TSTP Solution File: KLE066+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 01:51:13 EDT 2022
% Result : Theorem 27.69s 8.71s
% Output : Proof 28.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 15:14:02 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.63/0.62 ____ _
% 0.63/0.62 ___ / __ \_____(_)___ ________ __________
% 0.63/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.62
% 0.63/0.62 A Theorem Prover for First-Order Logic
% 0.63/0.62 (ePrincess v.1.0)
% 0.63/0.62
% 0.63/0.62 (c) Philipp Rümmer, 2009-2015
% 0.63/0.62 (c) Peter Backeman, 2014-2015
% 0.63/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.62 Bug reports to peter@backeman.se
% 0.63/0.62
% 0.63/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.62
% 0.63/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.98 Prover 0: Preprocessing ...
% 2.35/1.31 Prover 0: Constructing countermodel ...
% 18.04/5.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.04/5.99 Prover 1: Preprocessing ...
% 18.24/6.08 Prover 1: Constructing countermodel ...
% 26.69/8.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 27.04/8.58 Prover 2: Preprocessing ...
% 27.04/8.65 Prover 2: Warning: ignoring some quantifiers
% 27.04/8.66 Prover 2: Constructing countermodel ...
% 27.62/8.71 Prover 2: proved (153ms)
% 27.69/8.71 Prover 0: stopped
% 27.69/8.71 Prover 1: stopped
% 27.69/8.71
% 27.69/8.71 No countermodel exists, formula is valid
% 27.69/8.71 % SZS status Theorem for theBenchmark
% 27.69/8.71
% 27.69/8.71 Generating proof ... Warning: ignoring some quantifiers
% 28.15/8.88 found it (size 37)
% 28.15/8.88
% 28.15/8.88 % SZS output start Proof for theBenchmark
% 28.15/8.89 Assumed formulas after preprocessing and simplification:
% 28.15/8.89 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = zero) & domain(v1) = v2 & domain(zero) = zero & multiplication(v0, v2) = zero & multiplication(v0, v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v5, v6) = v8) | ~ (multiplication(v4, v6) = v7) | ~ (addition(v7, v8) = v9) | ? [v10] : (multiplication(v10, v6) = v9 & addition(v4, v5) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v4, v6) = v8) | ~ (multiplication(v4, v5) = v7) | ~ (addition(v7, v8) = v9) | ? [v10] : (multiplication(v4, v10) = v9 & addition(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (domain(v5) = v7) | ~ (domain(v4) = v6) | ~ (addition(v6, v7) = v8) | ? [v9] : (domain(v9) = v8 & addition(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v7, v6) = v8) | ~ (multiplication(v4, v5) = v7) | ? [v9] : (multiplication(v5, v6) = v9 & multiplication(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v7, v6) = v8) | ~ (addition(v4, v5) = v7) | ? [v9] : ? [v10] : (multiplication(v5, v6) = v10 & multiplication(v4, v6) = v9 & addition(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v5, v6) = v7) | ~ (multiplication(v4, v7) = v8) | ? [v9] : (multiplication(v9, v6) = v8 & multiplication(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v4, v7) = v8) | ~ (addition(v5, v6) = v7) | ? [v9] : ? [v10] : (multiplication(v4, v6) = v10 & multiplication(v4, v5) = v9 & addition(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v7, v4) = v8) | ~ (addition(v6, v5) = v7) | ? [v9] : (addition(v6, v9) = v8 & addition(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | ~ (addition(v5, v4) = v7) | ? [v9] : (addition(v9, v4) = v8 & addition(v6, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (leq(v7, v6) = v5) | ~ (leq(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (multiplication(v7, v6) = v5) | ~ (multiplication(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (addition(v7, v6) = v5) | ~ (addition(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (domain(v5) = v6) | ~ (multiplication(v4, v6) = v7) | ? [v8] : ? [v9] : (domain(v8) = v9 & domain(v7) = v9 & multiplication(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & leq(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (leq(v4, v5) = v6) | ? [v7] : ( ~ (v7 = v5) & addition(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (domain(v6) = v5) | ~ (domain(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (domain(v9) = v7 & domain(v6) = v7 & domain(v5) = v8 & multiplication(v4, v8) = v9)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v5, v4) = v6) | addition(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v4, v5) = v6) | addition(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (domain(v6) = v7 & domain(v5) = v9 & domain(v4) = v8 & addition(v8, v9) = v7)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (multiplication(v4, one) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (multiplication(one, v4) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (addition(v4, v4) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (addition(v4, zero) = v5)) & ! [v4] : ! [v5] : (v5 = zero | ~ (multiplication(v4, zero) = v5)) & ! [v4] : ! [v5] : (v5 = zero | ~ (multiplication(zero, v4) = v5)) & ! [v4] : ! [v5] : ( ~ (domain(v4) = v5) | addition(v5, one) = one) & ! [v4] : ! [v5] : ( ~ (domain(v4) = v5) | ? [v6] : (multiplication(v5, v4) = v6 & addition(v4, v6) = v6)) & ! [v4] : ! [v5] : ( ~ (leq(v4, v5) = 0) | addition(v4, v5) = v5) & ! [v4] : ! [v5] : ( ~ (addition(v4, v5) = v5) | leq(v4, v5) = 0) & ? [v4] : ? [v5] : ? [v6] : leq(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : multiplication(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : addition(v5, v4) = v6 & ? [v4] : ? [v5] : domain(v4) = v5)
% 28.54/8.92 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 28.54/8.92 | (1) ~ (all_0_0_0 = zero) & domain(all_0_2_2) = all_0_1_1 & domain(zero) = zero & multiplication(all_0_3_3, all_0_1_1) = zero & multiplication(all_0_3_3, all_0_2_2) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) & ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) & ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 & ? [v0] : ? [v1] : domain(v0) = v1
% 28.54/8.93 |
% 28.54/8.93 | Applying alpha-rule on (1) yields:
% 28.54/8.93 | (2) domain(all_0_2_2) = all_0_1_1
% 28.54/8.93 | (3) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 28.54/8.93 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 28.54/8.93 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 28.54/8.93 | (6) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 28.54/8.93 | (7) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 28.54/8.93 | (8) multiplication(all_0_3_3, all_0_1_1) = zero
% 28.54/8.93 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6))
% 28.54/8.93 | (10) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2))
% 28.54/8.93 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 28.54/8.93 | (12) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 28.54/8.93 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 28.54/8.93 | (14) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2
% 28.54/8.93 | (15) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 28.54/8.93 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4))
% 28.54/8.93 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 28.54/8.93 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 28.54/8.93 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 28.54/8.93 | (20) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2
% 28.54/8.93 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 28.54/8.93 | (22) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2
% 28.54/8.93 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 28.54/8.93 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4))
% 28.54/8.93 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 28.54/8.93 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 28.54/8.93 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 28.54/8.94 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 28.54/8.94 | (29) multiplication(all_0_3_3, all_0_2_2) = all_0_0_0
% 28.54/8.94 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 28.54/8.94 | (31) ~ (all_0_0_0 = zero)
% 28.54/8.94 | (32) ? [v0] : ? [v1] : domain(v0) = v1
% 28.54/8.94 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 28.54/8.94 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 28.54/8.94 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 28.54/8.94 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 28.54/8.94 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 28.54/8.94 | (38) domain(zero) = zero
% 28.54/8.94 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 28.54/8.94 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 28.54/8.94 |
% 28.54/8.94 | Instantiating formula (10) with zero, zero and discharging atoms domain(zero) = zero, yields:
% 28.54/8.94 | (41) ? [v0] : (multiplication(zero, zero) = v0 & addition(zero, v0) = v0)
% 28.54/8.94 |
% 28.54/8.94 | Instantiating formula (23) with zero, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms domain(all_0_2_2) = all_0_1_1, multiplication(all_0_3_3, all_0_1_1) = zero, yields:
% 28.54/8.94 | (42) ? [v0] : ? [v1] : (domain(v0) = v1 & domain(zero) = v1 & multiplication(all_0_3_3, all_0_2_2) = v0)
% 28.54/8.94 |
% 28.54/8.94 | Instantiating formula (5) with zero, all_0_1_1, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_1_1) = zero, yields:
% 28.54/8.94 | (43) ? [v0] : ? [v1] : ? [v2] : (domain(v2) = v0 & domain(all_0_1_1) = v1 & domain(zero) = v0 & multiplication(all_0_3_3, v1) = v2)
% 28.54/8.94 |
% 28.54/8.94 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 28.54/8.94 | (44) ? [v0] : ? [v1] : ? [v2] : (domain(v2) = v0 & domain(all_0_0_0) = v0 & domain(all_0_2_2) = v1 & multiplication(all_0_3_3, v1) = v2)
% 28.54/8.94 |
% 28.54/8.94 | Instantiating (44) with all_17_0_15, all_17_1_16, all_17_2_17 yields:
% 28.54/8.94 | (45) domain(all_17_0_15) = all_17_2_17 & domain(all_0_0_0) = all_17_2_17 & domain(all_0_2_2) = all_17_1_16 & multiplication(all_0_3_3, all_17_1_16) = all_17_0_15
% 28.54/8.94 |
% 28.54/8.94 | Applying alpha-rule on (45) yields:
% 28.54/8.94 | (46) domain(all_17_0_15) = all_17_2_17
% 28.54/8.94 | (47) domain(all_0_0_0) = all_17_2_17
% 28.54/8.94 | (48) domain(all_0_2_2) = all_17_1_16
% 28.54/8.94 | (49) multiplication(all_0_3_3, all_17_1_16) = all_17_0_15
% 28.54/8.94 |
% 28.54/8.94 | Instantiating (43) with all_19_0_18, all_19_1_19, all_19_2_20 yields:
% 28.54/8.94 | (50) domain(all_19_0_18) = all_19_2_20 & domain(all_0_1_1) = all_19_1_19 & domain(zero) = all_19_2_20 & multiplication(all_0_3_3, all_19_1_19) = all_19_0_18
% 28.54/8.94 |
% 28.54/8.94 | Applying alpha-rule on (50) yields:
% 28.54/8.94 | (51) domain(all_19_0_18) = all_19_2_20
% 28.54/8.94 | (52) domain(all_0_1_1) = all_19_1_19
% 28.54/8.94 | (53) domain(zero) = all_19_2_20
% 28.54/8.94 | (54) multiplication(all_0_3_3, all_19_1_19) = all_19_0_18
% 28.54/8.94 |
% 28.54/8.94 | Instantiating (42) with all_21_0_21, all_21_1_22 yields:
% 28.54/8.94 | (55) domain(all_21_1_22) = all_21_0_21 & domain(zero) = all_21_0_21 & multiplication(all_0_3_3, all_0_2_2) = all_21_1_22
% 28.54/8.94 |
% 28.54/8.94 | Applying alpha-rule on (55) yields:
% 28.54/8.94 | (56) domain(all_21_1_22) = all_21_0_21
% 28.54/8.94 | (57) domain(zero) = all_21_0_21
% 28.54/8.94 | (58) multiplication(all_0_3_3, all_0_2_2) = all_21_1_22
% 28.54/8.94 |
% 28.54/8.94 | Instantiating (41) with all_25_0_24 yields:
% 28.54/8.94 | (59) multiplication(zero, zero) = all_25_0_24 & addition(zero, all_25_0_24) = all_25_0_24
% 28.54/8.94 |
% 28.54/8.94 | Applying alpha-rule on (59) yields:
% 28.54/8.94 | (60) multiplication(zero, zero) = all_25_0_24
% 28.54/8.94 | (61) addition(zero, all_25_0_24) = all_25_0_24
% 28.54/8.94 |
% 28.54/8.94 | Instantiating formula (34) with zero, all_21_0_21, zero and discharging atoms domain(zero) = all_21_0_21, domain(zero) = zero, yields:
% 28.54/8.94 | (62) all_21_0_21 = zero
% 28.54/8.94 |
% 28.54/8.94 | Instantiating formula (34) with zero, all_19_2_20, all_21_0_21 and discharging atoms domain(zero) = all_21_0_21, domain(zero) = all_19_2_20, yields:
% 28.54/8.94 | (63) all_21_0_21 = all_19_2_20
% 28.54/8.94 |
% 28.54/8.94 | Instantiating formula (35) with all_0_3_3, all_0_2_2, all_21_1_22, all_0_0_0 and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_21_1_22, multiplication(all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 28.54/8.94 | (64) all_21_1_22 = all_0_0_0
% 28.54/8.94 |
% 28.54/8.95 | Instantiating formula (3) with all_25_0_24, zero and discharging atoms multiplication(zero, zero) = all_25_0_24, yields:
% 28.54/8.95 | (65) all_25_0_24 = zero
% 28.54/8.95 |
% 28.54/8.95 | Combining equations (62,63) yields a new equation:
% 28.54/8.95 | (66) all_19_2_20 = zero
% 28.54/8.95 |
% 28.54/8.95 | Combining equations (66,63) yields a new equation:
% 28.54/8.95 | (62) all_21_0_21 = zero
% 28.54/8.95 |
% 28.54/8.95 | From (64)(62) and (56) follows:
% 28.54/8.95 | (68) domain(all_0_0_0) = zero
% 28.54/8.95 |
% 28.54/8.95 | From (65) and (60) follows:
% 28.54/8.95 | (69) multiplication(zero, zero) = zero
% 28.54/8.95 |
% 28.54/8.95 | Instantiating formula (34) with all_0_0_0, zero, all_17_2_17 and discharging atoms domain(all_0_0_0) = all_17_2_17, domain(all_0_0_0) = zero, yields:
% 28.54/8.95 | (70) all_17_2_17 = zero
% 28.54/8.95 |
% 28.54/8.95 | From (70) and (47) follows:
% 28.54/8.95 | (68) domain(all_0_0_0) = zero
% 28.54/8.95 |
% 28.54/8.95 | Instantiating formula (10) with zero, all_0_0_0 and discharging atoms domain(all_0_0_0) = zero, yields:
% 28.54/8.95 | (72) ? [v0] : (multiplication(zero, all_0_0_0) = v0 & addition(all_0_0_0, v0) = v0)
% 28.54/8.95 |
% 28.54/8.95 | Instantiating formula (23) with zero, zero, all_0_0_0, zero and discharging atoms domain(all_0_0_0) = zero, multiplication(zero, zero) = zero, yields:
% 28.54/8.95 | (73) ? [v0] : ? [v1] : (domain(v0) = v1 & domain(zero) = v1 & multiplication(zero, all_0_0_0) = v0)
% 28.54/8.95 |
% 28.54/8.95 | Instantiating (72) with all_63_0_40 yields:
% 28.54/8.95 | (74) multiplication(zero, all_0_0_0) = all_63_0_40 & addition(all_0_0_0, all_63_0_40) = all_63_0_40
% 28.54/8.95 |
% 28.54/8.95 | Applying alpha-rule on (74) yields:
% 28.54/8.95 | (75) multiplication(zero, all_0_0_0) = all_63_0_40
% 28.54/8.95 | (76) addition(all_0_0_0, all_63_0_40) = all_63_0_40
% 28.54/8.95 |
% 28.54/8.95 | Instantiating (73) with all_75_0_50, all_75_1_51 yields:
% 28.54/8.95 | (77) domain(all_75_1_51) = all_75_0_50 & domain(zero) = all_75_0_50 & multiplication(zero, all_0_0_0) = all_75_1_51
% 28.54/8.95 |
% 28.54/8.95 | Applying alpha-rule on (77) yields:
% 28.54/8.95 | (78) domain(all_75_1_51) = all_75_0_50
% 28.54/8.95 | (79) domain(zero) = all_75_0_50
% 28.54/8.95 | (80) multiplication(zero, all_0_0_0) = all_75_1_51
% 28.54/8.95 |
% 28.54/8.95 | Instantiating formula (12) with all_75_1_51, all_0_0_0 and discharging atoms multiplication(zero, all_0_0_0) = all_75_1_51, yields:
% 28.54/8.95 | (81) all_75_1_51 = zero
% 28.54/8.95 |
% 28.54/8.95 | Instantiating formula (35) with zero, all_0_0_0, all_63_0_40, all_75_1_51 and discharging atoms multiplication(zero, all_0_0_0) = all_75_1_51, multiplication(zero, all_0_0_0) = all_63_0_40, yields:
% 28.54/8.95 | (82) all_75_1_51 = all_63_0_40
% 28.54/8.95 |
% 28.54/8.95 | Combining equations (81,82) yields a new equation:
% 28.54/8.95 | (83) all_63_0_40 = zero
% 28.54/8.95 |
% 28.54/8.95 | From (83)(83) and (76) follows:
% 28.54/8.95 | (84) addition(all_0_0_0, zero) = zero
% 28.54/8.95 |
% 28.54/8.95 | Instantiating formula (33) with zero, all_0_0_0 and discharging atoms addition(all_0_0_0, zero) = zero, yields:
% 28.54/8.95 | (85) all_0_0_0 = zero
% 28.54/8.95 |
% 28.54/8.95 | Equations (85) can reduce 31 to:
% 28.54/8.95 | (86) $false
% 28.54/8.95 |
% 28.54/8.95 |-The branch is then unsatisfiable
% 28.54/8.95 % SZS output end Proof for theBenchmark
% 28.54/8.95
% 28.54/8.95 8323ms
%------------------------------------------------------------------------------