TSTP Solution File: KRS150+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KRS150+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 : Sun Jul 17 02:56:42 EDT 2022
% Result : Theorem 3.63s 1.62s
% Output : Proof 6.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS150+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.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 : Tue Jun 7 16:45:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.50/0.62 ____ _
% 0.50/0.62 ___ / __ \_____(_)___ ________ __________
% 0.50/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.62
% 0.50/0.62 A Theorem Prover for First-Order Logic
% 0.50/0.62 (ePrincess v.1.0)
% 0.50/0.62
% 0.50/0.62 (c) Philipp Rümmer, 2009-2015
% 0.50/0.62 (c) Peter Backeman, 2014-2015
% 0.50/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.62 Bug reports to peter@backeman.se
% 0.50/0.62
% 0.50/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.62
% 0.65/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/1.00 Prover 0: Preprocessing ...
% 1.86/1.14 Prover 0: Warning: ignoring some quantifiers
% 2.05/1.16 Prover 0: Constructing countermodel ...
% 2.68/1.34 Prover 0: gave up
% 2.68/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.68/1.37 Prover 1: Preprocessing ...
% 3.27/1.50 Prover 1: Constructing countermodel ...
% 3.63/1.62 Prover 1: proved (282ms)
% 3.63/1.62
% 3.63/1.62 No countermodel exists, formula is valid
% 3.63/1.62 % SZS status Theorem for theBenchmark
% 3.63/1.62
% 3.63/1.62 Generating proof ... found it (size 129)
% 6.32/2.17
% 6.32/2.17 % SZS output start Proof for theBenchmark
% 6.32/2.17 Assumed formulas after preprocessing and simplification:
% 6.32/2.17 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = 0) & ~ (v0 = 0) & cTEST(iV16560) = 0 & cC6(iV16561) = v8 & cC4(iV16561) = v0 & cTOP(iV16560) = 0 & cC18(iV16560) = v4 & cC8(iV16560) = v7 & cC16(iV16560) = v5 & cC14(iV16560) = v6 & cC12(iV16562) = v9 & cC10(iV16562) = v2 & rR1(iV16560, iV16561) = 0 & rR1(iV16560, iV16562) = 0 & cC2(iV16561) = v1 & cC2(iV16562) = v3 & cowlThing(iV16561) = 0 & cowlThing(iV16562) = 0 & cowlThing(iV16560) = 0 & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (rR1(v16, v15) = v14) | ~ (rR1(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cTEST(v15) = v14) | ~ (cTEST(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cC6(v15) = v14) | ~ (cC6(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cC4(v15) = v14) | ~ (cC4(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cTOP(v15) = v14) | ~ (cTOP(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cC18(v15) = v14) | ~ (cC18(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cC8(v15) = v14) | ~ (cC8(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cC16(v15) = v14) | ~ (cC16(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cC14(v15) = v14) | ~ (cC14(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cC12(v15) = v14) | ~ (cC12(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cC10(v15) = v14) | ~ (cC10(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cC2(v15) = v14) | ~ (cC2(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (xsd_string(v15) = v14) | ~ (xsd_string(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (xsd_integer(v15) = v14) | ~ (xsd_integer(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cowlNothing(v15) = v14) | ~ (cowlNothing(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (cowlThing(v15) = v14) | ~ (cowlThing(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (cC6(v15) = 0) | ~ (cC8(v13) = v14) | ? [v16] : ( ~ (v16 = 0) & rR1(v13, v15) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (cC4(v13) = v14) | ~ (rR1(v13, v15) = 0) | cC2(v15) = 0) & ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (cC14(v13) = v14) | ~ (cC12(v15) = 0) | ? [v16] : ( ~ (v16 = 0) & rR1(v13, v15) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (cC10(v13) = v14) | ~ (rR1(v13, v15) = 0) | cC2(v15) = 0) & ! [v13] : ! [v14] : (v14 = 0 | ~ (cTEST(v13) = v14) | ? [v15] : ? [v16] : (cTOP(v13) = v16 & cC18(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v13] : ! [v14] : (v14 = 0 | ~ (cC6(v13) = v14) | ? [v15] : ? [v16] : (cC4(v13) = v16 & cC2(v13) = v15 & (v16 = 0 | v15 = 0))) & ! [v13] : ! [v14] : (v14 = 0 | ~ (cC12(v13) = v14) | ? [v15] : ? [v16] : (cC10(v13) = v16 & cC2(v13) = v15 & (v16 = 0 | v15 = 0))) & ! [v13] : ! [v14] : (v14 = 0 | ~ (xsd_string(v13) = v14) | xsd_integer(v13) = 0) & ! [v13] : ! [v14] : (v14 = 0 | ~ (cowlThing(v13) = v14)) & ! [v13] : ! [v14] : ( ~ (cTOP(v13) = v14) | ? [v15] : ? [v16] : (cC18(v13) = v15 & cC16(v13) = v16 & ( ~ (v15 = 0) | (v16 = 0 & v14 = 0)))) & ! [v13] : ! [v14] : ( ~ (cC8(v13) = v14) | ? [v15] : ? [v16] : (cC16(v13) = v15 & cC14(v13) = v16 & ( ~ (v15 = 0) | (v16 = 0 & v14 = 0)))) & ! [v13] : ( ~ (cTEST(v13) = 0) | (cTOP(v13) = 0 & cC18(v13) = 0)) & ! [v13] : ( ~ (cC6(v13) = 0) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & ~ (v14 = 0) & cC4(v13) = v15 & cC2(v13) = v14)) & ! [v13] : ( ~ (cC4(v13) = 0) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & rR1(v13, v14) = 0 & cC2(v14) = v15)) & ! [v13] : ( ~ (cTOP(v13) = 0) | ? [v14] : ? [v15] : (cC18(v13) = v15 & cC16(v13) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v13] : ( ~ (cC8(v13) = 0) | ? [v14] : ? [v15] : (cC16(v13) = v15 & cC14(v13) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v13] : ( ~ (cC8(v13) = 0) | ? [v14] : (cC6(v14) = 0 & rR1(v13, v14) = 0)) & ! [v13] : ( ~ (cC14(v13) = 0) | ? [v14] : (cC12(v14) = 0 & rR1(v13, v14) = 0)) & ! [v13] : ( ~ (cC12(v13) = 0) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & ~ (v14 = 0) & cC10(v13) = v15 & cC2(v13) = v14)) & ! [v13] : ( ~ (cC10(v13) = 0) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & rR1(v13, v14) = 0 & cC2(v14) = v15)) & ! [v13] : ( ~ (rR1(iV16561, v13) = 0) | cC2(v13) = 0) & ! [v13] : ( ~ (rR1(iV16562, v13) = 0) | cC2(v13) = 0) & ! [v13] : ( ~ (xsd_string(v13) = 0) | ? [v14] : ( ~ (v14 = 0) & xsd_integer(v13) = v14)) & ! [v13] : ~ (cowlNothing(v13) = 0) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (xsd_string(v10) = v11 & xsd_integer(v10) = v12 & ((v12 = 0 & v11 = 0) | ( ~ (v12 = 0) & ~ (v11 = 0)))) | (cowlNothing(v10) = v12 & cowlThing(v10) = v11 & ( ~ (v11 = 0) | v12 = 0))))
% 6.50/2.21 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields:
% 6.50/2.21 | (1) ~ (all_0_9_9 = 0) & ~ (all_0_10_10 = 0) & ~ (all_0_11_11 = 0) & ~ (all_0_12_12 = 0) & cTEST(iV16560) = 0 & cC6(iV16561) = all_0_4_4 & cC4(iV16561) = all_0_12_12 & cTOP(iV16560) = 0 & cC18(iV16560) = all_0_8_8 & cC8(iV16560) = all_0_5_5 & cC16(iV16560) = all_0_7_7 & cC14(iV16560) = all_0_6_6 & cC12(iV16562) = all_0_3_3 & cC10(iV16562) = all_0_10_10 & rR1(iV16560, iV16561) = 0 & rR1(iV16560, iV16562) = 0 & cC2(iV16561) = all_0_11_11 & cC2(iV16562) = all_0_9_9 & cowlThing(iV16561) = 0 & cowlThing(iV16562) = 0 & cowlThing(iV16560) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rR1(v3, v2) = v1) | ~ (rR1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cTEST(v2) = v1) | ~ (cTEST(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC6(v2) = v1) | ~ (cC6(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC4(v2) = v1) | ~ (cC4(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cTOP(v2) = v1) | ~ (cTOP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC18(v2) = v1) | ~ (cC18(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC8(v2) = v1) | ~ (cC8(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC16(v2) = v1) | ~ (cC16(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC14(v2) = v1) | ~ (cC14(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC12(v2) = v1) | ~ (cC12(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC10(v2) = v1) | ~ (cC10(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC2(v2) = v1) | ~ (cC2(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC6(v2) = 0) | ~ (cC8(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & rR1(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC4(v0) = v1) | ~ (rR1(v0, v2) = 0) | cC2(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC14(v0) = v1) | ~ (cC12(v2) = 0) | ? [v3] : ( ~ (v3 = 0) & rR1(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC10(v0) = v1) | ~ (rR1(v0, v2) = 0) | cC2(v2) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cTEST(v0) = v1) | ? [v2] : ? [v3] : (cTOP(v0) = v3 & cC18(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cC6(v0) = v1) | ? [v2] : ? [v3] : (cC4(v0) = v3 & cC2(v0) = v2 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cC12(v0) = v1) | ? [v2] : ? [v3] : (cC10(v0) = v3 & cC2(v0) = v2 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (cTOP(v0) = v1) | ? [v2] : ? [v3] : (cC18(v0) = v2 & cC16(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (cC8(v0) = v1) | ? [v2] : ? [v3] : (cC16(v0) = v2 & cC14(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ( ~ (cTEST(v0) = 0) | (cTOP(v0) = 0 & cC18(v0) = 0)) & ! [v0] : ( ~ (cC6(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & cC4(v0) = v2 & cC2(v0) = v1)) & ! [v0] : ( ~ (cC4(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & rR1(v0, v1) = 0 & cC2(v1) = v2)) & ! [v0] : ( ~ (cTOP(v0) = 0) | ? [v1] : ? [v2] : (cC18(v0) = v2 & cC16(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : ? [v2] : (cC16(v0) = v2 & cC14(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : (cC6(v1) = 0 & rR1(v0, v1) = 0)) & ! [v0] : ( ~ (cC14(v0) = 0) | ? [v1] : (cC12(v1) = 0 & rR1(v0, v1) = 0)) & ! [v0] : ( ~ (cC12(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & cC10(v0) = v2 & cC2(v0) = v1)) & ! [v0] : ( ~ (cC10(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & rR1(v0, v1) = 0 & cC2(v1) = v2)) & ! [v0] : ( ~ (rR1(iV16561, v0) = 0) | cC2(v0) = 0) & ! [v0] : ( ~ (rR1(iV16562, v0) = 0) | cC2(v0) = 0) & ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) & ! [v0] : ~ (cowlNothing(v0) = 0) & ( ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)))
% 6.50/2.22 |
% 6.50/2.22 | Applying alpha-rule on (1) yields:
% 6.50/2.22 | (2) rR1(iV16560, iV16561) = 0
% 6.50/2.22 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC18(v2) = v1) | ~ (cC18(v2) = v0))
% 6.50/2.22 | (4) cowlThing(iV16560) = 0
% 6.50/2.22 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (cTEST(v0) = v1) | ? [v2] : ? [v3] : (cTOP(v0) = v3 & cC18(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 6.50/2.22 | (6) ~ (all_0_10_10 = 0)
% 6.50/2.22 | (7) ! [v0] : ! [v1] : ( ~ (cTOP(v0) = v1) | ? [v2] : ? [v3] : (cC18(v0) = v2 & cC16(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 6.50/2.22 | (8) ! [v0] : ( ~ (xsd_string(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 6.50/2.22 | (9) cC4(iV16561) = all_0_12_12
% 6.50/2.22 | (10) ! [v0] : ~ (cowlNothing(v0) = 0)
% 6.50/2.22 | (11) cC12(iV16562) = all_0_3_3
% 6.50/2.22 | (12) rR1(iV16560, iV16562) = 0
% 6.50/2.22 | (13) cTEST(iV16560) = 0
% 6.50/2.22 | (14) ! [v0] : ( ~ (cC6(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & cC4(v0) = v2 & cC2(v0) = v1))
% 6.50/2.22 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC4(v2) = v1) | ~ (cC4(v2) = v0))
% 6.50/2.22 | (16) ! [v0] : ( ~ (rR1(iV16561, v0) = 0) | cC2(v0) = 0)
% 6.50/2.22 | (17) cC10(iV16562) = all_0_10_10
% 6.50/2.22 | (18) ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : ? [v2] : (cC16(v0) = v2 & cC14(v0) = v1 & ( ~ (v1 = 0) | v2 = 0)))
% 6.50/2.22 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC10(v2) = v1) | ~ (cC10(v2) = v0))
% 6.50/2.22 | (20) ~ (all_0_12_12 = 0)
% 6.50/2.22 | (21) ! [v0] : ( ~ (cC12(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & cC10(v0) = v2 & cC2(v0) = v1))
% 6.50/2.22 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC8(v2) = v1) | ~ (cC8(v2) = v0))
% 6.50/2.22 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlNothing(v2) = v1) | ~ (cowlNothing(v2) = v0))
% 6.50/2.22 | (24) cowlThing(iV16562) = 0
% 6.50/2.22 | (25) ! [v0] : ! [v1] : (v1 = 0 | ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 6.50/2.22 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC14(v0) = v1) | ~ (cC12(v2) = 0) | ? [v3] : ( ~ (v3 = 0) & rR1(v0, v2) = v3))
% 6.50/2.22 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC14(v2) = v1) | ~ (cC14(v2) = v0))
% 6.50/2.22 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (cowlThing(v0) = v1))
% 6.50/2.22 | (29) ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 6.50/2.22 | (30) ! [v0] : ( ~ (cC14(v0) = 0) | ? [v1] : (cC12(v1) = 0 & rR1(v0, v1) = 0))
% 6.50/2.22 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC10(v0) = v1) | ~ (rR1(v0, v2) = 0) | cC2(v2) = 0)
% 6.50/2.23 | (32) cC18(iV16560) = all_0_8_8
% 6.50/2.23 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC6(v2) = 0) | ~ (cC8(v0) = v1) | ? [v3] : ( ~ (v3 = 0) & rR1(v0, v2) = v3))
% 6.50/2.23 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cowlThing(v2) = v1) | ~ (cowlThing(v2) = v0))
% 6.50/2.23 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cTEST(v2) = v1) | ~ (cTEST(v2) = v0))
% 6.50/2.23 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC12(v2) = v1) | ~ (cC12(v2) = v0))
% 6.50/2.23 | (37) ! [v0] : ! [v1] : ( ~ (cC8(v0) = v1) | ? [v2] : ? [v3] : (cC16(v0) = v2 & cC14(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 6.50/2.23 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_string(v2) = v1) | ~ (xsd_string(v2) = v0))
% 6.50/2.23 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rR1(v3, v2) = v1) | ~ (rR1(v3, v2) = v0))
% 6.50/2.23 | (40) ! [v0] : ( ~ (cTEST(v0) = 0) | (cTOP(v0) = 0 & cC18(v0) = 0))
% 6.50/2.23 | (41) cowlThing(iV16561) = 0
% 6.50/2.23 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC2(v2) = v1) | ~ (cC2(v2) = v0))
% 6.50/2.23 | (43) cC14(iV16560) = all_0_6_6
% 6.50/2.23 | (44) ! [v0] : ( ~ (cTOP(v0) = 0) | ? [v1] : ? [v2] : (cC18(v0) = v2 & cC16(v0) = v1 & ( ~ (v1 = 0) | v2 = 0)))
% 6.50/2.23 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC6(v2) = v1) | ~ (cC6(v2) = v0))
% 6.50/2.23 | (46) ! [v0] : ( ~ (cC10(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & rR1(v0, v1) = 0 & cC2(v1) = v2))
% 6.50/2.23 | (47) ! [v0] : ( ~ (cC8(v0) = 0) | ? [v1] : (cC6(v1) = 0 & rR1(v0, v1) = 0))
% 6.50/2.23 | (48) ! [v0] : ! [v1] : (v1 = 0 | ~ (cC6(v0) = v1) | ? [v2] : ? [v3] : (cC4(v0) = v3 & cC2(v0) = v2 & (v3 = 0 | v2 = 0)))
% 6.50/2.23 | (49) cC16(iV16560) = all_0_7_7
% 6.50/2.23 | (50) cC8(iV16560) = all_0_5_5
% 6.50/2.23 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (xsd_integer(v2) = v1) | ~ (xsd_integer(v2) = v0))
% 6.50/2.23 | (52) ! [v0] : ( ~ (rR1(iV16562, v0) = 0) | cC2(v0) = 0)
% 6.50/2.23 | (53) cTOP(iV16560) = 0
% 6.50/2.23 | (54) ! [v0] : ( ~ (cC4(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & rR1(v0, v1) = 0 & cC2(v1) = v2))
% 6.50/2.23 | (55) ! [v0] : ! [v1] : (v1 = 0 | ~ (cC12(v0) = v1) | ? [v2] : ? [v3] : (cC10(v0) = v3 & cC2(v0) = v2 & (v3 = 0 | v2 = 0)))
% 6.50/2.23 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (cC4(v0) = v1) | ~ (rR1(v0, v2) = 0) | cC2(v2) = 0)
% 6.50/2.23 | (57) cC2(iV16562) = all_0_9_9
% 6.50/2.23 | (58) ~ (all_0_11_11 = 0)
% 6.50/2.23 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cTOP(v2) = v1) | ~ (cTOP(v2) = v0))
% 6.50/2.23 | (60) cC6(iV16561) = all_0_4_4
% 6.50/2.23 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cC16(v2) = v1) | ~ (cC16(v2) = v0))
% 6.50/2.23 | (62) cC2(iV16561) = all_0_11_11
% 6.50/2.23 | (63) ~ (all_0_9_9 = 0)
% 6.50/2.23 |
% 6.50/2.23 | Instantiating formula (40) with iV16560 and discharging atoms cTEST(iV16560) = 0, yields:
% 6.50/2.23 | (64) cTOP(iV16560) = 0 & cC18(iV16560) = 0
% 6.50/2.23 |
% 6.50/2.23 | Applying alpha-rule on (64) yields:
% 6.50/2.23 | (53) cTOP(iV16560) = 0
% 6.50/2.23 | (66) cC18(iV16560) = 0
% 6.50/2.23 |
% 6.50/2.23 | Instantiating formula (48) with all_0_4_4, iV16561 and discharging atoms cC6(iV16561) = all_0_4_4, yields:
% 6.50/2.23 | (67) all_0_4_4 = 0 | ? [v0] : ? [v1] : (cC4(iV16561) = v1 & cC2(iV16561) = v0 & (v1 = 0 | v0 = 0))
% 6.50/2.23 |
% 6.50/2.23 | Instantiating formula (44) with iV16560 and discharging atoms cTOP(iV16560) = 0, yields:
% 6.50/2.23 | (68) ? [v0] : ? [v1] : (cC18(iV16560) = v1 & cC16(iV16560) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 6.50/2.24 |
% 6.50/2.24 | Instantiating formula (7) with 0, iV16560 and discharging atoms cTOP(iV16560) = 0, yields:
% 6.50/2.24 | (69) ? [v0] : ? [v1] : (cC18(iV16560) = v0 & cC16(iV16560) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 6.50/2.24 |
% 6.50/2.24 | Instantiating formula (33) with iV16561, all_0_5_5, iV16560 and discharging atoms cC8(iV16560) = all_0_5_5, yields:
% 6.50/2.24 | (70) all_0_5_5 = 0 | ~ (cC6(iV16561) = 0) | ? [v0] : ( ~ (v0 = 0) & rR1(iV16560, iV16561) = v0)
% 6.50/2.24 |
% 6.50/2.24 | Instantiating formula (37) with all_0_5_5, iV16560 and discharging atoms cC8(iV16560) = all_0_5_5, yields:
% 6.50/2.24 | (71) ? [v0] : ? [v1] : (cC16(iV16560) = v0 & cC14(iV16560) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_0_5_5 = 0)))
% 6.50/2.24 |
% 6.50/2.24 | Instantiating formula (26) with iV16562, all_0_6_6, iV16560 and discharging atoms cC14(iV16560) = all_0_6_6, yields:
% 6.50/2.24 | (72) all_0_6_6 = 0 | ~ (cC12(iV16562) = 0) | ? [v0] : ( ~ (v0 = 0) & rR1(iV16560, iV16562) = v0)
% 6.50/2.24 |
% 6.50/2.24 | Instantiating formula (55) with all_0_3_3, iV16562 and discharging atoms cC12(iV16562) = all_0_3_3, yields:
% 6.50/2.24 | (73) all_0_3_3 = 0 | ? [v0] : ? [v1] : (cC10(iV16562) = v1 & cC2(iV16562) = v0 & (v1 = 0 | v0 = 0))
% 6.50/2.24 |
% 6.50/2.24 | Instantiating (71) with all_9_0_13, all_9_1_14 yields:
% 6.50/2.24 | (74) cC16(iV16560) = all_9_1_14 & cC14(iV16560) = all_9_0_13 & ( ~ (all_9_1_14 = 0) | (all_9_0_13 = 0 & all_0_5_5 = 0))
% 6.50/2.24 |
% 6.50/2.24 | Applying alpha-rule on (74) yields:
% 6.50/2.24 | (75) cC16(iV16560) = all_9_1_14
% 6.50/2.24 | (76) cC14(iV16560) = all_9_0_13
% 6.50/2.24 | (77) ~ (all_9_1_14 = 0) | (all_9_0_13 = 0 & all_0_5_5 = 0)
% 6.50/2.24 |
% 6.50/2.24 | Instantiating (69) with all_11_0_15, all_11_1_16 yields:
% 6.50/2.24 | (78) cC18(iV16560) = all_11_1_16 & cC16(iV16560) = all_11_0_15 & ( ~ (all_11_1_16 = 0) | all_11_0_15 = 0)
% 6.50/2.24 |
% 6.50/2.24 | Applying alpha-rule on (78) yields:
% 6.50/2.24 | (79) cC18(iV16560) = all_11_1_16
% 6.50/2.24 | (80) cC16(iV16560) = all_11_0_15
% 6.50/2.24 | (81) ~ (all_11_1_16 = 0) | all_11_0_15 = 0
% 6.50/2.24 |
% 6.50/2.24 | Instantiating (68) with all_13_0_17, all_13_1_18 yields:
% 6.50/2.24 | (82) cC18(iV16560) = all_13_0_17 & cC16(iV16560) = all_13_1_18 & ( ~ (all_13_1_18 = 0) | all_13_0_17 = 0)
% 6.50/2.24 |
% 6.50/2.24 | Applying alpha-rule on (82) yields:
% 6.50/2.24 | (83) cC18(iV16560) = all_13_0_17
% 6.50/2.24 | (84) cC16(iV16560) = all_13_1_18
% 6.50/2.24 | (85) ~ (all_13_1_18 = 0) | all_13_0_17 = 0
% 6.50/2.24 |
% 6.50/2.24 +-Applying beta-rule and splitting (67), into two cases.
% 6.50/2.24 |-Branch one:
% 6.50/2.24 | (86) all_0_4_4 = 0
% 6.50/2.24 |
% 6.50/2.24 | From (86) and (60) follows:
% 6.50/2.24 | (87) cC6(iV16561) = 0
% 6.50/2.24 |
% 6.50/2.24 +-Applying beta-rule and splitting (73), into two cases.
% 6.50/2.24 |-Branch one:
% 6.50/2.24 | (88) all_0_3_3 = 0
% 6.50/2.24 |
% 6.50/2.24 | From (88) and (11) follows:
% 6.50/2.24 | (89) cC12(iV16562) = 0
% 6.50/2.24 |
% 6.50/2.24 +-Applying beta-rule and splitting (72), into two cases.
% 6.50/2.24 |-Branch one:
% 6.50/2.24 | (90) ~ (cC12(iV16562) = 0)
% 6.50/2.24 |
% 6.50/2.24 | Using (89) and (90) yields:
% 6.50/2.24 | (91) $false
% 6.50/2.24 |
% 6.50/2.24 |-The branch is then unsatisfiable
% 6.50/2.24 |-Branch two:
% 6.50/2.24 | (89) cC12(iV16562) = 0
% 6.50/2.24 | (93) all_0_6_6 = 0 | ? [v0] : ( ~ (v0 = 0) & rR1(iV16560, iV16562) = v0)
% 6.50/2.24 |
% 6.50/2.24 +-Applying beta-rule and splitting (93), into two cases.
% 6.50/2.24 |-Branch one:
% 6.50/2.24 | (94) all_0_6_6 = 0
% 6.50/2.24 |
% 6.50/2.24 +-Applying beta-rule and splitting (70), into two cases.
% 6.50/2.24 |-Branch one:
% 6.50/2.24 | (95) ~ (cC6(iV16561) = 0)
% 6.50/2.24 |
% 6.50/2.24 | Using (87) and (95) yields:
% 6.50/2.24 | (91) $false
% 6.50/2.24 |
% 6.50/2.24 |-The branch is then unsatisfiable
% 6.50/2.24 |-Branch two:
% 6.50/2.24 | (87) cC6(iV16561) = 0
% 6.50/2.24 | (98) all_0_5_5 = 0 | ? [v0] : ( ~ (v0 = 0) & rR1(iV16560, iV16561) = v0)
% 6.50/2.24 |
% 6.50/2.24 +-Applying beta-rule and splitting (98), into two cases.
% 6.50/2.24 |-Branch one:
% 6.50/2.24 | (99) all_0_5_5 = 0
% 6.50/2.24 |
% 6.50/2.24 | Instantiating formula (3) with iV16560, all_11_1_16, all_0_8_8 and discharging atoms cC18(iV16560) = all_11_1_16, cC18(iV16560) = all_0_8_8, yields:
% 6.50/2.24 | (100) all_11_1_16 = all_0_8_8
% 6.50/2.24 |
% 6.50/2.24 | Instantiating formula (3) with iV16560, all_11_1_16, all_13_0_17 and discharging atoms cC18(iV16560) = all_13_0_17, cC18(iV16560) = all_11_1_16, yields:
% 6.50/2.25 | (101) all_13_0_17 = all_11_1_16
% 6.50/2.25 |
% 6.50/2.25 | Instantiating formula (3) with iV16560, 0, all_13_0_17 and discharging atoms cC18(iV16560) = all_13_0_17, cC18(iV16560) = 0, yields:
% 6.50/2.25 | (102) all_13_0_17 = 0
% 6.50/2.25 |
% 6.50/2.25 | Instantiating formula (61) with iV16560, all_13_1_18, all_0_7_7 and discharging atoms cC16(iV16560) = all_13_1_18, cC16(iV16560) = all_0_7_7, yields:
% 6.50/2.25 | (103) all_13_1_18 = all_0_7_7
% 6.50/2.25 |
% 6.50/2.25 | Instantiating formula (61) with iV16560, all_11_0_15, all_13_1_18 and discharging atoms cC16(iV16560) = all_13_1_18, cC16(iV16560) = all_11_0_15, yields:
% 6.50/2.25 | (104) all_13_1_18 = all_11_0_15
% 6.50/2.25 |
% 6.50/2.25 | Instantiating formula (61) with iV16560, all_9_1_14, all_11_0_15 and discharging atoms cC16(iV16560) = all_11_0_15, cC16(iV16560) = all_9_1_14, yields:
% 6.50/2.25 | (105) all_11_0_15 = all_9_1_14
% 6.50/2.25 |
% 6.50/2.25 | Combining equations (101,102) yields a new equation:
% 6.50/2.25 | (106) all_11_1_16 = 0
% 6.50/2.25 |
% 6.50/2.25 | Simplifying 106 yields:
% 6.50/2.25 | (107) all_11_1_16 = 0
% 6.50/2.25 |
% 6.50/2.25 | Combining equations (104,103) yields a new equation:
% 6.50/2.25 | (108) all_11_0_15 = all_0_7_7
% 6.50/2.25 |
% 6.50/2.25 | Simplifying 108 yields:
% 6.50/2.25 | (109) all_11_0_15 = all_0_7_7
% 6.50/2.25 |
% 6.50/2.25 | Combining equations (109,105) yields a new equation:
% 6.50/2.25 | (110) all_9_1_14 = all_0_7_7
% 6.50/2.25 |
% 6.50/2.25 | Combining equations (100,107) yields a new equation:
% 6.50/2.25 | (111) all_0_8_8 = 0
% 6.50/2.25 |
% 6.50/2.25 | Simplifying 111 yields:
% 6.50/2.25 | (112) all_0_8_8 = 0
% 6.50/2.25 |
% 6.50/2.25 | Combining equations (110,105) yields a new equation:
% 6.50/2.25 | (109) all_11_0_15 = all_0_7_7
% 6.50/2.25 |
% 6.50/2.25 +-Applying beta-rule and splitting (81), into two cases.
% 6.50/2.25 |-Branch one:
% 6.50/2.25 | (114) ~ (all_11_1_16 = 0)
% 6.50/2.25 |
% 6.50/2.25 | Equations (107) can reduce 114 to:
% 6.50/2.25 | (115) $false
% 6.50/2.25 |
% 6.50/2.25 |-The branch is then unsatisfiable
% 6.50/2.25 |-Branch two:
% 6.50/2.25 | (107) all_11_1_16 = 0
% 6.50/2.25 | (117) all_11_0_15 = 0
% 6.50/2.25 |
% 6.50/2.25 | Combining equations (117,109) yields a new equation:
% 6.50/2.25 | (118) all_0_7_7 = 0
% 6.50/2.25 |
% 6.50/2.25 +-Applying beta-rule and splitting (29), into two cases.
% 6.50/2.25 |-Branch one:
% 6.50/2.25 | (119) ~ (all_0_3_3 = 0)
% 6.50/2.25 |
% 6.50/2.25 | Equations (88) can reduce 119 to:
% 6.50/2.25 | (115) $false
% 6.50/2.25 |
% 6.50/2.25 |-The branch is then unsatisfiable
% 6.50/2.25 |-Branch two:
% 6.50/2.25 | (88) all_0_3_3 = 0
% 6.77/2.25 | (122) ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 6.77/2.25 |
% 6.77/2.25 +-Applying beta-rule and splitting (122), into two cases.
% 6.77/2.25 |-Branch one:
% 6.77/2.25 | (123) ~ (all_0_4_4 = 0)
% 6.77/2.25 |
% 6.77/2.25 | Equations (86) can reduce 123 to:
% 6.77/2.25 | (115) $false
% 6.77/2.25 |
% 6.77/2.25 |-The branch is then unsatisfiable
% 6.77/2.25 |-Branch two:
% 6.77/2.25 | (86) all_0_4_4 = 0
% 6.77/2.25 | (126) ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 6.77/2.25 |
% 6.77/2.25 +-Applying beta-rule and splitting (126), into two cases.
% 6.77/2.25 |-Branch one:
% 6.77/2.25 | (127) ~ (all_0_5_5 = 0)
% 6.77/2.25 |
% 6.77/2.25 | Equations (99) can reduce 127 to:
% 6.77/2.25 | (115) $false
% 6.77/2.25 |
% 6.77/2.25 |-The branch is then unsatisfiable
% 6.77/2.25 |-Branch two:
% 6.77/2.25 | (99) all_0_5_5 = 0
% 6.77/2.25 | (130) ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 6.77/2.25 |
% 6.77/2.25 +-Applying beta-rule and splitting (130), into two cases.
% 6.77/2.25 |-Branch one:
% 6.77/2.25 | (131) ~ (all_0_6_6 = 0)
% 6.77/2.25 |
% 6.77/2.25 | Equations (94) can reduce 131 to:
% 6.77/2.25 | (115) $false
% 6.77/2.25 |
% 6.77/2.25 |-The branch is then unsatisfiable
% 6.77/2.25 |-Branch two:
% 6.77/2.25 | (94) all_0_6_6 = 0
% 6.77/2.25 | (134) ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 6.77/2.25 |
% 6.77/2.25 +-Applying beta-rule and splitting (134), into two cases.
% 6.77/2.25 |-Branch one:
% 6.77/2.25 | (135) ~ (all_0_7_7 = 0)
% 6.77/2.26 |
% 6.77/2.26 | Equations (118) can reduce 135 to:
% 6.77/2.26 | (115) $false
% 6.77/2.26 |
% 6.77/2.26 |-The branch is then unsatisfiable
% 6.77/2.26 |-Branch two:
% 6.77/2.26 | (118) all_0_7_7 = 0
% 6.77/2.26 | (138) ~ (all_0_8_8 = 0) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 6.77/2.26 |
% 6.77/2.26 +-Applying beta-rule and splitting (138), into two cases.
% 6.77/2.26 |-Branch one:
% 6.77/2.26 | (139) ~ (all_0_8_8 = 0)
% 6.77/2.26 |
% 6.77/2.26 | Equations (112) can reduce 139 to:
% 6.77/2.26 | (115) $false
% 6.77/2.26 |
% 6.77/2.26 |-The branch is then unsatisfiable
% 6.77/2.26 |-Branch two:
% 6.77/2.26 | (112) all_0_8_8 = 0
% 6.77/2.26 | (142) (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 6.77/2.26 |
% 6.77/2.26 +-Applying beta-rule and splitting (142), into two cases.
% 6.77/2.26 |-Branch one:
% 6.77/2.26 | (143) xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)))
% 6.77/2.26 |
% 6.77/2.26 | Applying alpha-rule on (143) yields:
% 6.77/2.26 | (144) xsd_string(all_0_2_2) = all_0_1_1
% 6.77/2.26 | (145) xsd_integer(all_0_2_2) = all_0_0_0
% 6.77/2.26 | (146) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0))
% 6.77/2.26 |
% 6.77/2.26 | Instantiating formula (8) with all_0_2_2 yields:
% 6.77/2.26 | (147) ~ (xsd_string(all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 6.77/2.26 |
% 6.77/2.26 | Instantiating formula (25) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields:
% 6.77/2.26 | (148) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0
% 6.77/2.26 |
% 6.77/2.26 +-Applying beta-rule and splitting (146), into two cases.
% 6.77/2.26 |-Branch one:
% 6.77/2.26 | (149) all_0_0_0 = 0 & all_0_1_1 = 0
% 6.77/2.26 |
% 6.77/2.26 | Applying alpha-rule on (149) yields:
% 6.77/2.26 | (150) all_0_0_0 = 0
% 6.77/2.26 | (151) all_0_1_1 = 0
% 6.77/2.26 |
% 6.77/2.26 | From (151) and (144) follows:
% 6.77/2.26 | (152) xsd_string(all_0_2_2) = 0
% 6.77/2.26 |
% 6.77/2.26 | From (150) and (145) follows:
% 6.77/2.26 | (153) xsd_integer(all_0_2_2) = 0
% 6.77/2.26 |
% 6.77/2.26 +-Applying beta-rule and splitting (147), into two cases.
% 6.77/2.26 |-Branch one:
% 6.77/2.26 | (154) ~ (xsd_string(all_0_2_2) = 0)
% 6.77/2.26 |
% 6.77/2.26 | Using (152) and (154) yields:
% 6.77/2.26 | (91) $false
% 6.77/2.26 |
% 6.77/2.26 |-The branch is then unsatisfiable
% 6.77/2.26 |-Branch two:
% 6.77/2.26 | (152) xsd_string(all_0_2_2) = 0
% 6.77/2.26 | (157) ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 6.77/2.26 |
% 6.77/2.26 | Instantiating (157) with all_265_0_27 yields:
% 6.77/2.26 | (158) ~ (all_265_0_27 = 0) & xsd_integer(all_0_2_2) = all_265_0_27
% 6.77/2.26 |
% 6.77/2.26 | Applying alpha-rule on (158) yields:
% 6.77/2.26 | (159) ~ (all_265_0_27 = 0)
% 6.77/2.26 | (160) xsd_integer(all_0_2_2) = all_265_0_27
% 6.77/2.26 |
% 6.77/2.26 | Instantiating formula (51) with all_0_2_2, 0, all_265_0_27 and discharging atoms xsd_integer(all_0_2_2) = all_265_0_27, xsd_integer(all_0_2_2) = 0, yields:
% 6.77/2.26 | (161) all_265_0_27 = 0
% 6.77/2.26 |
% 6.77/2.26 | Equations (161) can reduce 159 to:
% 6.77/2.26 | (115) $false
% 6.77/2.26 |
% 6.77/2.26 |-The branch is then unsatisfiable
% 6.77/2.26 |-Branch two:
% 6.77/2.26 | (163) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0)
% 6.77/2.26 |
% 6.77/2.26 | Applying alpha-rule on (163) yields:
% 6.77/2.26 | (164) ~ (all_0_0_0 = 0)
% 6.77/2.26 | (165) ~ (all_0_1_1 = 0)
% 6.77/2.26 |
% 6.77/2.26 +-Applying beta-rule and splitting (148), into two cases.
% 6.77/2.26 |-Branch one:
% 6.77/2.26 | (153) xsd_integer(all_0_2_2) = 0
% 6.77/2.26 |
% 6.77/2.26 | Instantiating formula (51) with all_0_2_2, 0, all_0_0_0 and discharging atoms xsd_integer(all_0_2_2) = all_0_0_0, xsd_integer(all_0_2_2) = 0, yields:
% 6.77/2.27 | (150) all_0_0_0 = 0
% 6.77/2.27 |
% 6.77/2.27 | Equations (150) can reduce 164 to:
% 6.77/2.27 | (115) $false
% 6.77/2.27 |
% 6.77/2.27 |-The branch is then unsatisfiable
% 6.77/2.27 |-Branch two:
% 6.77/2.27 | (169) ~ (xsd_integer(all_0_2_2) = 0)
% 6.77/2.27 | (151) all_0_1_1 = 0
% 6.77/2.27 |
% 6.77/2.27 | Equations (151) can reduce 165 to:
% 6.77/2.27 | (115) $false
% 6.77/2.27 |
% 6.77/2.27 |-The branch is then unsatisfiable
% 6.77/2.27 |-Branch two:
% 6.77/2.27 | (172) cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)
% 6.77/2.27 |
% 6.77/2.27 | Applying alpha-rule on (172) yields:
% 6.77/2.27 | (173) cowlNothing(all_0_2_2) = all_0_0_0
% 6.77/2.27 | (174) cowlThing(all_0_2_2) = all_0_1_1
% 6.77/2.27 | (175) ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 6.77/2.27 |
% 6.77/2.27 | Instantiating formula (10) with all_0_2_2 yields:
% 6.77/2.27 | (176) ~ (cowlNothing(all_0_2_2) = 0)
% 6.77/2.27 |
% 6.77/2.27 | Instantiating formula (28) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields:
% 6.77/2.27 | (151) all_0_1_1 = 0
% 6.77/2.27 |
% 6.77/2.27 +-Applying beta-rule and splitting (175), into two cases.
% 6.77/2.27 |-Branch one:
% 6.77/2.27 | (165) ~ (all_0_1_1 = 0)
% 6.77/2.27 |
% 6.77/2.27 | Equations (151) can reduce 165 to:
% 6.77/2.27 | (115) $false
% 6.77/2.27 |
% 6.77/2.27 |-The branch is then unsatisfiable
% 6.77/2.27 |-Branch two:
% 6.77/2.27 | (151) all_0_1_1 = 0
% 6.77/2.27 | (150) all_0_0_0 = 0
% 6.77/2.27 |
% 6.77/2.27 | From (150) and (173) follows:
% 6.77/2.27 | (182) cowlNothing(all_0_2_2) = 0
% 6.77/2.27 |
% 6.77/2.27 | Using (182) and (176) yields:
% 6.77/2.27 | (91) $false
% 6.77/2.27 |
% 6.77/2.27 |-The branch is then unsatisfiable
% 6.77/2.27 |-Branch two:
% 6.77/2.27 | (127) ~ (all_0_5_5 = 0)
% 6.77/2.27 | (185) ? [v0] : ( ~ (v0 = 0) & rR1(iV16560, iV16561) = v0)
% 6.77/2.27 |
% 6.77/2.27 | Instantiating (185) with all_60_0_28 yields:
% 6.77/2.27 | (186) ~ (all_60_0_28 = 0) & rR1(iV16560, iV16561) = all_60_0_28
% 6.77/2.27 |
% 6.77/2.27 | Applying alpha-rule on (186) yields:
% 6.77/2.27 | (187) ~ (all_60_0_28 = 0)
% 6.77/2.27 | (188) rR1(iV16560, iV16561) = all_60_0_28
% 6.77/2.27 |
% 6.77/2.27 | Instantiating formula (39) with iV16560, iV16561, all_60_0_28, 0 and discharging atoms rR1(iV16560, iV16561) = all_60_0_28, rR1(iV16560, iV16561) = 0, yields:
% 6.77/2.27 | (189) all_60_0_28 = 0
% 6.77/2.27 |
% 6.77/2.27 | Equations (189) can reduce 187 to:
% 6.77/2.27 | (115) $false
% 6.77/2.27 |
% 6.77/2.27 |-The branch is then unsatisfiable
% 6.77/2.27 |-Branch two:
% 6.77/2.27 | (131) ~ (all_0_6_6 = 0)
% 6.77/2.27 | (192) ? [v0] : ( ~ (v0 = 0) & rR1(iV16560, iV16562) = v0)
% 6.77/2.27 |
% 6.77/2.27 | Instantiating (192) with all_43_0_29 yields:
% 6.77/2.27 | (193) ~ (all_43_0_29 = 0) & rR1(iV16560, iV16562) = all_43_0_29
% 6.77/2.27 |
% 6.77/2.27 | Applying alpha-rule on (193) yields:
% 6.77/2.27 | (194) ~ (all_43_0_29 = 0)
% 6.77/2.27 | (195) rR1(iV16560, iV16562) = all_43_0_29
% 6.77/2.27 |
% 6.77/2.27 | Instantiating formula (39) with iV16560, iV16562, all_43_0_29, 0 and discharging atoms rR1(iV16560, iV16562) = all_43_0_29, rR1(iV16560, iV16562) = 0, yields:
% 6.77/2.27 | (196) all_43_0_29 = 0
% 6.77/2.27 |
% 6.77/2.27 | Equations (196) can reduce 194 to:
% 6.77/2.27 | (115) $false
% 6.77/2.27 |
% 6.77/2.27 |-The branch is then unsatisfiable
% 6.77/2.27 |-Branch two:
% 6.77/2.27 | (119) ~ (all_0_3_3 = 0)
% 6.77/2.27 | (199) ? [v0] : ? [v1] : (cC10(iV16562) = v1 & cC2(iV16562) = v0 & (v1 = 0 | v0 = 0))
% 6.77/2.27 |
% 6.77/2.27 | Instantiating (199) with all_35_0_31, all_35_1_32 yields:
% 6.77/2.28 | (200) cC10(iV16562) = all_35_0_31 & cC2(iV16562) = all_35_1_32 & (all_35_0_31 = 0 | all_35_1_32 = 0)
% 6.77/2.28 |
% 6.77/2.28 | Applying alpha-rule on (200) yields:
% 6.77/2.28 | (201) cC10(iV16562) = all_35_0_31
% 6.77/2.28 | (202) cC2(iV16562) = all_35_1_32
% 6.77/2.28 | (203) all_35_0_31 = 0 | all_35_1_32 = 0
% 6.77/2.28 |
% 6.77/2.28 | Instantiating formula (19) with iV16562, all_35_0_31, all_0_10_10 and discharging atoms cC10(iV16562) = all_35_0_31, cC10(iV16562) = all_0_10_10, yields:
% 6.77/2.28 | (204) all_35_0_31 = all_0_10_10
% 6.77/2.28 |
% 6.77/2.28 | Instantiating formula (42) with iV16562, all_35_1_32, all_0_9_9 and discharging atoms cC2(iV16562) = all_35_1_32, cC2(iV16562) = all_0_9_9, yields:
% 6.77/2.28 | (205) all_35_1_32 = all_0_9_9
% 6.77/2.28 |
% 6.77/2.28 +-Applying beta-rule and splitting (203), into two cases.
% 6.77/2.28 |-Branch one:
% 6.77/2.28 | (206) all_35_0_31 = 0
% 6.77/2.28 |
% 6.77/2.28 | Combining equations (206,204) yields a new equation:
% 6.77/2.28 | (207) all_0_10_10 = 0
% 6.77/2.28 |
% 6.77/2.28 | Equations (207) can reduce 6 to:
% 6.77/2.28 | (115) $false
% 6.77/2.28 |
% 6.77/2.28 |-The branch is then unsatisfiable
% 6.77/2.28 |-Branch two:
% 6.77/2.28 | (209) ~ (all_35_0_31 = 0)
% 6.77/2.28 | (210) all_35_1_32 = 0
% 6.77/2.28 |
% 6.77/2.28 | Combining equations (210,205) yields a new equation:
% 6.77/2.28 | (211) all_0_9_9 = 0
% 6.77/2.28 |
% 6.77/2.28 | Equations (211) can reduce 63 to:
% 6.77/2.28 | (115) $false
% 6.77/2.28 |
% 6.77/2.28 |-The branch is then unsatisfiable
% 6.77/2.28 |-Branch two:
% 6.77/2.28 | (123) ~ (all_0_4_4 = 0)
% 6.77/2.28 | (214) ? [v0] : ? [v1] : (cC4(iV16561) = v1 & cC2(iV16561) = v0 & (v1 = 0 | v0 = 0))
% 6.77/2.28 |
% 6.77/2.28 | Instantiating (214) with all_23_0_34, all_23_1_35 yields:
% 6.77/2.28 | (215) cC4(iV16561) = all_23_0_34 & cC2(iV16561) = all_23_1_35 & (all_23_0_34 = 0 | all_23_1_35 = 0)
% 6.77/2.28 |
% 6.77/2.28 | Applying alpha-rule on (215) yields:
% 6.77/2.28 | (216) cC4(iV16561) = all_23_0_34
% 6.77/2.28 | (217) cC2(iV16561) = all_23_1_35
% 6.77/2.28 | (218) all_23_0_34 = 0 | all_23_1_35 = 0
% 6.77/2.28 |
% 6.77/2.28 | Instantiating formula (15) with iV16561, all_23_0_34, all_0_12_12 and discharging atoms cC4(iV16561) = all_23_0_34, cC4(iV16561) = all_0_12_12, yields:
% 6.77/2.28 | (219) all_23_0_34 = all_0_12_12
% 6.77/2.28 |
% 6.77/2.28 | Instantiating formula (42) with iV16561, all_23_1_35, all_0_11_11 and discharging atoms cC2(iV16561) = all_23_1_35, cC2(iV16561) = all_0_11_11, yields:
% 6.77/2.28 | (220) all_23_1_35 = all_0_11_11
% 6.77/2.28 |
% 6.77/2.28 +-Applying beta-rule and splitting (218), into two cases.
% 6.77/2.28 |-Branch one:
% 6.77/2.28 | (221) all_23_0_34 = 0
% 6.77/2.28 |
% 6.77/2.28 | Combining equations (221,219) yields a new equation:
% 6.77/2.28 | (222) all_0_12_12 = 0
% 6.77/2.28 |
% 6.77/2.28 | Equations (222) can reduce 20 to:
% 6.77/2.28 | (115) $false
% 6.77/2.28 |
% 6.77/2.28 |-The branch is then unsatisfiable
% 6.77/2.28 |-Branch two:
% 6.77/2.28 | (224) ~ (all_23_0_34 = 0)
% 6.77/2.28 | (225) all_23_1_35 = 0
% 6.77/2.28 |
% 6.77/2.28 | Combining equations (225,220) yields a new equation:
% 6.77/2.28 | (226) all_0_11_11 = 0
% 6.77/2.28 |
% 6.77/2.28 | Equations (226) can reduce 58 to:
% 6.77/2.28 | (115) $false
% 6.77/2.28 |
% 6.77/2.28 |-The branch is then unsatisfiable
% 6.77/2.28 % SZS output end Proof for theBenchmark
% 6.77/2.28
% 6.77/2.28 1643ms
%------------------------------------------------------------------------------