TSTP Solution File: SET888+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET888+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 00:22:56 EDT 2022
% Result : Theorem 39.43s 17.21s
% Output : Proof 72.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET888+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 21:52:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.48/0.58 ____ _
% 0.48/0.58 ___ / __ \_____(_)___ ________ __________
% 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.58
% 0.48/0.58 A Theorem Prover for First-Order Logic
% 0.48/0.58 (ePrincess v.1.0)
% 0.48/0.58
% 0.48/0.58 (c) Philipp Rümmer, 2009-2015
% 0.48/0.58 (c) Peter Backeman, 2014-2015
% 0.48/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.58 Bug reports to peter@backeman.se
% 0.48/0.58
% 0.48/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.58
% 0.48/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.90 Prover 0: Preprocessing ...
% 1.95/1.11 Prover 0: Warning: ignoring some quantifiers
% 2.05/1.13 Prover 0: Constructing countermodel ...
% 3.36/1.48 Prover 0: gave up
% 3.36/1.48 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.36/1.50 Prover 1: Preprocessing ...
% 3.65/1.56 Prover 1: Warning: ignoring some quantifiers
% 3.65/1.57 Prover 1: Constructing countermodel ...
% 3.86/1.62 Prover 1: gave up
% 3.86/1.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.86/1.63 Prover 2: Preprocessing ...
% 4.34/1.70 Prover 2: Warning: ignoring some quantifiers
% 4.34/1.71 Prover 2: Constructing countermodel ...
% 4.70/1.81 Prover 2: gave up
% 4.70/1.81 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.98/1.82 Prover 3: Preprocessing ...
% 4.98/1.85 Prover 3: Warning: ignoring some quantifiers
% 4.98/1.85 Prover 3: Constructing countermodel ...
% 5.19/1.92 Prover 3: gave up
% 5.19/1.92 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.19/1.93 Prover 4: Preprocessing ...
% 5.75/1.99 Prover 4: Warning: ignoring some quantifiers
% 5.75/2.00 Prover 4: Constructing countermodel ...
% 8.24/2.57 Prover 4: gave up
% 8.24/2.57 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 8.24/2.58 Prover 5: Preprocessing ...
% 8.42/2.61 Prover 5: Warning: ignoring some quantifiers
% 8.42/2.62 Prover 5: Constructing countermodel ...
% 8.60/2.70 Prover 5: gave up
% 8.60/2.70 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 8.60/2.71 Prover 6: Preprocessing ...
% 8.94/2.74 Prover 6: Warning: ignoring some quantifiers
% 8.94/2.74 Prover 6: Constructing countermodel ...
% 9.22/2.80 Prover 6: gave up
% 9.22/2.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 9.22/2.81 Prover 7: Preprocessing ...
% 9.22/2.84 Prover 7: Proving ...
% 32.66/13.20 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 32.66/13.23 Prover 8: Preprocessing ...
% 32.83/13.27 Prover 8: Proving ...
% 39.43/17.21 Prover 8: proved (4006ms)
% 39.43/17.21 Prover 7: stopped
% 39.43/17.21
% 39.43/17.21 % SZS status Theorem for theBenchmark
% 39.43/17.21
% 39.43/17.21 Generating proof ... found it (size 90)
% 72.46/41.81
% 72.46/41.81 % SZS output start Proof for theBenchmark
% 72.46/41.81 Assumed formulas after preprocessing and simplification:
% 72.46/41.81 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (symmetric_difference(v1, v2) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : (in(v0, v2) = v6 & in(v0, v1) = v5 & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v0) = v3) | ~ (set_difference(v0, v1) = v2) | ~ (set_union2(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (symmetric_difference(v1, v2) = v3) | ~ (in(v0, v3) = 0) | ? [v4] : ? [v5] : (in(v0, v2) = v5 & in(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ? [v5] : (in(v4, v3) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v1) & ~ (v4 = v0))) & (v5 = 0 | v4 = v1 | v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v2) = v4) | ( ~ (v3 = v1) & ~ (v3 = v0))) & ! [v3] : (v3 = v1 | v3 = v0 | ~ (in(v3, v2) = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : ? [v4] : (in(v3, v2) = v4 & ( ~ (v4 = 0) | ~ (v3 = v0)) & (v4 = 0 | v3 = v0)))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ( ! [v2] : (v2 = v0 | ~ (in(v2, v1) = 0)) & ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2)))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & ~ (v1 = v0) & singleton(v1) = v3 & singleton(v0) = v2 & symmetric_difference(v2, v3) = v4 & unordered_pair(v0, v1) = v5) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) & ? [v0] : empty(v0) = 0
% 72.82/41.83 | Applying alpha-rule on (0) yields:
% 72.82/41.83 | (1) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2)
% 72.82/41.83 | (2) ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1)
% 72.82/41.83 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v2) = v4) | ( ~ (v3 = v1) & ~ (v3 = v0))) & ! [v3] : (v3 = v1 | v3 = v0 | ~ (in(v3, v2) = 0))))
% 72.82/41.83 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 72.82/41.83 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 72.82/41.83 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 72.82/41.83 | (7) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ( ! [v2] : (v2 = v0 | ~ (in(v2, v1) = 0)) & ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2))))
% 72.82/41.84 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 72.82/41.84 | (9) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ! [v2] : (v2 = v1 | ? [v3] : ? [v4] : (in(v3, v2) = v4 & ( ~ (v4 = 0) | ~ (v3 = v0)) & (v4 = 0 | v3 = v0))))
% 72.82/41.84 | (10) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 72.82/41.84 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0))
% 72.82/41.84 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 72.82/41.84 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 72.82/41.84 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 72.82/41.84 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 72.82/41.84 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (symmetric_difference(v1, v2) = v3) | ~ (in(v0, v3) = 0) | ? [v4] : ? [v5] : (in(v0, v2) = v5 & in(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 72.82/41.84 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 72.82/41.84 | (18) ? [v0] : empty(v0) = 0
% 72.82/41.84 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 72.82/41.84 | (20) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & ~ (v1 = v0) & singleton(v1) = v3 & singleton(v0) = v2 & symmetric_difference(v2, v3) = v4 & unordered_pair(v0, v1) = v5)
% 72.82/41.84 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ? [v5] : (in(v4, v3) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v1) & ~ (v4 = v0))) & (v5 = 0 | v4 = v1 | v4 = v0))))
% 72.82/41.84 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v0) = v3) | ~ (set_difference(v0, v1) = v2) | ~ (set_union2(v2, v3) = v4) | symmetric_difference(v0, v1) = v4)
% 72.82/41.84 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (symmetric_difference(v1, v2) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : (in(v0, v2) = v6 & in(v0, v1) = v5 & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0)))
% 72.82/41.84 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 72.82/41.84 |
% 72.82/41.84 | Instantiating (20) with all_5_0_3, all_5_1_4, all_5_2_5, all_5_3_6, all_5_4_7, all_5_5_8 yields:
% 72.82/41.84 | (25) ~ (all_5_0_3 = all_5_1_4) & ~ (all_5_4_7 = all_5_5_8) & singleton(all_5_4_7) = all_5_2_5 & singleton(all_5_5_8) = all_5_3_6 & symmetric_difference(all_5_3_6, all_5_2_5) = all_5_1_4 & unordered_pair(all_5_5_8, all_5_4_7) = all_5_0_3
% 72.82/41.84 |
% 72.82/41.84 | Applying alpha-rule on (25) yields:
% 72.82/41.84 | (26) singleton(all_5_5_8) = all_5_3_6
% 72.82/41.84 | (27) symmetric_difference(all_5_3_6, all_5_2_5) = all_5_1_4
% 72.82/41.84 | (28) singleton(all_5_4_7) = all_5_2_5
% 72.82/41.84 | (29) unordered_pair(all_5_5_8, all_5_4_7) = all_5_0_3
% 72.82/41.84 | (30) ~ (all_5_0_3 = all_5_1_4)
% 72.82/41.84 | (31) ~ (all_5_4_7 = all_5_5_8)
% 72.82/41.84 |
% 72.82/41.84 | Instantiating formula (7) with all_5_2_5, all_5_4_7 and discharging atoms singleton(all_5_4_7) = all_5_2_5, yields:
% 72.82/41.85 | (32) ! [v0] : (v0 = all_5_4_7 | ~ (in(v0, all_5_2_5) = 0)) & ! [v0] : (v0 = 0 | ~ (in(all_5_4_7, all_5_2_5) = v0))
% 72.82/41.85 |
% 72.82/41.85 | Applying alpha-rule on (32) yields:
% 72.82/41.85 | (33) ! [v0] : (v0 = all_5_4_7 | ~ (in(v0, all_5_2_5) = 0))
% 72.82/41.85 | (34) ! [v0] : (v0 = 0 | ~ (in(all_5_4_7, all_5_2_5) = v0))
% 72.82/41.85 |
% 72.82/41.85 | Instantiating formula (7) with all_5_3_6, all_5_5_8 and discharging atoms singleton(all_5_5_8) = all_5_3_6, yields:
% 72.82/41.85 | (35) ! [v0] : (v0 = all_5_5_8 | ~ (in(v0, all_5_3_6) = 0)) & ! [v0] : (v0 = 0 | ~ (in(all_5_5_8, all_5_3_6) = v0))
% 72.82/41.85 |
% 72.82/41.85 | Applying alpha-rule on (35) yields:
% 72.82/41.85 | (36) ! [v0] : (v0 = all_5_5_8 | ~ (in(v0, all_5_3_6) = 0))
% 72.82/41.85 | (37) ! [v0] : (v0 = 0 | ~ (in(all_5_5_8, all_5_3_6) = v0))
% 72.82/41.85 |
% 72.82/41.85 | Instantiating formula (1) with all_5_1_4, all_5_2_5, all_5_3_6 and discharging atoms symmetric_difference(all_5_3_6, all_5_2_5) = all_5_1_4, yields:
% 72.82/41.85 | (38) symmetric_difference(all_5_2_5, all_5_3_6) = all_5_1_4
% 72.82/41.85 |
% 72.82/41.85 | Instantiating formula (13) with all_5_0_3, all_5_4_7, all_5_5_8 and discharging atoms unordered_pair(all_5_5_8, all_5_4_7) = all_5_0_3, yields:
% 72.82/41.85 | (39) unordered_pair(all_5_4_7, all_5_5_8) = all_5_0_3
% 72.82/41.85 |
% 72.82/41.85 | Instantiating formula (21) with all_5_0_3, all_5_5_8, all_5_4_7 and discharging atoms unordered_pair(all_5_4_7, all_5_5_8) = all_5_0_3, yields:
% 72.82/41.85 | (40) ! [v0] : (v0 = all_5_0_3 | ? [v1] : ? [v2] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ( ~ (v1 = all_5_4_7) & ~ (v1 = all_5_5_8))) & (v2 = 0 | v1 = all_5_4_7 | v1 = all_5_5_8)))
% 72.82/41.85 |
% 72.82/41.85 | Introducing new symbol ex_24_0_9 defined by:
% 72.82/41.85 | (41) ex_24_0_9 = all_5_1_4
% 72.82/41.85 |
% 72.82/41.85 | Instantiating formula (40) with ex_24_0_9 yields:
% 72.82/41.85 | (42) ex_24_0_9 = all_5_0_3 | ? [v0] : ? [v1] : (in(v0, ex_24_0_9) = v1 & ( ~ (v1 = 0) | ( ~ (v0 = all_5_4_7) & ~ (v0 = all_5_5_8))) & (v1 = 0 | v0 = all_5_4_7 | v0 = all_5_5_8))
% 72.82/41.85 |
% 72.82/41.85 +-Applying beta-rule and splitting (42), into two cases.
% 72.82/41.85 |-Branch one:
% 72.82/41.85 | (43) ex_24_0_9 = all_5_0_3
% 72.82/41.85 |
% 72.82/41.85 | Combining equations (41,43) yields a new equation:
% 72.82/41.85 | (44) all_5_0_3 = all_5_1_4
% 72.82/41.85 |
% 72.82/41.85 | Equations (44) can reduce 30 to:
% 72.82/41.85 | (45) $false
% 72.82/41.85 |
% 72.82/41.85 |-The branch is then unsatisfiable
% 72.82/41.85 |-Branch two:
% 72.82/41.85 | (46) ? [v0] : ? [v1] : (in(v0, ex_24_0_9) = v1 & ( ~ (v1 = 0) | ( ~ (v0 = all_5_4_7) & ~ (v0 = all_5_5_8))) & (v1 = 0 | v0 = all_5_4_7 | v0 = all_5_5_8))
% 72.82/41.85 |
% 72.82/41.85 | Instantiating (46) with all_27_0_10, all_27_1_11 yields:
% 72.82/41.85 | (47) in(all_27_1_11, ex_24_0_9) = all_27_0_10 & ( ~ (all_27_0_10 = 0) | ( ~ (all_27_1_11 = all_5_4_7) & ~ (all_27_1_11 = all_5_5_8))) & (all_27_0_10 = 0 | all_27_1_11 = all_5_4_7 | all_27_1_11 = all_5_5_8)
% 72.82/41.85 |
% 72.82/41.85 | Applying alpha-rule on (47) yields:
% 72.82/41.85 | (48) in(all_27_1_11, ex_24_0_9) = all_27_0_10
% 72.82/41.85 | (49) ~ (all_27_0_10 = 0) | ( ~ (all_27_1_11 = all_5_4_7) & ~ (all_27_1_11 = all_5_5_8))
% 72.82/41.85 | (50) all_27_0_10 = 0 | all_27_1_11 = all_5_4_7 | all_27_1_11 = all_5_5_8
% 72.82/41.85 |
% 72.82/41.85 | Instantiating formula (23) with all_27_0_10, all_5_1_4, all_5_3_6, all_5_2_5, all_27_1_11 and discharging atoms symmetric_difference(all_5_2_5, all_5_3_6) = all_5_1_4, yields:
% 72.82/41.85 | (51) all_27_0_10 = 0 | ~ (in(all_27_1_11, all_5_1_4) = all_27_0_10) | ? [v0] : ? [v1] : (in(all_27_1_11, all_5_2_5) = v0 & in(all_27_1_11, all_5_3_6) = v1 & ( ~ (v1 = 0) | v0 = 0) & ( ~ (v0 = 0) | v1 = 0))
% 72.82/41.85 |
% 72.82/41.85 | Instantiating formula (23) with all_27_0_10, all_5_1_4, all_5_2_5, all_5_3_6, all_27_1_11 and discharging atoms symmetric_difference(all_5_3_6, all_5_2_5) = all_5_1_4, yields:
% 72.82/41.85 | (52) all_27_0_10 = 0 | ~ (in(all_27_1_11, all_5_1_4) = all_27_0_10) | ? [v0] : ? [v1] : (in(all_27_1_11, all_5_2_5) = v1 & in(all_27_1_11, all_5_3_6) = v0 & ( ~ (v1 = 0) | v0 = 0) & ( ~ (v0 = 0) | v1 = 0))
% 72.82/41.85 |
% 72.82/41.85 +-Applying beta-rule and splitting (49), into two cases.
% 72.82/41.85 |-Branch one:
% 72.82/41.85 | (53) ~ (all_27_0_10 = 0)
% 72.82/41.85 |
% 72.82/41.85 +-Applying beta-rule and splitting (51), into two cases.
% 72.82/41.85 |-Branch one:
% 72.82/41.85 | (54) ~ (in(all_27_1_11, all_5_1_4) = all_27_0_10)
% 72.82/41.85 |
% 72.82/41.85 | From (41) and (48) follows:
% 72.82/41.85 | (55) in(all_27_1_11, all_5_1_4) = all_27_0_10
% 72.82/41.85 |
% 72.82/41.85 | Using (55) and (54) yields:
% 72.82/41.85 | (56) $false
% 72.82/41.85 |
% 72.82/41.85 |-The branch is then unsatisfiable
% 72.82/41.85 |-Branch two:
% 72.82/41.85 | (55) in(all_27_1_11, all_5_1_4) = all_27_0_10
% 72.82/41.85 | (58) all_27_0_10 = 0 | ? [v0] : ? [v1] : (in(all_27_1_11, all_5_2_5) = v0 & in(all_27_1_11, all_5_3_6) = v1 & ( ~ (v1 = 0) | v0 = 0) & ( ~ (v0 = 0) | v1 = 0))
% 72.82/41.86 |
% 72.82/41.86 +-Applying beta-rule and splitting (52), into two cases.
% 72.82/41.86 |-Branch one:
% 72.82/41.86 | (54) ~ (in(all_27_1_11, all_5_1_4) = all_27_0_10)
% 72.82/41.86 |
% 72.82/41.86 | Using (55) and (54) yields:
% 72.82/41.86 | (56) $false
% 72.82/41.86 |
% 72.82/41.86 |-The branch is then unsatisfiable
% 72.82/41.86 |-Branch two:
% 72.82/41.86 | (61) all_27_0_10 = 0 | ? [v0] : ? [v1] : (in(all_27_1_11, all_5_2_5) = v1 & in(all_27_1_11, all_5_3_6) = v0 & ( ~ (v1 = 0) | v0 = 0) & ( ~ (v0 = 0) | v1 = 0))
% 72.82/41.86 |
% 72.82/41.86 +-Applying beta-rule and splitting (50), into two cases.
% 72.82/41.86 |-Branch one:
% 72.82/41.86 | (62) all_27_0_10 = 0
% 72.82/41.86 |
% 72.82/41.86 | Equations (62) can reduce 53 to:
% 72.82/41.86 | (45) $false
% 72.82/41.86 |
% 72.82/41.86 |-The branch is then unsatisfiable
% 72.82/41.86 |-Branch two:
% 72.82/41.86 | (64) all_27_1_11 = all_5_4_7 | all_27_1_11 = all_5_5_8
% 72.82/41.86 |
% 72.82/41.86 +-Applying beta-rule and splitting (61), into two cases.
% 72.82/41.86 |-Branch one:
% 72.82/41.86 | (62) all_27_0_10 = 0
% 72.82/41.86 |
% 72.82/41.86 | Equations (62) can reduce 53 to:
% 72.82/41.86 | (45) $false
% 72.82/41.86 |
% 72.82/41.86 |-The branch is then unsatisfiable
% 72.82/41.86 |-Branch two:
% 72.82/41.86 | (67) ? [v0] : ? [v1] : (in(all_27_1_11, all_5_2_5) = v1 & in(all_27_1_11, all_5_3_6) = v0 & ( ~ (v1 = 0) | v0 = 0) & ( ~ (v0 = 0) | v1 = 0))
% 72.82/41.86 |
% 72.82/41.86 | Instantiating (67) with all_49_0_49, all_49_1_50 yields:
% 72.82/41.86 | (68) in(all_27_1_11, all_5_2_5) = all_49_0_49 & in(all_27_1_11, all_5_3_6) = all_49_1_50 & ( ~ (all_49_0_49 = 0) | all_49_1_50 = 0) & ( ~ (all_49_1_50 = 0) | all_49_0_49 = 0)
% 72.82/41.86 |
% 72.82/41.86 | Applying alpha-rule on (68) yields:
% 72.82/41.86 | (69) in(all_27_1_11, all_5_2_5) = all_49_0_49
% 72.82/41.86 | (70) in(all_27_1_11, all_5_3_6) = all_49_1_50
% 72.82/41.86 | (71) ~ (all_49_0_49 = 0) | all_49_1_50 = 0
% 72.82/41.86 | (72) ~ (all_49_1_50 = 0) | all_49_0_49 = 0
% 72.82/41.86 |
% 72.82/41.86 +-Applying beta-rule and splitting (58), into two cases.
% 72.82/41.86 |-Branch one:
% 72.82/41.86 | (62) all_27_0_10 = 0
% 72.82/41.86 |
% 72.82/41.86 | Equations (62) can reduce 53 to:
% 72.82/41.86 | (45) $false
% 72.82/41.86 |
% 72.82/41.86 |-The branch is then unsatisfiable
% 72.82/41.86 |-Branch two:
% 72.82/41.86 | (75) ? [v0] : ? [v1] : (in(all_27_1_11, all_5_2_5) = v0 & in(all_27_1_11, all_5_3_6) = v1 & ( ~ (v1 = 0) | v0 = 0) & ( ~ (v0 = 0) | v1 = 0))
% 72.82/41.86 |
% 72.82/41.86 | Instantiating (75) with all_54_0_51, all_54_1_52 yields:
% 72.82/41.86 | (76) in(all_27_1_11, all_5_2_5) = all_54_1_52 & in(all_27_1_11, all_5_3_6) = all_54_0_51 & ( ~ (all_54_0_51 = 0) | all_54_1_52 = 0) & ( ~ (all_54_1_52 = 0) | all_54_0_51 = 0)
% 72.82/41.86 |
% 72.82/41.86 | Applying alpha-rule on (76) yields:
% 72.82/41.86 | (77) in(all_27_1_11, all_5_2_5) = all_54_1_52
% 72.82/41.86 | (78) in(all_27_1_11, all_5_3_6) = all_54_0_51
% 72.82/41.86 | (79) ~ (all_54_0_51 = 0) | all_54_1_52 = 0
% 72.82/41.86 | (80) ~ (all_54_1_52 = 0) | all_54_0_51 = 0
% 72.82/41.86 |
% 72.82/41.86 | Instantiating formula (12) with all_27_1_11, all_5_2_5, all_49_0_49, all_54_1_52 and discharging atoms in(all_27_1_11, all_5_2_5) = all_54_1_52, in(all_27_1_11, all_5_2_5) = all_49_0_49, yields:
% 72.82/41.86 | (81) all_54_1_52 = all_49_0_49
% 72.82/41.86 |
% 72.82/41.86 | Instantiating formula (12) with all_27_1_11, all_5_3_6, all_49_1_50, all_54_0_51 and discharging atoms in(all_27_1_11, all_5_3_6) = all_54_0_51, in(all_27_1_11, all_5_3_6) = all_49_1_50, yields:
% 72.82/41.86 | (82) all_54_0_51 = all_49_1_50
% 72.82/41.86 |
% 72.82/41.86 +-Applying beta-rule and splitting (64), into two cases.
% 72.82/41.86 |-Branch one:
% 72.82/41.86 | (83) all_27_1_11 = all_5_4_7
% 72.82/41.86 |
% 72.82/41.86 | From (83) and (69) follows:
% 72.82/41.86 | (84) in(all_5_4_7, all_5_2_5) = all_49_0_49
% 72.82/41.86 |
% 72.82/41.86 | From (83) and (70) follows:
% 72.82/41.86 | (85) in(all_5_4_7, all_5_3_6) = all_49_1_50
% 72.82/41.86 |
% 72.82/41.86 | Instantiating formula (34) with all_49_0_49 and discharging atoms in(all_5_4_7, all_5_2_5) = all_49_0_49, yields:
% 72.82/41.86 | (86) all_49_0_49 = 0
% 72.82/41.86 |
% 72.82/41.86 | Combining equations (86,81) yields a new equation:
% 72.82/41.86 | (87) all_54_1_52 = 0
% 72.82/41.86 |
% 72.82/41.86 +-Applying beta-rule and splitting (80), into two cases.
% 72.82/41.86 |-Branch one:
% 72.82/41.86 | (88) ~ (all_54_1_52 = 0)
% 72.82/41.86 |
% 72.82/41.86 | Equations (87) can reduce 88 to:
% 72.82/41.86 | (45) $false
% 72.82/41.86 |
% 72.82/41.86 |-The branch is then unsatisfiable
% 72.82/41.86 |-Branch two:
% 72.82/41.86 | (90) all_54_0_51 = 0
% 72.82/41.86 |
% 72.82/41.86 | Combining equations (90,82) yields a new equation:
% 72.82/41.86 | (91) all_49_1_50 = 0
% 72.82/41.86 |
% 72.82/41.86 | From (91) and (85) follows:
% 72.82/41.86 | (92) in(all_5_4_7, all_5_3_6) = 0
% 72.82/41.86 |
% 72.82/41.86 | Instantiating formula (36) with all_5_4_7 and discharging atoms in(all_5_4_7, all_5_3_6) = 0, yields:
% 72.82/41.86 | (93) all_5_4_7 = all_5_5_8
% 72.82/41.86 |
% 72.82/41.86 | Equations (93) can reduce 31 to:
% 72.82/41.86 | (45) $false
% 72.82/41.86 |
% 72.82/41.86 |-The branch is then unsatisfiable
% 72.82/41.86 |-Branch two:
% 72.82/41.86 | (95) all_27_1_11 = all_5_5_8
% 72.82/41.86 |
% 72.82/41.86 | From (95) and (69) follows:
% 72.82/41.86 | (96) in(all_5_5_8, all_5_2_5) = all_49_0_49
% 72.82/41.86 |
% 72.82/41.86 | From (95) and (70) follows:
% 72.82/41.86 | (97) in(all_5_5_8, all_5_3_6) = all_49_1_50
% 72.82/41.86 |
% 72.82/41.86 | Instantiating formula (37) with all_49_1_50 and discharging atoms in(all_5_5_8, all_5_3_6) = all_49_1_50, yields:
% 72.82/41.86 | (91) all_49_1_50 = 0
% 72.82/41.86 |
% 72.82/41.86 +-Applying beta-rule and splitting (72), into two cases.
% 72.82/41.86 |-Branch one:
% 72.82/41.86 | (99) ~ (all_49_1_50 = 0)
% 72.82/41.86 |
% 72.82/41.86 | Equations (91) can reduce 99 to:
% 72.82/41.86 | (45) $false
% 72.82/41.86 |
% 72.82/41.86 |-The branch is then unsatisfiable
% 72.82/41.86 |-Branch two:
% 72.82/41.86 | (86) all_49_0_49 = 0
% 72.82/41.86 |
% 72.82/41.86 | From (86) and (96) follows:
% 72.82/41.86 | (102) in(all_5_5_8, all_5_2_5) = 0
% 72.82/41.86 |
% 72.82/41.86 | Instantiating formula (33) with all_5_5_8 and discharging atoms in(all_5_5_8, all_5_2_5) = 0, yields:
% 72.82/41.86 | (93) all_5_4_7 = all_5_5_8
% 72.82/41.86 |
% 72.82/41.86 | Equations (93) can reduce 31 to:
% 72.82/41.86 | (45) $false
% 72.82/41.86 |
% 72.82/41.86 |-The branch is then unsatisfiable
% 72.82/41.87 |-Branch two:
% 72.82/41.87 | (62) all_27_0_10 = 0
% 72.82/41.87 | (106) ~ (all_27_1_11 = all_5_4_7) & ~ (all_27_1_11 = all_5_5_8)
% 72.82/41.87 |
% 72.82/41.87 | Applying alpha-rule on (106) yields:
% 72.82/41.87 | (107) ~ (all_27_1_11 = all_5_4_7)
% 72.82/41.87 | (108) ~ (all_27_1_11 = all_5_5_8)
% 72.82/41.87 |
% 72.82/41.87 | From (62) and (48) follows:
% 72.82/41.87 | (109) in(all_27_1_11, ex_24_0_9) = 0
% 72.82/41.87 |
% 72.82/41.87 | Instantiating formula (33) with all_27_1_11 yields:
% 72.82/41.87 | (110) all_27_1_11 = all_5_4_7 | ~ (in(all_27_1_11, all_5_2_5) = 0)
% 72.82/41.87 |
% 72.82/41.87 | Instantiating formula (36) with all_27_1_11 yields:
% 72.82/41.87 | (111) all_27_1_11 = all_5_5_8 | ~ (in(all_27_1_11, all_5_3_6) = 0)
% 72.82/41.87 |
% 72.82/41.87 | Instantiating formula (16) with all_5_1_4, all_5_3_6, all_5_2_5, all_27_1_11 and discharging atoms symmetric_difference(all_5_2_5, all_5_3_6) = all_5_1_4, yields:
% 72.82/41.87 | (112) ~ (in(all_27_1_11, all_5_1_4) = 0) | ? [v0] : ? [v1] : (in(all_27_1_11, all_5_2_5) = v0 & in(all_27_1_11, all_5_3_6) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)) & (v1 = 0 | v0 = 0))
% 72.82/41.87 |
% 72.82/41.87 +-Applying beta-rule and splitting (111), into two cases.
% 72.82/41.87 |-Branch one:
% 72.82/41.87 | (113) ~ (in(all_27_1_11, all_5_3_6) = 0)
% 72.82/41.87 |
% 72.82/41.87 +-Applying beta-rule and splitting (110), into two cases.
% 72.82/41.87 |-Branch one:
% 72.82/41.87 | (114) ~ (in(all_27_1_11, all_5_2_5) = 0)
% 72.82/41.87 |
% 72.82/41.87 +-Applying beta-rule and splitting (112), into two cases.
% 72.82/41.87 |-Branch one:
% 72.82/41.87 | (115) ~ (in(all_27_1_11, all_5_1_4) = 0)
% 72.82/41.87 |
% 72.82/41.87 | From (41) and (109) follows:
% 72.82/41.87 | (116) in(all_27_1_11, all_5_1_4) = 0
% 72.82/41.87 |
% 72.82/41.87 | Using (116) and (115) yields:
% 72.82/41.87 | (56) $false
% 72.82/41.87 |
% 72.82/41.87 |-The branch is then unsatisfiable
% 72.82/41.87 |-Branch two:
% 72.82/41.87 | (118) ? [v0] : ? [v1] : (in(all_27_1_11, all_5_2_5) = v0 & in(all_27_1_11, all_5_3_6) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)) & (v1 = 0 | v0 = 0))
% 72.82/41.87 |
% 72.82/41.87 | Instantiating (118) with all_57_0_17, all_57_1_18 yields:
% 72.82/41.87 | (119) in(all_27_1_11, all_5_2_5) = all_57_1_18 & in(all_27_1_11, all_5_3_6) = all_57_0_17 & ( ~ (all_57_0_17 = 0) | ~ (all_57_1_18 = 0)) & (all_57_0_17 = 0 | all_57_1_18 = 0)
% 72.82/41.87 |
% 72.82/41.87 | Applying alpha-rule on (119) yields:
% 72.82/41.87 | (120) in(all_27_1_11, all_5_2_5) = all_57_1_18
% 72.82/41.87 | (121) in(all_27_1_11, all_5_3_6) = all_57_0_17
% 72.82/41.87 | (122) ~ (all_57_0_17 = 0) | ~ (all_57_1_18 = 0)
% 72.82/41.87 | (123) all_57_0_17 = 0 | all_57_1_18 = 0
% 72.82/41.87 |
% 72.82/41.87 +-Applying beta-rule and splitting (123), into two cases.
% 72.82/41.87 |-Branch one:
% 72.82/41.87 | (124) all_57_0_17 = 0
% 72.82/41.87 |
% 72.82/41.87 | From (124) and (121) follows:
% 72.82/41.87 | (125) in(all_27_1_11, all_5_3_6) = 0
% 72.82/41.87 |
% 72.82/41.87 | Using (125) and (113) yields:
% 72.82/41.87 | (56) $false
% 72.82/41.87 |
% 72.82/41.87 |-The branch is then unsatisfiable
% 72.82/41.87 |-Branch two:
% 72.82/41.87 | (127) all_57_1_18 = 0
% 72.82/41.87 |
% 72.82/41.87 | From (127) and (120) follows:
% 72.82/41.87 | (128) in(all_27_1_11, all_5_2_5) = 0
% 72.82/41.87 |
% 72.82/41.87 | Using (128) and (114) yields:
% 72.82/41.87 | (56) $false
% 72.82/41.87 |
% 72.82/41.87 |-The branch is then unsatisfiable
% 72.82/41.87 |-Branch two:
% 72.82/41.87 | (83) all_27_1_11 = all_5_4_7
% 72.82/41.87 |
% 72.82/41.87 | Equations (83) can reduce 107 to:
% 72.82/41.87 | (45) $false
% 72.82/41.87 |
% 72.82/41.87 |-The branch is then unsatisfiable
% 72.82/41.87 |-Branch two:
% 72.82/41.87 | (95) all_27_1_11 = all_5_5_8
% 72.82/41.87 |
% 72.82/41.87 | Equations (95) can reduce 108 to:
% 72.82/41.87 | (45) $false
% 72.82/41.87 |
% 72.82/41.87 |-The branch is then unsatisfiable
% 72.82/41.87 % SZS output end Proof for theBenchmark
% 72.82/41.87
% 72.82/41.87 41279ms
%------------------------------------------------------------------------------