TSTP Solution File: KLE072+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE072+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 01:51:14 EDT 2022
% Result : Theorem 2.04s 1.16s
% Output : Proof 4.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : KLE072+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.10 % Command : ePrincess-casc -timeout=%d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Thu Jun 16 09:02:14 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.14/0.48 ____ _
% 0.14/0.48 ___ / __ \_____(_)___ ________ __________
% 0.14/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.14/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.14/0.48
% 0.14/0.48 A Theorem Prover for First-Order Logic
% 0.14/0.48 (ePrincess v.1.0)
% 0.14/0.48
% 0.14/0.48 (c) Philipp Rümmer, 2009-2015
% 0.14/0.48 (c) Peter Backeman, 2014-2015
% 0.14/0.48 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.48 Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.48 Bug reports to peter@backeman.se
% 0.14/0.48
% 0.14/0.48 For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.48
% 0.14/0.48 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.17/0.76 Prover 0: Preprocessing ...
% 1.77/1.01 Prover 0: Constructing countermodel ...
% 2.04/1.16 Prover 0: proved (630ms)
% 2.04/1.16
% 2.04/1.16 No countermodel exists, formula is valid
% 2.04/1.16 % SZS status Theorem for theBenchmark
% 2.04/1.16
% 2.04/1.16 Generating proof ... found it (size 26)
% 3.39/1.45
% 3.39/1.45 % SZS output start Proof for theBenchmark
% 3.39/1.45 Assumed formulas after preprocessing and simplification:
% 3.39/1.46 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = v6) & domain(v9) = v10 & domain(v7) = v8 & domain(v5) = v6 & domain(v2) = v4 & domain(zero) = zero & multiplication(v3, v4) = v5 & multiplication(v1, v4) = v9 & multiplication(v0, v4) = v7 & addition(v8, v10) = v11 & addition(v0, v1) = v3 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (multiplication(v13, v14) = v16) | ~ (multiplication(v12, v14) = v15) | ~ (addition(v15, v16) = v17) | ? [v18] : (multiplication(v18, v14) = v17 & addition(v12, v13) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (multiplication(v12, v14) = v16) | ~ (multiplication(v12, v13) = v15) | ~ (addition(v15, v16) = v17) | ? [v18] : (multiplication(v12, v18) = v17 & addition(v13, v14) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (domain(v13) = v15) | ~ (domain(v12) = v14) | ~ (addition(v14, v15) = v16) | ? [v17] : (domain(v17) = v16 & addition(v12, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (multiplication(v15, v14) = v16) | ~ (multiplication(v12, v13) = v15) | ? [v17] : (multiplication(v13, v14) = v17 & multiplication(v12, v17) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (multiplication(v15, v14) = v16) | ~ (addition(v12, v13) = v15) | ? [v17] : ? [v18] : (multiplication(v13, v14) = v18 & multiplication(v12, v14) = v17 & addition(v17, v18) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (multiplication(v13, v14) = v15) | ~ (multiplication(v12, v15) = v16) | ? [v17] : (multiplication(v17, v14) = v16 & multiplication(v12, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (multiplication(v12, v15) = v16) | ~ (addition(v13, v14) = v15) | ? [v17] : ? [v18] : (multiplication(v12, v14) = v18 & multiplication(v12, v13) = v17 & addition(v17, v18) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (addition(v15, v12) = v16) | ~ (addition(v14, v13) = v15) | ? [v17] : (addition(v14, v17) = v16 & addition(v13, v12) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (addition(v14, v15) = v16) | ~ (addition(v13, v12) = v15) | ? [v17] : (addition(v17, v12) = v16 & addition(v14, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (domain(v12) = v13) | ~ (multiplication(v13, v12) = v14) | ~ (addition(v12, v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (multiplication(v15, v14) = v13) | ~ (multiplication(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (addition(v15, v14) = v13) | ~ (addition(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (domain(v13) = v14) | ~ (multiplication(v12, v14) = v15) | ? [v16] : ? [v17] : (domain(v16) = v17 & domain(v15) = v17 & multiplication(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (addition(v12, v13) = v14) | ~ leq(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (domain(v14) = v13) | ~ (domain(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (domain(v12) = v13) | ~ (multiplication(v13, v12) = v14) | addition(v12, v14) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (domain(v17) = v15 & domain(v14) = v15 & domain(v13) = v16 & multiplication(v12, v16) = v17)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (addition(v13, v12) = v14) | addition(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (addition(v12, v13) = v14) | addition(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (addition(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (domain(v14) = v15 & domain(v13) = v17 & domain(v12) = v16 & addition(v16, v17) = v15)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (multiplication(v12, one) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (multiplication(one, v12) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (addition(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (addition(v12, zero) = v13)) & ! [v12] : ! [v13] : (v13 = zero | ~ (multiplication(v12, zero) = v13)) & ! [v12] : ! [v13] : (v13 = zero | ~ (multiplication(zero, v12) = v13)) & ! [v12] : ! [v13] : ( ~ (domain(v12) = v13) | addition(v13, one) = one) & ! [v12] : ! [v13] : ( ~ (addition(v12, v13) = v13) | leq(v12, v13)))
% 3.72/1.50 | 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 yields:
% 3.72/1.50 | (1) ~ (all_0_0_0 = all_0_5_5) & domain(all_0_2_2) = all_0_1_1 & domain(all_0_4_4) = all_0_3_3 & domain(all_0_6_6) = all_0_5_5 & domain(all_0_9_9) = all_0_7_7 & domain(zero) = zero & multiplication(all_0_8_8, all_0_7_7) = all_0_6_6 & multiplication(all_0_10_10, all_0_7_7) = all_0_2_2 & multiplication(all_0_11_11, all_0_7_7) = all_0_4_4 & addition(all_0_3_3, all_0_1_1) = all_0_0_0 & addition(all_0_11_11, all_0_10_10) = all_0_8_8 & ! [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] : (v3 = v2 | ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | ~ (addition(v0, v2) = v3)) & ! [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) | ~ leq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2) & ! [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] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 3.87/1.51 |
% 3.87/1.51 | Applying alpha-rule on (1) yields:
% 3.87/1.51 | (2) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 3.87/1.51 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 3.87/1.51 | (4) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 3.87/1.51 | (5) multiplication(all_0_8_8, all_0_7_7) = all_0_6_6
% 3.87/1.51 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 3.87/1.51 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2)
% 3.87/1.51 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 3.87/1.51 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 3.87/1.51 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 3.87/1.52 | (11) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 3.87/1.52 | (12) ! [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))
% 3.87/1.52 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 3.87/1.52 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 3.87/1.52 | (15) domain(all_0_2_2) = all_0_1_1
% 3.87/1.52 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 3.87/1.52 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 3.87/1.52 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 3.87/1.52 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 3.87/1.52 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 3.87/1.52 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 3.87/1.52 | (22) ! [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))
% 3.87/1.52 | (23) domain(all_0_6_6) = all_0_5_5
% 3.87/1.52 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1))
% 3.87/1.52 | (25) domain(all_0_9_9) = all_0_7_7
% 3.87/1.52 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 3.87/1.52 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 3.87/1.52 | (28) domain(all_0_4_4) = all_0_3_3
% 3.87/1.52 | (29) ~ (all_0_0_0 = all_0_5_5)
% 3.87/1.52 | (30) ! [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))
% 3.87/1.52 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | ~ (addition(v0, v2) = v3))
% 3.87/1.52 | (32) domain(zero) = zero
% 3.87/1.52 | (33) addition(all_0_11_11, all_0_10_10) = all_0_8_8
% 3.87/1.52 | (34) multiplication(all_0_10_10, all_0_7_7) = all_0_2_2
% 3.87/1.52 | (35) addition(all_0_3_3, all_0_1_1) = all_0_0_0
% 3.87/1.52 | (36) multiplication(all_0_11_11, all_0_7_7) = all_0_4_4
% 3.87/1.52 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 3.87/1.52 | (38) ! [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))
% 3.87/1.53 | (39) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 3.87/1.53 | (40) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 3.87/1.53 |
% 3.87/1.53 | Instantiating formula (10) with all_0_6_6, all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms domain(all_0_9_9) = all_0_7_7, multiplication(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 3.87/1.53 | (41) ? [v0] : ? [v1] : (domain(v0) = v1 & domain(all_0_6_6) = v1 & multiplication(all_0_8_8, all_0_9_9) = v0)
% 3.87/1.53 |
% 3.87/1.53 | Instantiating formula (27) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 3.87/1.53 | (42) ? [v0] : ? [v1] : ? [v2] : (domain(v2) = v0 & domain(all_0_6_6) = v0 & domain(all_0_7_7) = v1 & multiplication(all_0_8_8, v1) = v2)
% 3.87/1.53 |
% 3.87/1.53 | Instantiating formula (13) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms domain(all_0_2_2) = all_0_1_1, domain(all_0_4_4) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 3.87/1.53 | (43) ? [v0] : (domain(v0) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = v0)
% 3.87/1.53 |
% 3.87/1.53 | Instantiating formula (30) with all_0_6_6, all_0_8_8, all_0_7_7, all_0_10_10, all_0_11_11 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_0_6_6, addition(all_0_11_11, all_0_10_10) = all_0_8_8, yields:
% 3.87/1.53 | (44) ? [v0] : ? [v1] : (multiplication(all_0_10_10, all_0_7_7) = v1 & multiplication(all_0_11_11, all_0_7_7) = v0 & addition(v0, v1) = all_0_6_6)
% 3.87/1.53 |
% 3.87/1.53 | Instantiating (44) with all_15_0_20, all_15_1_21 yields:
% 3.87/1.53 | (45) multiplication(all_0_10_10, all_0_7_7) = all_15_0_20 & multiplication(all_0_11_11, all_0_7_7) = all_15_1_21 & addition(all_15_1_21, all_15_0_20) = all_0_6_6
% 3.87/1.53 |
% 3.87/1.53 | Applying alpha-rule on (45) yields:
% 3.87/1.53 | (46) multiplication(all_0_10_10, all_0_7_7) = all_15_0_20
% 3.87/1.53 | (47) multiplication(all_0_11_11, all_0_7_7) = all_15_1_21
% 4.01/1.53 | (48) addition(all_15_1_21, all_15_0_20) = all_0_6_6
% 4.01/1.53 |
% 4.01/1.53 | Instantiating (42) with all_17_0_22, all_17_1_23, all_17_2_24 yields:
% 4.01/1.53 | (49) domain(all_17_0_22) = all_17_2_24 & domain(all_0_6_6) = all_17_2_24 & domain(all_0_7_7) = all_17_1_23 & multiplication(all_0_8_8, all_17_1_23) = all_17_0_22
% 4.01/1.53 |
% 4.01/1.53 | Applying alpha-rule on (49) yields:
% 4.01/1.53 | (50) domain(all_17_0_22) = all_17_2_24
% 4.01/1.53 | (51) domain(all_0_6_6) = all_17_2_24
% 4.01/1.53 | (52) domain(all_0_7_7) = all_17_1_23
% 4.01/1.53 | (53) multiplication(all_0_8_8, all_17_1_23) = all_17_0_22
% 4.01/1.53 |
% 4.01/1.53 | Instantiating (41) with all_19_0_25, all_19_1_26 yields:
% 4.01/1.53 | (54) domain(all_19_1_26) = all_19_0_25 & domain(all_0_6_6) = all_19_0_25 & multiplication(all_0_8_8, all_0_9_9) = all_19_1_26
% 4.01/1.53 |
% 4.01/1.53 | Applying alpha-rule on (54) yields:
% 4.01/1.53 | (55) domain(all_19_1_26) = all_19_0_25
% 4.01/1.53 | (56) domain(all_0_6_6) = all_19_0_25
% 4.01/1.53 | (57) multiplication(all_0_8_8, all_0_9_9) = all_19_1_26
% 4.01/1.53 |
% 4.01/1.53 | Instantiating (43) with all_21_0_27 yields:
% 4.01/1.53 | (58) domain(all_21_0_27) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = all_21_0_27
% 4.01/1.53 |
% 4.01/1.53 | Applying alpha-rule on (58) yields:
% 4.01/1.53 | (59) domain(all_21_0_27) = all_0_0_0
% 4.01/1.53 | (60) addition(all_0_4_4, all_0_2_2) = all_21_0_27
% 4.01/1.53 |
% 4.01/1.53 | Instantiating formula (37) with all_0_6_6, all_19_0_25, all_0_5_5 and discharging atoms domain(all_0_6_6) = all_19_0_25, domain(all_0_6_6) = all_0_5_5, yields:
% 4.01/1.53 | (61) all_19_0_25 = all_0_5_5
% 4.01/1.53 |
% 4.01/1.53 | Instantiating formula (37) with all_0_6_6, all_17_2_24, all_19_0_25 and discharging atoms domain(all_0_6_6) = all_19_0_25, domain(all_0_6_6) = all_17_2_24, yields:
% 4.01/1.53 | (62) all_19_0_25 = all_17_2_24
% 4.01/1.53 |
% 4.01/1.53 | Instantiating formula (16) with all_0_10_10, all_0_7_7, all_15_0_20, all_0_2_2 and discharging atoms multiplication(all_0_10_10, all_0_7_7) = all_15_0_20, multiplication(all_0_10_10, all_0_7_7) = all_0_2_2, yields:
% 4.01/1.53 | (63) all_15_0_20 = all_0_2_2
% 4.01/1.53 |
% 4.01/1.53 | Instantiating formula (16) with all_0_11_11, all_0_7_7, all_15_1_21, all_0_4_4 and discharging atoms multiplication(all_0_11_11, all_0_7_7) = all_15_1_21, multiplication(all_0_11_11, all_0_7_7) = all_0_4_4, yields:
% 4.01/1.54 | (64) all_15_1_21 = all_0_4_4
% 4.01/1.54 |
% 4.01/1.54 | Combining equations (61,62) yields a new equation:
% 4.01/1.54 | (65) all_17_2_24 = all_0_5_5
% 4.01/1.54 |
% 4.01/1.54 | From (65) and (51) follows:
% 4.01/1.54 | (23) domain(all_0_6_6) = all_0_5_5
% 4.01/1.54 |
% 4.01/1.54 | From (64)(63) and (48) follows:
% 4.01/1.54 | (67) addition(all_0_4_4, all_0_2_2) = all_0_6_6
% 4.01/1.54 |
% 4.01/1.54 | Instantiating formula (18) with all_0_4_4, all_0_2_2, all_0_6_6, all_21_0_27 and discharging atoms addition(all_0_4_4, all_0_2_2) = all_21_0_27, addition(all_0_4_4, all_0_2_2) = all_0_6_6, yields:
% 4.01/1.54 | (68) all_21_0_27 = all_0_6_6
% 4.01/1.54 |
% 4.01/1.54 | From (68) and (59) follows:
% 4.01/1.54 | (69) domain(all_0_6_6) = all_0_0_0
% 4.01/1.54 |
% 4.01/1.54 | Instantiating formula (37) with all_0_6_6, all_0_0_0, all_0_5_5 and discharging atoms domain(all_0_6_6) = all_0_0_0, domain(all_0_6_6) = all_0_5_5, yields:
% 4.01/1.54 | (70) all_0_0_0 = all_0_5_5
% 4.01/1.54 |
% 4.01/1.54 | Equations (70) can reduce 29 to:
% 4.01/1.54 | (71) $false
% 4.01/1.54 |
% 4.01/1.54 |-The branch is then unsatisfiable
% 4.01/1.54 % SZS output end Proof for theBenchmark
% 4.01/1.54
% 4.01/1.54 1050ms
%------------------------------------------------------------------------------