, all_3_3_4, all_3_4_5, all_3_5_6 yields:
% 75.39/32.97 | (15) ~ (all_3_0_1 = all_3_1_2) & cartesian_product2(all_3_3_4, all_3_2_3) = all_3_0_1 & cartesian_product2(all_3_5_6, all_3_4_5) = all_3_1_2 & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ in(v2, all_3_0_1) | in(v2, all_3_1_2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ in(v2, all_3_1_2) | in(v2, all_3_0_1))
% 75.39/32.97 |
% 75.39/32.97 | Applying alpha-rule on (15) yields:
% 75.39/32.97 | (16) cartesian_product2(all_3_3_4, all_3_2_3) = all_3_0_1
% 75.39/32.97 | (17) ~ (all_3_0_1 = all_3_1_2)
% 75.39/32.97 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ in(v2, all_3_1_2) | in(v2, all_3_0_1))
% 75.39/32.97 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ in(v2, all_3_0_1) | in(v2, all_3_1_2))
% 75.39/32.97 | (20) cartesian_product2(all_3_5_6, all_3_4_5) = all_3_1_2
% 75.39/32.97 |
% 75.39/32.97 | Instantiating formula (8) with all_3_0_1, all_3_2_3, all_3_3_4 and discharging atoms cartesian_product2(all_3_3_4, all_3_2_3) = all_3_0_1, yields:
% 75.39/32.97 | (21) ! [v0] : ( ~ in(v0, all_3_0_1) | ? [v1] : ? [v2] : (ordered_pair(v1, v2) = v0 & in(v2, all_3_2_3) & in(v1, all_3_3_4))) & ! [v0] : (in(v0, all_3_0_1) | ! [v1] : ! [v2] : ( ~ in(v2, all_3_2_3) | ~ in(v1, all_3_3_4) | ? [v3] : ( ~ (v3 = v0) & ordered_pair(v1, v2) = v3)))
% 75.39/32.97 |
% 75.39/32.97 | Applying alpha-rule on (21) yields:
% 75.39/32.97 | (22) ! [v0] : ( ~ in(v0, all_3_0_1) | ? [v1] : ? [v2] : (ordered_pair(v1, v2) = v0 & in(v2, all_3_2_3) & in(v1, all_3_3_4)))
% 75.39/32.97 | (23) ! [v0] : (in(v0, all_3_0_1) | ! [v1] : ! [v2] : ( ~ in(v2, all_3_2_3) | ~ in(v1, all_3_3_4) | ? [v3] : ( ~ (v3 = v0) & ordered_pair(v1, v2) = v3)))
% 75.39/32.97 |
% 75.39/32.97 | Instantiating formula (8) with all_3_1_2, all_3_4_5, all_3_5_6 and discharging atoms cartesian_product2(all_3_5_6, all_3_4_5) = all_3_1_2, yields:
% 75.39/32.97 | (24) ! [v0] : ( ~ in(v0, all_3_1_2) | ? [v1] : ? [v2] : (ordered_pair(v1, v2) = v0 & in(v2, all_3_4_5) & in(v1, all_3_5_6))) & ! [v0] : (in(v0, all_3_1_2) | ! [v1] : ! [v2] : ( ~ in(v2, all_3_4_5) | ~ in(v1, all_3_5_6) | ? [v3] : ( ~ (v3 = v0) & ordered_pair(v1, v2) = v3)))
% 75.39/32.97 |
% 75.39/32.97 | Applying alpha-rule on (24) yields:
% 75.39/32.97 | (25) ! [v0] : ( ~ in(v0, all_3_1_2) | ? [v1] : ? [v2] : (ordered_pair(v1, v2) = v0 & in(v2, all_3_4_5) & in(v1, all_3_5_6)))
% 75.39/32.97 | (26) ! [v0] : (in(v0, all_3_1_2) | ! [v1] : ! [v2] : ( ~ in(v2, all_3_4_5) | ~ in(v1, all_3_5_6) | ? [v3] : ( ~ (v3 = v0) & ordered_pair(v1, v2) = v3)))
% 75.39/32.97 |
% 75.39/32.97 | Introducing new symbol ex_18_1_9 defined by:
% 75.39/32.97 | (27) ex_18_1_9 = all_3_0_1
% 75.39/32.97 |
% 75.39/32.97 | Introducing new symbol ex_18_0_8 defined by:
% 75.39/32.97 | (28) ex_18_0_8 = all_3_1_2
% 75.39/32.97 |
% 75.39/32.97 | Instantiating formula (1) with ex_18_0_8, ex_18_1_9 yields:
% 75.39/32.97 | (29) ex_18_0_8 = ex_18_1_9 | ? [v0] : (( ~ in(v0, ex_18_0_8) | ~ in(v0, ex_18_1_9)) & (in(v0, ex_18_0_8) | in(v0, ex_18_1_9)))
% 75.39/32.97 |
% 75.39/32.97 +-Applying beta-rule and splitting (29), into two cases.
% 75.39/32.97 |-Branch one:
% 75.39/32.97 | (30) ex_18_0_8 = ex_18_1_9
% 75.39/32.97 |
% 75.39/32.97 | Combining equations (28,30) yields a new equation:
% 75.39/32.97 | (31) ex_18_1_9 = all_3_1_2
% 75.39/32.97 |
% 75.39/32.97 | Combining equations (31,27) yields a new equation:
% 75.39/32.97 | (32) all_3_0_1 = all_3_1_2
% 75.39/32.97 |
% 75.39/32.97 | Equations (32) can reduce 17 to:
% 75.39/32.97 | (33) $false
% 75.39/32.97 |
% 75.39/32.97 |-The branch is then unsatisfiable
% 75.39/32.97 |-Branch two:
% 75.39/32.97 | (34) ? [v0] : (( ~ in(v0, ex_18_0_8) | ~ in(v0, ex_18_1_9)) & (in(v0, ex_18_0_8) | in(v0, ex_18_1_9)))
% 75.39/32.97 |
% 75.39/32.97 | Instantiating (34) with all_21_0_10 yields:
% 75.39/32.97 | (35) ( ~ in(all_21_0_10, ex_18_0_8) | ~ in(all_21_0_10, ex_18_1_9)) & (in(all_21_0_10, ex_18_0_8) | in(all_21_0_10, ex_18_1_9))
% 75.39/32.98 |
% 75.39/32.98 | Applying alpha-rule on (35) yields:
% 75.39/32.98 | (36) ~ in(all_21_0_10, ex_18_0_8) | ~ in(all_21_0_10, ex_18_1_9)
% 75.39/32.98 | (37) in(all_21_0_10, ex_18_0_8) | in(all_21_0_10, ex_18_1_9)
% 75.39/32.98 |
% 75.39/32.98 +-Applying beta-rule and splitting (37), into two cases.
% 75.39/32.98 |-Branch one:
% 75.39/32.98 | (38) in(all_21_0_10, ex_18_0_8)
% 75.39/32.98 |
% 75.39/32.98 +-Applying beta-rule and splitting (36), into two cases.
% 75.39/32.98 |-Branch one:
% 75.39/32.98 | (39) ~ in(all_21_0_10, ex_18_0_8)
% 75.39/32.98 |
% 75.39/32.98 | Using (38) and (39) yields:
% 75.39/32.98 | (40) $false
% 75.39/32.98 |
% 75.39/32.98 |-The branch is then unsatisfiable
% 75.39/32.98 |-Branch two:
% 75.39/32.98 | (41) ~ in(all_21_0_10, ex_18_1_9)
% 75.39/32.98 |
% 75.39/32.98 | Instantiating formula (22) with all_21_0_10 yields:
% 75.39/32.98 | (42) ~ in(all_21_0_10, all_3_0_1) | ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_21_0_10 & in(v1, all_3_2_3) & in(v0, all_3_3_4))
% 75.39/32.98 |
% 75.39/32.98 | Instantiating formula (25) with all_21_0_10 yields:
% 75.39/32.98 | (43) ~ in(all_21_0_10, all_3_1_2) | ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_21_0_10 & in(v1, all_3_4_5) & in(v0, all_3_5_6))
% 75.39/32.98 |
% 75.39/32.98 +-Applying beta-rule and splitting (43), into two cases.
% 75.39/32.98 |-Branch one:
% 75.39/32.98 | (44) ~ in(all_21_0_10, all_3_1_2)
% 75.39/32.98 |
% 75.39/32.98 | From (28) and (38) follows:
% 75.39/32.98 | (45) in(all_21_0_10, all_3_1_2)
% 75.39/32.98 |
% 75.39/32.98 | Using (45) and (44) yields:
% 75.39/32.98 | (40) $false
% 75.39/32.98 |
% 75.39/32.98 |-The branch is then unsatisfiable
% 75.39/32.98 |-Branch two:
% 75.39/32.98 | (45) in(all_21_0_10, all_3_1_2)
% 75.39/32.98 | (48) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_21_0_10 & in(v1, all_3_4_5) & in(v0, all_3_5_6))
% 75.39/32.98 |
% 75.39/32.98 | Instantiating (48) with all_39_0_24, all_39_1_25 yields:
% 75.39/32.98 | (49) ordered_pair(all_39_1_25, all_39_0_24) = all_21_0_10 & in(all_39_0_24, all_3_4_5) & in(all_39_1_25, all_3_5_6)
% 75.39/32.98 |
% 75.39/32.98 | Applying alpha-rule on (49) yields:
% 75.39/32.98 | (50) ordered_pair(all_39_1_25, all_39_0_24) = all_21_0_10
% 75.39/32.98 | (51) in(all_39_0_24, all_3_4_5)
% 75.39/32.98 | (52) in(all_39_1_25, all_3_5_6)
% 75.39/32.98 |
% 75.39/32.98 | Instantiating formula (18) with all_21_0_10, all_39_0_24, all_39_1_25 and discharging atoms ordered_pair(all_39_1_25, all_39_0_24) = all_21_0_10, yields:
% 75.39/32.98 | (53) ~ in(all_21_0_10, all_3_1_2) | in(all_21_0_10, all_3_0_1)
% 75.39/32.98 |
% 75.39/32.98 +-Applying beta-rule and splitting (42), into two cases.
% 75.39/32.98 |-Branch one:
% 75.39/32.98 | (54) ~ in(all_21_0_10, all_3_0_1)
% 75.39/32.98 |
% 75.39/32.98 +-Applying beta-rule and splitting (53), into two cases.
% 75.39/32.98 |-Branch one:
% 75.39/32.98 | (44) ~ in(all_21_0_10, all_3_1_2)
% 75.39/32.98 |
% 75.39/32.98 | Using (45) and (44) yields:
% 75.39/32.98 | (40) $false
% 75.39/32.98 |
% 75.39/32.98 |-The branch is then unsatisfiable
% 75.39/32.98 |-Branch two:
% 75.39/32.98 | (57) in(all_21_0_10, all_3_0_1)
% 75.39/32.98 |
% 75.39/32.98 | Using (57) and (54) yields:
% 75.39/32.98 | (40) $false
% 75.39/32.98 |
% 75.39/32.98 |-The branch is then unsatisfiable
% 75.39/32.98 |-Branch two:
% 75.39/32.98 | (57) in(all_21_0_10, all_3_0_1)
% 75.39/32.98 | (60) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_21_0_10 & in(v1, all_3_2_3) & in(v0, all_3_3_4))
% 75.39/32.98 |
% 75.39/32.98 | From (27) and (41) follows:
% 75.39/32.98 | (54) ~ in(all_21_0_10, all_3_0_1)
% 75.39/32.98 |
% 75.39/32.98 | Using (57) and (54) yields:
% 75.39/32.98 | (40) $false
% 75.39/32.98 |
% 75.39/32.98 |-The branch is then unsatisfiable
% 75.39/32.98 |-Branch two:
% 75.39/32.98 | (39) ~ in(all_21_0_10, ex_18_0_8)
% 75.39/32.98 | (64) in(all_21_0_10, ex_18_1_9)
% 75.39/32.98 |
% 75.39/32.98 | Instantiating formula (22) with all_21_0_10 yields:
% 75.39/32.98 | (42) ~ in(all_21_0_10, all_3_0_1) | ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_21_0_10 & in(v1, all_3_2_3) & in(v0, all_3_3_4))
% 75.39/32.98 |
% 75.39/32.98 | Instantiating formula (25) with all_21_0_10 yields:
% 75.39/32.98 | (43) ~ in(all_21_0_10, all_3_1_2) | ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_21_0_10 & in(v1, all_3_4_5) & in(v0, all_3_5_6))
% 75.39/32.98 |
% 75.39/32.98 +-Applying beta-rule and splitting (43), into two cases.
% 75.39/32.98 |-Branch one:
% 75.39/32.98 | (44) ~ in(all_21_0_10, all_3_1_2)
% 75.39/32.98 |
% 75.39/32.98 +-Applying beta-rule and splitting (42), into two cases.
% 75.39/32.98 |-Branch one:
% 75.39/32.98 | (54) ~ in(all_21_0_10, all_3_0_1)
% 75.39/32.98 |
% 75.39/32.98 | From (27) and (64) follows:
% 75.39/32.98 | (57) in(all_21_0_10, all_3_0_1)
% 75.39/32.98 |
% 75.39/32.98 | Using (57) and (54) yields:
% 75.39/32.98 | (40) $false
% 75.39/32.98 |
% 75.39/32.98 |-The branch is then unsatisfiable
% 75.39/32.98 |-Branch two:
% 75.39/32.98 | (57) in(all_21_0_10, all_3_0_1)
% 75.39/32.98 | (60) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_21_0_10 & in(v1, all_3_2_3) & in(v0, all_3_3_4))
% 75.39/32.98 |
% 75.39/32.98 | Instantiating (60) with all_46_0_26, all_46_1_27 yields:
% 75.39/32.98 | (73) ordered_pair(all_46_1_27, all_46_0_26) = all_21_0_10 & in(all_46_0_26, all_3_2_3) & in(all_46_1_27, all_3_3_4)
% 75.39/32.98 |
% 75.39/32.98 | Applying alpha-rule on (73) yields:
% 75.39/32.98 | (74) ordered_pair(all_46_1_27, all_46_0_26) = all_21_0_10
% 75.39/32.98 | (75) in(all_46_0_26, all_3_2_3)
% 75.39/32.98 | (76) in(all_46_1_27, all_3_3_4)
% 75.39/32.98 |
% 75.39/32.98 | Instantiating formula (19) with all_21_0_10, all_46_0_26, all_46_1_27 and discharging atoms ordered_pair(all_46_1_27, all_46_0_26) = all_21_0_10, ~ in(all_21_0_10, all_3_1_2), yields:
% 75.39/32.98 | (54) ~ in(all_21_0_10, all_3_0_1)
% 75.39/32.98 |
% 75.39/32.98 | Using (57) and (54) yields:
% 75.39/32.98 | (40) $false
% 75.39/32.98 |
% 75.39/32.98 |-The branch is then unsatisfiable
% 75.39/32.98 |-Branch two:
% 75.39/32.98 | (45) in(all_21_0_10, all_3_1_2)
% 75.39/32.98 | (48) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_21_0_10 & in(v1, all_3_4_5) & in(v0, all_3_5_6))
% 75.39/32.98 |
% 75.39/32.98 | From (28) and (39) follows:
% 75.39/32.98 | (44) ~ in(all_21_0_10, all_3_1_2)
% 75.39/32.98 |
% 75.39/32.98 | Using (45) and (44) yields:
% 75.39/32.98 | (40) $false
% 75.39/32.98 |
% 75.39/32.98 |-The branch is then unsatisfiable
% 75.39/32.98 % SZS output end Proof for theBenchmark
% 75.39/32.99
% 75.39/32.99 32401ms
%------------------------------------------------------------------------------