TSTP Solution File: SEU119+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU119+2 : 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 08:46:41 EDT 2022
% Result : Theorem 37.72s 17.78s
% Output : Proof 44.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU119+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n020.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 : Mon Jun 20 12:22:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.44/0.92 Prover 0: Preprocessing ...
% 1.71/1.07 Prover 0: Warning: ignoring some quantifiers
% 1.86/1.09 Prover 0: Constructing countermodel ...
% 2.21/1.22 Prover 0: gave up
% 2.21/1.22 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.32/1.24 Prover 1: Preprocessing ...
% 2.58/1.32 Prover 1: Warning: ignoring some quantifiers
% 2.58/1.32 Prover 1: Constructing countermodel ...
% 2.79/1.46 Prover 1: gave up
% 2.79/1.46 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.19/1.47 Prover 2: Preprocessing ...
% 3.49/1.55 Prover 2: Warning: ignoring some quantifiers
% 3.49/1.56 Prover 2: Constructing countermodel ...
% 3.85/1.68 Prover 2: gave up
% 3.85/1.68 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.21/1.69 Prover 3: Preprocessing ...
% 4.21/1.71 Prover 3: Warning: ignoring some quantifiers
% 4.21/1.71 Prover 3: Constructing countermodel ...
% 4.21/1.73 Prover 3: gave up
% 4.21/1.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 4.21/1.75 Prover 4: Preprocessing ...
% 4.66/1.80 Prover 4: Warning: ignoring some quantifiers
% 4.66/1.80 Prover 4: Constructing countermodel ...
% 5.61/2.06 Prover 4: gave up
% 5.61/2.06 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.98/2.07 Prover 5: Preprocessing ...
% 6.14/2.11 Prover 5: Warning: ignoring some quantifiers
% 6.14/2.11 Prover 5: Constructing countermodel ...
% 6.22/2.20 Prover 5: gave up
% 6.22/2.20 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.22/2.21 Prover 6: Preprocessing ...
% 6.61/2.25 Prover 6: Warning: ignoring some quantifiers
% 6.61/2.25 Prover 6: Constructing countermodel ...
% 7.02/2.32 Prover 6: gave up
% 7.02/2.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 7.02/2.33 Prover 7: Preprocessing ...
% 7.02/2.35 Prover 7: Proving ...
% 28.64/12.95 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 28.64/12.97 Prover 8: Preprocessing ...
% 28.98/13.01 Prover 8: Proving ...
% 37.72/17.78 Prover 8: proved (4833ms)
% 37.72/17.78 Prover 7: stopped
% 37.72/17.78
% 37.72/17.78 % SZS status Theorem for theBenchmark
% 37.72/17.78
% 37.72/17.78 Generating proof ... found it (size 67)
% 44.55/21.49
% 44.55/21.49 % SZS output start Proof for theBenchmark
% 44.55/21.49 Assumed formulas after preprocessing and simplification:
% 44.55/21.49 | (0) ? [v0] : (empty(v0) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (disjoint(v4, v3) = v2) | ~ (disjoint(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_intersection2(v4, v3) = v2) | ~ (set_intersection2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (in(v4, v3) = v2) | ~ (in(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = v3) | ? [v4] : ( ~ (v4 = v0) & set_intersection2(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (empty(v3) = v2) | ~ (empty(v3) = v1)) & ! [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] : ? [v6] : ? [v7] : ? [v8] : (in(v5, v4) = v6 & in(v5, v2) = v8 & in(v5, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v8 = 0 & v7 = 0))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ( ! [v4] : ! [v5] : ( ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : (in(v4, v3) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | (v7 = 0 & v5 = 0)))) & ! [v4] : ( ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : (in(v4, v3) = v6 & in(v4, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))))) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_intersection2(v1, v1) = v2)) & ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | disjoint(v2, v1) = 0) & ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | set_intersection2(v1, v2) = v0) & ! [v1] : ! [v2] : ( ~ (in(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v1] : (v1 = v0 | ? [v2] : in(v2, v1) = 0) & ! [v1] : ~ (in(v1, v0) = 0) & ? [v1] : ? [v2] : ? [v3] : (disjoint(v1, v2) = v3 & ((v3 = 0 & ? [v4] : (in(v4, v2) = 0 & in(v4, v1) = 0)) | ( ~ (v3 = 0) & ! [v4] : ( ~ (in(v4, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & in(v4, v2) = v5))))) & ? [v1] : ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2) & ? [v1] : empty(v1) = 0)
% 44.78/21.51 | Instantiating (0) with all_0_0_0 yields:
% 44.78/21.51 | (1) empty(all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = all_0_0_0) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [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] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v3) = v5 & in(v4, v1) = v7 & in(v4, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ! [v4] : ( ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3] : ( ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = all_0_0_0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0) = 0) & ! [v0] : ~ (in(v0, all_0_0_0) = 0) & ? [v0] : ? [v1] : ? [v2] : (disjoint(v0, v1) = v2 & ((v2 = 0 & ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) | ( ~ (v2 = 0) & ! [v3] : ( ~ (in(v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4))))) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) & ? [v0] : empty(v0) = 0
% 44.78/21.52 |
% 44.78/21.52 | Applying alpha-rule on (1) yields:
% 44.78/21.52 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 44.78/21.52 | (3) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 44.78/21.52 | (4) ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1)
% 44.78/21.52 | (5) ? [v0] : empty(v0) = 0
% 44.78/21.52 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 44.78/21.52 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 44.78/21.52 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 44.78/21.52 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = all_0_0_0) & set_intersection2(v0, v1) = v3))
% 44.78/21.52 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 44.78/21.52 | (11) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = all_0_0_0)
% 44.78/21.52 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 44.78/21.52 | (13) empty(all_0_0_0) = 0
% 44.78/21.52 | (14) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 44.78/21.52 | (15) ? [v0] : ? [v1] : ? [v2] : (disjoint(v0, v1) = v2 & ((v2 = 0 & ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) | ( ~ (v2 = 0) & ! [v3] : ( ~ (in(v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4)))))
% 44.78/21.52 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ! [v4] : ( ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3] : ( ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 44.78/21.52 | (17) ! [v0] : ~ (in(v0, all_0_0_0) = 0)
% 44.78/21.52 | (18) ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0) = 0)
% 44.78/21.52 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v3) = v5 & in(v4, v1) = v7 & in(v4, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))))
% 44.78/21.52 |
% 44.78/21.52 | Instantiating (15) with all_7_0_4, all_7_1_5, all_7_2_6 yields:
% 44.78/21.52 | (20) disjoint(all_7_2_6, all_7_1_5) = all_7_0_4 & ((all_7_0_4 = 0 & ? [v0] : (in(v0, all_7_1_5) = 0 & in(v0, all_7_2_6) = 0)) | ( ~ (all_7_0_4 = 0) & ! [v0] : ( ~ (in(v0, all_7_2_6) = 0) | ? [v1] : ( ~ (v1 = 0) & in(v0, all_7_1_5) = v1))))
% 44.78/21.52 |
% 44.78/21.52 | Applying alpha-rule on (20) yields:
% 44.78/21.52 | (21) disjoint(all_7_2_6, all_7_1_5) = all_7_0_4
% 44.78/21.52 | (22) (all_7_0_4 = 0 & ? [v0] : (in(v0, all_7_1_5) = 0 & in(v0, all_7_2_6) = 0)) | ( ~ (all_7_0_4 = 0) & ! [v0] : ( ~ (in(v0, all_7_2_6) = 0) | ? [v1] : ( ~ (v1 = 0) & in(v0, all_7_1_5) = v1)))
% 44.78/21.52 |
% 44.78/21.53 | Instantiating formula (9) with all_7_0_4, all_7_1_5, all_7_2_6 and discharging atoms disjoint(all_7_2_6, all_7_1_5) = all_7_0_4, yields:
% 44.78/21.53 | (23) all_7_0_4 = 0 | ? [v0] : ( ~ (v0 = all_0_0_0) & set_intersection2(all_7_2_6, all_7_1_5) = v0)
% 44.78/21.53 |
% 44.78/21.53 +-Applying beta-rule and splitting (22), into two cases.
% 44.78/21.53 |-Branch one:
% 44.78/21.53 | (24) all_7_0_4 = 0 & ? [v0] : (in(v0, all_7_1_5) = 0 & in(v0, all_7_2_6) = 0)
% 44.78/21.53 |
% 44.78/21.53 | Applying alpha-rule on (24) yields:
% 44.78/21.53 | (25) all_7_0_4 = 0
% 44.78/21.53 | (26) ? [v0] : (in(v0, all_7_1_5) = 0 & in(v0, all_7_2_6) = 0)
% 44.78/21.53 |
% 44.78/21.53 | Instantiating (26) with all_16_0_7 yields:
% 44.78/21.53 | (27) in(all_16_0_7, all_7_1_5) = 0 & in(all_16_0_7, all_7_2_6) = 0
% 44.78/21.53 |
% 44.78/21.53 | Applying alpha-rule on (27) yields:
% 44.78/21.53 | (28) in(all_16_0_7, all_7_1_5) = 0
% 44.78/21.53 | (29) in(all_16_0_7, all_7_2_6) = 0
% 44.78/21.53 |
% 44.78/21.53 | From (25) and (21) follows:
% 44.78/21.53 | (30) disjoint(all_7_2_6, all_7_1_5) = 0
% 44.78/21.53 |
% 44.78/21.53 | Instantiating formula (11) with all_7_1_5, all_7_2_6 and discharging atoms disjoint(all_7_2_6, all_7_1_5) = 0, yields:
% 44.78/21.53 | (31) set_intersection2(all_7_2_6, all_7_1_5) = all_0_0_0
% 44.78/21.53 |
% 44.78/21.53 | Instantiating formula (16) with all_0_0_0, all_7_1_5, all_7_2_6 and discharging atoms set_intersection2(all_7_2_6, all_7_1_5) = all_0_0_0, yields:
% 44.78/21.53 | (32) ! [v0] : ! [v1] : ( ~ (in(v0, all_7_2_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_7_1_5) = v3 & in(v0, all_0_0_0) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ( ~ (in(v0, all_7_2_6) = 0) | ? [v1] : ? [v2] : (in(v0, all_7_1_5) = v1 & in(v0, all_0_0_0) = v2 & ( ~ (v1 = 0) | v2 = 0)))
% 44.78/21.53 |
% 44.78/21.53 | Applying alpha-rule on (32) yields:
% 44.78/21.53 | (33) ! [v0] : ! [v1] : ( ~ (in(v0, all_7_2_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_7_1_5) = v3 & in(v0, all_0_0_0) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 44.78/21.53 | (34) ! [v0] : ( ~ (in(v0, all_7_2_6) = 0) | ? [v1] : ? [v2] : (in(v0, all_7_1_5) = v1 & in(v0, all_0_0_0) = v2 & ( ~ (v1 = 0) | v2 = 0)))
% 44.78/21.53 |
% 44.78/21.53 | Instantiating formula (34) with all_16_0_7 and discharging atoms in(all_16_0_7, all_7_2_6) = 0, yields:
% 44.78/21.53 | (35) ? [v0] : ? [v1] : (in(all_16_0_7, all_7_1_5) = v0 & in(all_16_0_7, all_0_0_0) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 44.78/21.53 |
% 44.78/21.53 | Instantiating formula (33) with 0, all_16_0_7 and discharging atoms in(all_16_0_7, all_7_2_6) = 0, yields:
% 44.78/21.53 | (36) ? [v0] : ? [v1] : (in(all_16_0_7, all_7_1_5) = v1 & in(all_16_0_7, all_0_0_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 44.78/21.53 |
% 44.78/21.53 | Instantiating (36) with all_35_0_10, all_35_1_11 yields:
% 44.78/21.53 | (37) in(all_16_0_7, all_7_1_5) = all_35_0_10 & in(all_16_0_7, all_0_0_0) = all_35_1_11 & ( ~ (all_35_1_11 = 0) | all_35_0_10 = 0)
% 44.78/21.53 |
% 44.78/21.53 | Applying alpha-rule on (37) yields:
% 44.78/21.53 | (38) in(all_16_0_7, all_7_1_5) = all_35_0_10
% 44.78/21.53 | (39) in(all_16_0_7, all_0_0_0) = all_35_1_11
% 44.78/21.53 | (40) ~ (all_35_1_11 = 0) | all_35_0_10 = 0
% 44.78/21.53 |
% 44.78/21.53 | Instantiating (35) with all_37_0_12, all_37_1_13 yields:
% 44.78/21.53 | (41) in(all_16_0_7, all_7_1_5) = all_37_1_13 & in(all_16_0_7, all_0_0_0) = all_37_0_12 & ( ~ (all_37_1_13 = 0) | all_37_0_12 = 0)
% 44.78/21.53 |
% 44.78/21.53 | Applying alpha-rule on (41) yields:
% 44.78/21.53 | (42) in(all_16_0_7, all_7_1_5) = all_37_1_13
% 44.78/21.53 | (43) in(all_16_0_7, all_0_0_0) = all_37_0_12
% 44.78/21.53 | (44) ~ (all_37_1_13 = 0) | all_37_0_12 = 0
% 44.78/21.53 |
% 44.78/21.53 | Instantiating formula (2) with all_16_0_7, all_7_1_5, all_37_1_13, 0 and discharging atoms in(all_16_0_7, all_7_1_5) = all_37_1_13, in(all_16_0_7, all_7_1_5) = 0, yields:
% 44.78/21.53 | (45) all_37_1_13 = 0
% 44.78/21.53 |
% 44.78/21.53 | Instantiating formula (2) with all_16_0_7, all_0_0_0, all_35_1_11, all_37_0_12 and discharging atoms in(all_16_0_7, all_0_0_0) = all_37_0_12, in(all_16_0_7, all_0_0_0) = all_35_1_11, yields:
% 44.78/21.53 | (46) all_37_0_12 = all_35_1_11
% 44.78/21.53 |
% 44.78/21.53 +-Applying beta-rule and splitting (44), into two cases.
% 44.78/21.53 |-Branch one:
% 44.78/21.53 | (47) ~ (all_37_1_13 = 0)
% 44.78/21.53 |
% 44.78/21.53 | Equations (45) can reduce 47 to:
% 44.78/21.53 | (48) $false
% 44.78/21.53 |
% 44.78/21.53 |-The branch is then unsatisfiable
% 44.78/21.53 |-Branch two:
% 44.78/21.53 | (49) all_37_0_12 = 0
% 44.78/21.53 |
% 44.78/21.53 | Combining equations (49,46) yields a new equation:
% 44.78/21.53 | (50) all_35_1_11 = 0
% 44.78/21.53 |
% 44.78/21.53 | From (50) and (39) follows:
% 44.78/21.53 | (51) in(all_16_0_7, all_0_0_0) = 0
% 44.78/21.53 |
% 44.78/21.53 | Instantiating formula (17) with all_16_0_7 and discharging atoms in(all_16_0_7, all_0_0_0) = 0, yields:
% 44.78/21.53 | (52) $false
% 44.78/21.53 |
% 44.78/21.53 |-The branch is then unsatisfiable
% 44.78/21.53 |-Branch two:
% 44.78/21.53 | (53) ~ (all_7_0_4 = 0) & ! [v0] : ( ~ (in(v0, all_7_2_6) = 0) | ? [v1] : ( ~ (v1 = 0) & in(v0, all_7_1_5) = v1))
% 44.78/21.53 |
% 44.78/21.53 | Applying alpha-rule on (53) yields:
% 44.78/21.53 | (54) ~ (all_7_0_4 = 0)
% 44.78/21.53 | (55) ! [v0] : ( ~ (in(v0, all_7_2_6) = 0) | ? [v1] : ( ~ (v1 = 0) & in(v0, all_7_1_5) = v1))
% 44.78/21.53 |
% 44.78/21.53 +-Applying beta-rule and splitting (23), into two cases.
% 44.78/21.53 |-Branch one:
% 44.78/21.53 | (25) all_7_0_4 = 0
% 44.78/21.53 |
% 44.78/21.54 | Equations (25) can reduce 54 to:
% 44.78/21.54 | (48) $false
% 44.78/21.54 |
% 44.78/21.54 |-The branch is then unsatisfiable
% 44.78/21.54 |-Branch two:
% 44.78/21.54 | (58) ? [v0] : ( ~ (v0 = all_0_0_0) & set_intersection2(all_7_2_6, all_7_1_5) = v0)
% 44.78/21.54 |
% 44.78/21.54 | Instantiating (58) with all_21_0_14 yields:
% 44.78/21.54 | (59) ~ (all_21_0_14 = all_0_0_0) & set_intersection2(all_7_2_6, all_7_1_5) = all_21_0_14
% 44.78/21.54 |
% 44.78/21.54 | Applying alpha-rule on (59) yields:
% 44.78/21.54 | (60) ~ (all_21_0_14 = all_0_0_0)
% 44.78/21.54 | (61) set_intersection2(all_7_2_6, all_7_1_5) = all_21_0_14
% 44.78/21.54 |
% 44.78/21.54 | Instantiating formula (19) with all_21_0_14, all_7_1_5, all_7_2_6 and discharging atoms set_intersection2(all_7_2_6, all_7_1_5) = all_21_0_14, yields:
% 44.78/21.54 | (62) ! [v0] : (v0 = all_21_0_14 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (in(v1, v0) = v2 & in(v1, all_7_1_5) = v4 & in(v1, all_7_2_6) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0)) & (v2 = 0 | (v4 = 0 & v3 = 0))))
% 44.78/21.54 |
% 44.78/21.54 | Instantiating formula (16) with all_21_0_14, all_7_1_5, all_7_2_6 and discharging atoms set_intersection2(all_7_2_6, all_7_1_5) = all_21_0_14, yields:
% 44.78/21.54 | (63) ! [v0] : ! [v1] : ( ~ (in(v0, all_7_2_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_21_0_14) = v2 & in(v0, all_7_1_5) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ( ~ (in(v0, all_7_2_6) = 0) | ? [v1] : ? [v2] : (in(v0, all_21_0_14) = v2 & in(v0, all_7_1_5) = v1 & ( ~ (v1 = 0) | v2 = 0)))
% 44.78/21.54 |
% 44.78/21.54 | Applying alpha-rule on (63) yields:
% 44.78/21.54 | (64) ! [v0] : ! [v1] : ( ~ (in(v0, all_7_2_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_21_0_14) = v2 & in(v0, all_7_1_5) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 44.78/21.54 | (65) ! [v0] : ( ~ (in(v0, all_7_2_6) = 0) | ? [v1] : ? [v2] : (in(v0, all_21_0_14) = v2 & in(v0, all_7_1_5) = v1 & ( ~ (v1 = 0) | v2 = 0)))
% 44.78/21.54 |
% 44.78/21.54 | Introducing new symbol ex_47_0_18 defined by:
% 44.78/21.54 | (66) ex_47_0_18 = all_0_0_0
% 44.78/21.54 |
% 44.78/21.54 | Instantiating formula (62) with ex_47_0_18 yields:
% 44.78/21.54 | (67) ex_47_0_18 = all_21_0_14 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (in(v0, ex_47_0_18) = v1 & in(v0, all_7_1_5) = v3 & in(v0, all_7_2_6) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)) & (v1 = 0 | (v3 = 0 & v2 = 0)))
% 44.78/21.54 |
% 44.78/21.54 +-Applying beta-rule and splitting (67), into two cases.
% 44.78/21.54 |-Branch one:
% 44.78/21.54 | (68) ex_47_0_18 = all_21_0_14
% 44.78/21.54 |
% 44.78/21.54 | Combining equations (68,66) yields a new equation:
% 44.78/21.54 | (69) all_21_0_14 = all_0_0_0
% 44.78/21.54 |
% 44.78/21.54 | Simplifying 69 yields:
% 44.78/21.54 | (70) all_21_0_14 = all_0_0_0
% 44.78/21.54 |
% 44.78/21.54 | Equations (70) can reduce 60 to:
% 44.78/21.54 | (48) $false
% 44.78/21.54 |
% 44.78/21.54 |-The branch is then unsatisfiable
% 44.78/21.54 |-Branch two:
% 44.78/21.54 | (72) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (in(v0, ex_47_0_18) = v1 & in(v0, all_7_1_5) = v3 & in(v0, all_7_2_6) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)) & (v1 = 0 | (v3 = 0 & v2 = 0)))
% 44.78/21.54 |
% 44.78/21.54 | Instantiating (72) with all_50_0_19, all_50_1_20, all_50_2_21, all_50_3_22 yields:
% 44.78/21.54 | (73) in(all_50_3_22, ex_47_0_18) = all_50_2_21 & in(all_50_3_22, all_7_1_5) = all_50_0_19 & in(all_50_3_22, all_7_2_6) = all_50_1_20 & ( ~ (all_50_0_19 = 0) | ~ (all_50_1_20 = 0) | ~ (all_50_2_21 = 0)) & (all_50_2_21 = 0 | (all_50_0_19 = 0 & all_50_1_20 = 0))
% 44.78/21.54 |
% 44.78/21.54 | Applying alpha-rule on (73) yields:
% 44.78/21.54 | (74) all_50_2_21 = 0 | (all_50_0_19 = 0 & all_50_1_20 = 0)
% 44.78/21.54 | (75) in(all_50_3_22, all_7_2_6) = all_50_1_20
% 44.78/21.54 | (76) in(all_50_3_22, all_7_1_5) = all_50_0_19
% 44.78/21.54 | (77) in(all_50_3_22, ex_47_0_18) = all_50_2_21
% 44.78/21.54 | (78) ~ (all_50_0_19 = 0) | ~ (all_50_1_20 = 0) | ~ (all_50_2_21 = 0)
% 44.78/21.54 |
% 44.78/21.54 +-Applying beta-rule and splitting (74), into two cases.
% 44.78/21.54 |-Branch one:
% 44.78/21.54 | (79) all_50_2_21 = 0
% 44.78/21.54 |
% 44.78/21.54 | From (79) and (77) follows:
% 44.78/21.54 | (80) in(all_50_3_22, ex_47_0_18) = 0
% 44.78/21.54 |
% 44.78/21.54 | Instantiating formula (17) with all_50_3_22 yields:
% 44.78/21.54 | (81) ~ (in(all_50_3_22, all_0_0_0) = 0)
% 44.78/21.54 |
% 44.78/21.54 | From (66) and (80) follows:
% 44.78/21.54 | (82) in(all_50_3_22, all_0_0_0) = 0
% 44.78/21.54 |
% 44.78/21.54 | Using (82) and (81) yields:
% 44.78/21.54 | (52) $false
% 44.78/21.54 |
% 44.78/21.54 |-The branch is then unsatisfiable
% 44.78/21.54 |-Branch two:
% 44.78/21.54 | (84) all_50_0_19 = 0 & all_50_1_20 = 0
% 44.78/21.54 |
% 44.78/21.54 | Applying alpha-rule on (84) yields:
% 44.78/21.54 | (85) all_50_0_19 = 0
% 44.78/21.54 | (86) all_50_1_20 = 0
% 44.78/21.54 |
% 44.78/21.54 | From (85) and (76) follows:
% 44.78/21.54 | (87) in(all_50_3_22, all_7_1_5) = 0
% 44.78/21.54 |
% 44.78/21.54 | From (86) and (75) follows:
% 44.78/21.54 | (88) in(all_50_3_22, all_7_2_6) = 0
% 44.78/21.54 |
% 44.78/21.54 | Instantiating formula (65) with all_50_3_22 and discharging atoms in(all_50_3_22, all_7_2_6) = 0, yields:
% 44.78/21.54 | (89) ? [v0] : ? [v1] : (in(all_50_3_22, all_21_0_14) = v1 & in(all_50_3_22, all_7_1_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 44.78/21.54 |
% 44.78/21.54 | Instantiating formula (55) with all_50_3_22 and discharging atoms in(all_50_3_22, all_7_2_6) = 0, yields:
% 44.78/21.54 | (90) ? [v0] : ( ~ (v0 = 0) & in(all_50_3_22, all_7_1_5) = v0)
% 44.78/21.54 |
% 44.78/21.54 | Instantiating (90) with all_79_0_47 yields:
% 44.78/21.54 | (91) ~ (all_79_0_47 = 0) & in(all_50_3_22, all_7_1_5) = all_79_0_47
% 44.78/21.54 |
% 44.78/21.54 | Applying alpha-rule on (91) yields:
% 44.78/21.54 | (92) ~ (all_79_0_47 = 0)
% 44.78/21.54 | (93) in(all_50_3_22, all_7_1_5) = all_79_0_47
% 44.78/21.54 |
% 44.78/21.54 | Instantiating (89) with all_85_0_51, all_85_1_52 yields:
% 44.78/21.55 | (94) in(all_50_3_22, all_21_0_14) = all_85_0_51 & in(all_50_3_22, all_7_1_5) = all_85_1_52 & ( ~ (all_85_1_52 = 0) | all_85_0_51 = 0)
% 44.78/21.55 |
% 44.78/21.55 | Applying alpha-rule on (94) yields:
% 44.78/21.55 | (95) in(all_50_3_22, all_21_0_14) = all_85_0_51
% 44.78/21.55 | (96) in(all_50_3_22, all_7_1_5) = all_85_1_52
% 44.78/21.55 | (97) ~ (all_85_1_52 = 0) | all_85_0_51 = 0
% 44.78/21.55 |
% 44.78/21.55 | Instantiating formula (2) with all_50_3_22, all_7_1_5, all_85_1_52, 0 and discharging atoms in(all_50_3_22, all_7_1_5) = all_85_1_52, in(all_50_3_22, all_7_1_5) = 0, yields:
% 44.78/21.55 | (98) all_85_1_52 = 0
% 44.78/21.55 |
% 44.78/21.55 | Instantiating formula (2) with all_50_3_22, all_7_1_5, all_79_0_47, all_85_1_52 and discharging atoms in(all_50_3_22, all_7_1_5) = all_85_1_52, in(all_50_3_22, all_7_1_5) = all_79_0_47, yields:
% 44.78/21.55 | (99) all_85_1_52 = all_79_0_47
% 44.78/21.55 |
% 44.78/21.55 | Combining equations (99,98) yields a new equation:
% 44.78/21.55 | (100) all_79_0_47 = 0
% 44.78/21.55 |
% 44.78/21.55 | Simplifying 100 yields:
% 44.78/21.55 | (101) all_79_0_47 = 0
% 44.78/21.55 |
% 44.78/21.55 | Equations (101) can reduce 92 to:
% 44.78/21.55 | (48) $false
% 44.78/21.55 |
% 44.78/21.55 |-The branch is then unsatisfiable
% 44.78/21.55 % SZS output end Proof for theBenchmark
% 44.78/21.55
% 44.78/21.55 20959ms
%------------------------------------------------------------------------------