TSTP Solution File: KLE051+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE051+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 01:51:09 EDT 2022
% Result : Theorem 2.30s 1.30s
% Output : Proof 3.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE051+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 11:38:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.61 ____ _
% 0.51/0.61 ___ / __ \_____(_)___ ________ __________
% 0.51/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.61
% 0.51/0.61 A Theorem Prover for First-Order Logic
% 0.51/0.62 (ePrincess v.1.0)
% 0.51/0.62
% 0.51/0.62 (c) Philipp Rümmer, 2009-2015
% 0.51/0.62 (c) Peter Backeman, 2014-2015
% 0.51/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.62 Bug reports to peter@backeman.se
% 0.51/0.62
% 0.51/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.62
% 0.51/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.78/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.59/0.97 Prover 0: Preprocessing ...
% 2.24/1.24 Prover 0: Constructing countermodel ...
% 2.30/1.30 Prover 0: proved (624ms)
% 2.30/1.30
% 2.30/1.30 No countermodel exists, formula is valid
% 2.30/1.30 % SZS status Theorem for theBenchmark
% 2.30/1.30
% 2.30/1.30 Generating proof ... found it (size 5)
% 3.20/1.51
% 3.20/1.51 % SZS output start Proof for theBenchmark
% 3.20/1.51 Assumed formulas after preprocessing and simplification:
% 3.20/1.51 | (0) ? [v0] : ? [v1] : ( ~ (v1 = v0) & domain(zero) = zero & addition(v0, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v3, v4) = v6) | ~ (multiplication(v2, v4) = v5) | ~ (addition(v5, v6) = v7) | ? [v8] : (multiplication(v8, v4) = v7 & addition(v2, v3) = v8)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v2, v4) = v6) | ~ (multiplication(v2, v3) = v5) | ~ (addition(v5, v6) = v7) | ? [v8] : (multiplication(v2, v8) = v7 & addition(v3, v4) = v8)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (domain(v3) = v5) | ~ (domain(v2) = v4) | ~ (addition(v4, v5) = v6) | ? [v7] : (domain(v7) = v6 & addition(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v5, v4) = v6) | ~ (multiplication(v2, v3) = v5) | ? [v7] : (multiplication(v3, v4) = v7 & multiplication(v2, v7) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v5, v4) = v6) | ~ (addition(v2, v3) = v5) | ? [v7] : ? [v8] : (multiplication(v3, v4) = v8 & multiplication(v2, v4) = v7 & addition(v7, v8) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v3, v4) = v5) | ~ (multiplication(v2, v5) = v6) | ? [v7] : (multiplication(v7, v4) = v6 & multiplication(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v2, v5) = v6) | ~ (addition(v3, v4) = v5) | ? [v7] : ? [v8] : (multiplication(v2, v4) = v8 & multiplication(v2, v3) = v7 & addition(v7, v8) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v5, v2) = v6) | ~ (addition(v4, v3) = v5) | ? [v7] : (addition(v4, v7) = v6 & addition(v3, v2) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v4, v5) = v6) | ~ (addition(v3, v2) = v5) | ? [v7] : (addition(v7, v2) = v6 & addition(v4, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (domain(v2) = v3) | ~ (multiplication(v3, v2) = v4) | ~ (addition(v2, v4) = v5)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (multiplication(v5, v4) = v3) | ~ (multiplication(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (addition(v5, v4) = v3) | ~ (addition(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (domain(v3) = v4) | ~ (multiplication(v2, v4) = v5) | ? [v6] : ? [v7] : (domain(v6) = v7 & domain(v5) = v7 & multiplication(v2, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (addition(v2, v3) = v4) | ~ leq(v2, v3)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (domain(v4) = v3) | ~ (domain(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v2) = v3) | ~ (multiplication(v3, v2) = v4) | addition(v2, v4) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (domain(v7) = v5 & domain(v4) = v5 & domain(v3) = v6 & multiplication(v2, v6) = v7)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v2) = v4) | addition(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | addition(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (domain(v4) = v5 & domain(v3) = v7 & domain(v2) = v6 & addition(v6, v7) = v5)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (multiplication(v2, one) = v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (multiplication(one, v2) = v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (addition(v2, v2) = v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (addition(v2, zero) = v3)) & ! [v2] : ! [v3] : (v3 = zero | ~ (multiplication(v2, zero) = v3)) & ! [v2] : ! [v3] : (v3 = zero | ~ (multiplication(zero, v2) = v3)) & ! [v2] : ! [v3] : ( ~ (domain(v2) = v3) | addition(v3, one) = one) & ! [v2] : ! [v3] : ( ~ (addition(v2, v3) = v3) | leq(v2, v3)))
% 3.54/1.56 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 3.54/1.56 | (1) ~ (all_0_0_0 = all_0_1_1) & domain(zero) = zero & addition(all_0_1_1, all_0_1_1) = 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] : (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))
% 3.54/1.57 |
% 3.54/1.57 | Applying alpha-rule on (1) yields:
% 3.54/1.57 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2)
% 3.54/1.57 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 3.54/1.57 | (4) ! [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))
% 3.54/1.57 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1))
% 3.54/1.57 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 3.54/1.57 | (7) domain(zero) = zero
% 3.54/1.57 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 3.54/1.57 | (9) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 3.54/1.57 | (10) ! [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))
% 3.54/1.57 | (11) addition(all_0_1_1, all_0_1_1) = all_0_0_0
% 3.54/1.57 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 3.54/1.57 | (13) ! [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))
% 3.54/1.57 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0))
% 3.54/1.57 | (15) ! [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))
% 3.54/1.58 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | ~ (addition(v0, v2) = v3))
% 3.54/1.58 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 3.54/1.58 | (18) ~ (all_0_0_0 = all_0_1_1)
% 3.54/1.58 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 3.54/1.58 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 3.54/1.58 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 3.54/1.58 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 3.54/1.58 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 3.54/1.58 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 3.54/1.58 | (25) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 3.54/1.58 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 3.54/1.58 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 3.54/1.58 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 3.54/1.58 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 3.54/1.58 | (30) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 3.54/1.58 | (31) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1))
% 3.54/1.58 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 3.54/1.58 |
% 3.54/1.58 | Instantiating formula (19) with all_0_0_0, all_0_1_1 and discharging atoms addition(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 3.54/1.58 | (33) all_0_0_0 = all_0_1_1
% 3.54/1.58 |
% 3.54/1.58 | Equations (33) can reduce 18 to:
% 3.54/1.58 | (34) $false
% 3.54/1.58 |
% 3.54/1.58 |-The branch is then unsatisfiable
% 3.54/1.58 % SZS output end Proof for theBenchmark
% 3.54/1.58
% 3.54/1.58 953ms
%------------------------------------------------------------------------------