TSTP Solution File: PUZ130+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : PUZ130+1 : TPTP v8.1.0. Released v4.1.0.
% 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 : Mon Jul 18 18:08:58 EDT 2022
% Result : Theorem 3.11s 1.42s
% Output : Proof 4.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : PUZ130+1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 600
% 0.09/0.27 % DateTime : Sat May 28 22:52:10 EDT 2022
% 0.09/0.27 % CPUTime :
% 0.13/0.47 ____ _
% 0.13/0.47 ___ / __ \_____(_)___ ________ __________
% 0.13/0.47 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.13/0.47 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.13/0.47 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.13/0.47
% 0.13/0.47 A Theorem Prover for First-Order Logic
% 0.13/0.47 (ePrincess v.1.0)
% 0.13/0.47
% 0.13/0.47 (c) Philipp Rümmer, 2009-2015
% 0.13/0.47 (c) Peter Backeman, 2014-2015
% 0.13/0.47 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.13/0.47 Free software under GNU Lesser General Public License (LGPL).
% 0.13/0.47 Bug reports to peter@backeman.se
% 0.13/0.47
% 0.13/0.47 For more information, visit http://user.uu.se/~petba168/breu/
% 0.13/0.47
% 0.13/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.13/0.52 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.06/0.77 Prover 0: Preprocessing ...
% 1.38/0.88 Prover 0: Warning: ignoring some quantifiers
% 1.41/0.90 Prover 0: Constructing countermodel ...
% 1.77/1.05 Prover 0: gave up
% 1.77/1.05 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.77/1.07 Prover 1: Preprocessing ...
% 2.04/1.15 Prover 1: Warning: ignoring some quantifiers
% 2.04/1.16 Prover 1: Constructing countermodel ...
% 2.49/1.30 Prover 1: gave up
% 2.49/1.30 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.49/1.31 Prover 2: Preprocessing ...
% 2.81/1.37 Prover 2: Warning: ignoring some quantifiers
% 2.81/1.38 Prover 2: Constructing countermodel ...
% 3.11/1.41 Prover 2: proved (114ms)
% 3.11/1.42
% 3.11/1.42 No countermodel exists, formula is valid
% 3.11/1.42 % SZS status Theorem for theBenchmark
% 3.11/1.42
% 3.11/1.42 Generating proof ... Warning: ignoring some quantifiers
% 3.71/1.61 found it (size 49)
% 3.71/1.61
% 3.71/1.61 % SZS output start Proof for theBenchmark
% 3.71/1.61 Assumed formulas after preprocessing and simplification:
% 3.71/1.61 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v0 = 0) & chased(odie, garfield) = 0 & hates(jon, jon) = v0 & owner(jon, odie) = 0 & owner(jon, garfield) = 0 & human(v7) = 0 & human(jon) = 0 & pet(v8) = 0 & dog(v9) = 0 & dog(odie) = 0 & cat(v10) = 0 & cat(garfield) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (hates(v13, v14) = v15) | ~ (owner_of(v12) = v14) | ~ (owner_of(v11) = v13) | ? [v16] : (( ~ (v16 = 0) & chased(v12, v11) = v16) | ( ~ (v16 = 0) & dog(v12) = v16) | ( ~ (v16 = 0) & cat(v11) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (chased(v14, v13) = v12) | ~ (chased(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (hates(v14, v13) = v12) | ~ (hates(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (owner(v14, v13) = v12) | ~ (owner(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (owner_of(v13) = v12) | ~ (owner_of(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (human(v13) = v12) | ~ (human(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (pet(v13) = v12) | ~ (pet(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (dog(v13) = v12) | ~ (dog(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (cat(v13) = v12) | ~ (cat(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (owner(v11, v12) = v13) | ? [v14] : (( ~ (v14 = 0) & human(v11) = v14) | ( ~ (v14 = 0) & pet(v12) = v14) | (( ~ (v13 = 0) | (v14 = v11 & owner_of(v12) = v11)) & (v13 = 0 | ( ~ (v14 = v11) & owner_of(v12) = v14))))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (pet(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & dog(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (pet(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & cat(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (chased(v12, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ((v15 = 0 & hates(v13, v14) = 0 & owner_of(v12) = v14 & owner_of(v11) = v13) | ( ~ (v13 = 0) & dog(v12) = v13) | ( ~ (v13 = 0) & cat(v11) = v13))) & ! [v11] : ! [v12] : ( ~ (owner_of(v11) = v12) | ? [v13] : ((v13 = 0 & human(v12) = 0) | ( ~ (v13 = 0) & pet(v11) = v13))) & ! [v11] : ( ~ (pet(v11) = 0) | ? [v12] : (owner(v11, v12) = 0 & human(v12) = 0)) & ! [v11] : ( ~ (pet(v11) = 0) | ? [v12] : (owner_of(v11) = v12 & human(v12) = 0)) & ! [v11] : ( ~ (dog(v11) = 0) | pet(v11) = 0) & ! [v11] : ( ~ (cat(v11) = 0) | pet(v11) = 0) & ? [v11] : ? [v12] : ? [v13] : chased(v12, v11) = v13 & ? [v11] : ? [v12] : ? [v13] : hates(v12, v11) = v13 & ? [v11] : ? [v12] : ? [v13] : owner(v12, v11) = v13 & ? [v11] : ? [v12] : owner_of(v11) = v12 & ? [v11] : ? [v12] : human(v11) = v12 & ? [v11] : ? [v12] : pet(v11) = v12 & ? [v11] : ? [v12] : dog(v11) = v12 & ? [v11] : ? [v12] : cat(v11) = v12 & ( ? [v11] : v11 = odie | (v2 = 0 & ~ (v3 = 0) & owner(jon, v1) = v3 & dog(v1) = 0)) & ( ? [v11] : v11 = garfield | (v5 = 0 & ~ (v6 = 0) & owner(jon, v4) = v6 & cat(v4) = 0)))
% 4.13/1.64 | 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 yields:
% 4.13/1.64 | (1) ~ (all_0_10_10 = 0) & chased(odie, garfield) = 0 & hates(jon, jon) = all_0_10_10 & owner(jon, odie) = 0 & owner(jon, garfield) = 0 & human(all_0_3_3) = 0 & human(jon) = 0 & pet(all_0_2_2) = 0 & dog(all_0_1_1) = 0 & dog(odie) = 0 & cat(all_0_0_0) = 0 & cat(garfield) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (hates(v2, v3) = v4) | ~ (owner_of(v1) = v3) | ~ (owner_of(v0) = v2) | ? [v5] : (( ~ (v5 = 0) & chased(v1, v0) = v5) | ( ~ (v5 = 0) & dog(v1) = v5) | ( ~ (v5 = 0) & cat(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (chased(v3, v2) = v1) | ~ (chased(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (hates(v3, v2) = v1) | ~ (hates(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (owner(v3, v2) = v1) | ~ (owner(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (owner_of(v2) = v1) | ~ (owner_of(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (human(v2) = v1) | ~ (human(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pet(v2) = v1) | ~ (pet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (dog(v2) = v1) | ~ (dog(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cat(v2) = v1) | ~ (cat(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (owner(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & human(v0) = v3) | ( ~ (v3 = 0) & pet(v1) = v3) | (( ~ (v2 = 0) | (v3 = v0 & owner_of(v1) = v0)) & (v2 = 0 | ( ~ (v3 = v0) & owner_of(v1) = v3))))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pet(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & dog(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pet(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & cat(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (chased(v1, v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & hates(v2, v3) = 0 & owner_of(v1) = v3 & owner_of(v0) = v2) | ( ~ (v2 = 0) & dog(v1) = v2) | ( ~ (v2 = 0) & cat(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (owner_of(v0) = v1) | ? [v2] : ((v2 = 0 & human(v1) = 0) | ( ~ (v2 = 0) & pet(v0) = v2))) & ! [v0] : ( ~ (pet(v0) = 0) | ? [v1] : (owner(v0, v1) = 0 & human(v1) = 0)) & ! [v0] : ( ~ (pet(v0) = 0) | ? [v1] : (owner_of(v0) = v1 & human(v1) = 0)) & ! [v0] : ( ~ (dog(v0) = 0) | pet(v0) = 0) & ! [v0] : ( ~ (cat(v0) = 0) | pet(v0) = 0) & ? [v0] : ? [v1] : ? [v2] : chased(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : hates(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : owner(v1, v0) = v2 & ? [v0] : ? [v1] : owner_of(v0) = v1 & ? [v0] : ? [v1] : human(v0) = v1 & ? [v0] : ? [v1] : pet(v0) = v1 & ? [v0] : ? [v1] : dog(v0) = v1 & ? [v0] : ? [v1] : cat(v0) = v1 & ( ? [v0] : v0 = odie | (all_0_8_8 = 0 & ~ (all_0_7_7 = 0) & owner(jon, all_0_9_9) = all_0_7_7 & dog(all_0_9_9) = 0)) & ( ? [v0] : v0 = garfield | (all_0_5_5 = 0 & ~ (all_0_4_4 = 0) & owner(jon, all_0_6_6) = all_0_4_4 & cat(all_0_6_6) = 0))
% 4.13/1.65 |
% 4.13/1.65 | Applying alpha-rule on (1) yields:
% 4.13/1.65 | (2) ~ (all_0_10_10 = 0)
% 4.13/1.65 | (3) owner(jon, garfield) = 0
% 4.13/1.65 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (owner(v3, v2) = v1) | ~ (owner(v3, v2) = v0))
% 4.13/1.65 | (5) ! [v0] : ! [v1] : ( ~ (chased(v1, v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & hates(v2, v3) = 0 & owner_of(v1) = v3 & owner_of(v0) = v2) | ( ~ (v2 = 0) & dog(v1) = v2) | ( ~ (v2 = 0) & cat(v0) = v2)))
% 4.13/1.65 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (hates(v3, v2) = v1) | ~ (hates(v3, v2) = v0))
% 4.13/1.65 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pet(v2) = v1) | ~ (pet(v2) = v0))
% 4.13/1.65 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (pet(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & cat(v0) = v2))
% 4.13/1.65 | (9) dog(all_0_1_1) = 0
% 4.13/1.65 | (10) ? [v0] : ? [v1] : human(v0) = v1
% 4.13/1.65 | (11) cat(garfield) = 0
% 4.13/1.65 | (12) pet(all_0_2_2) = 0
% 4.13/1.65 | (13) ! [v0] : ( ~ (cat(v0) = 0) | pet(v0) = 0)
% 4.13/1.65 | (14) ? [v0] : ? [v1] : pet(v0) = v1
% 4.13/1.65 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (hates(v2, v3) = v4) | ~ (owner_of(v1) = v3) | ~ (owner_of(v0) = v2) | ? [v5] : (( ~ (v5 = 0) & chased(v1, v0) = v5) | ( ~ (v5 = 0) & dog(v1) = v5) | ( ~ (v5 = 0) & cat(v0) = v5)))
% 4.13/1.65 | (16) cat(all_0_0_0) = 0
% 4.13/1.65 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (chased(v3, v2) = v1) | ~ (chased(v3, v2) = v0))
% 4.13/1.65 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (owner_of(v2) = v1) | ~ (owner_of(v2) = v0))
% 4.13/1.65 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cat(v2) = v1) | ~ (cat(v2) = v0))
% 4.13/1.65 | (20) ! [v0] : ( ~ (pet(v0) = 0) | ? [v1] : (owner_of(v0) = v1 & human(v1) = 0))
% 4.13/1.65 | (21) ? [v0] : ? [v1] : ? [v2] : chased(v1, v0) = v2
% 4.13/1.65 | (22) ! [v0] : ( ~ (pet(v0) = 0) | ? [v1] : (owner(v0, v1) = 0 & human(v1) = 0))
% 4.13/1.65 | (23) ! [v0] : ! [v1] : (v1 = 0 | ~ (pet(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & dog(v0) = v2))
% 4.13/1.65 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (owner(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & human(v0) = v3) | ( ~ (v3 = 0) & pet(v1) = v3) | (( ~ (v2 = 0) | (v3 = v0 & owner_of(v1) = v0)) & (v2 = 0 | ( ~ (v3 = v0) & owner_of(v1) = v3)))))
% 4.13/1.65 | (25) ? [v0] : ? [v1] : cat(v0) = v1
% 4.13/1.65 | (26) chased(odie, garfield) = 0
% 4.13/1.66 | (27) human(jon) = 0
% 4.13/1.66 | (28) ! [v0] : ! [v1] : ( ~ (owner_of(v0) = v1) | ? [v2] : ((v2 = 0 & human(v1) = 0) | ( ~ (v2 = 0) & pet(v0) = v2)))
% 4.13/1.66 | (29) owner(jon, odie) = 0
% 4.13/1.66 | (30) human(all_0_3_3) = 0
% 4.13/1.66 | (31) ? [v0] : ? [v1] : ? [v2] : hates(v1, v0) = v2
% 4.13/1.66 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (human(v2) = v1) | ~ (human(v2) = v0))
% 4.13/1.66 | (33) ? [v0] : v0 = garfield | (all_0_5_5 = 0 & ~ (all_0_4_4 = 0) & owner(jon, all_0_6_6) = all_0_4_4 & cat(all_0_6_6) = 0)
% 4.13/1.66 | (34) ? [v0] : ? [v1] : owner_of(v0) = v1
% 4.13/1.66 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (dog(v2) = v1) | ~ (dog(v2) = v0))
% 4.13/1.66 | (36) ? [v0] : v0 = odie | (all_0_8_8 = 0 & ~ (all_0_7_7 = 0) & owner(jon, all_0_9_9) = all_0_7_7 & dog(all_0_9_9) = 0)
% 4.13/1.66 | (37) ? [v0] : ? [v1] : ? [v2] : owner(v1, v0) = v2
% 4.13/1.66 | (38) hates(jon, jon) = all_0_10_10
% 4.13/1.66 | (39) ? [v0] : ? [v1] : dog(v0) = v1
% 4.13/1.66 | (40) ! [v0] : ( ~ (dog(v0) = 0) | pet(v0) = 0)
% 4.13/1.66 | (41) dog(odie) = 0
% 4.13/1.66 |
% 4.13/1.66 | Instantiating formula (5) with odie, garfield and discharging atoms chased(odie, garfield) = 0, yields:
% 4.13/1.66 | (42) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & hates(v0, v1) = 0 & owner_of(odie) = v1 & owner_of(garfield) = v0) | ( ~ (v0 = 0) & dog(odie) = v0) | ( ~ (v0 = 0) & cat(garfield) = v0))
% 4.13/1.66 |
% 4.13/1.66 | Instantiating formula (24) with 0, odie, jon and discharging atoms owner(jon, odie) = 0, yields:
% 4.13/1.66 | (43) ? [v0] : ((v0 = jon & owner_of(odie) = jon) | ( ~ (v0 = 0) & human(jon) = v0) | ( ~ (v0 = 0) & pet(odie) = v0))
% 4.13/1.66 |
% 4.13/1.66 | Instantiating formula (24) with 0, garfield, jon and discharging atoms owner(jon, garfield) = 0, yields:
% 4.13/1.66 | (44) ? [v0] : ((v0 = jon & owner_of(garfield) = jon) | ( ~ (v0 = 0) & human(jon) = v0) | ( ~ (v0 = 0) & pet(garfield) = v0))
% 4.13/1.66 |
% 4.13/1.66 | Instantiating formula (40) with odie and discharging atoms dog(odie) = 0, yields:
% 4.13/1.66 | (45) pet(odie) = 0
% 4.13/1.66 |
% 4.13/1.66 | Instantiating formula (13) with garfield and discharging atoms cat(garfield) = 0, yields:
% 4.13/1.66 | (46) pet(garfield) = 0
% 4.13/1.66 |
% 4.13/1.66 | Instantiating (44) with all_27_0_31 yields:
% 4.13/1.66 | (47) (all_27_0_31 = jon & owner_of(garfield) = jon) | ( ~ (all_27_0_31 = 0) & human(jon) = all_27_0_31) | ( ~ (all_27_0_31 = 0) & pet(garfield) = all_27_0_31)
% 4.13/1.66 |
% 4.13/1.66 | Instantiating (43) with all_30_0_33 yields:
% 4.13/1.66 | (48) (all_30_0_33 = jon & owner_of(odie) = jon) | ( ~ (all_30_0_33 = 0) & human(jon) = all_30_0_33) | ( ~ (all_30_0_33 = 0) & pet(odie) = all_30_0_33)
% 4.13/1.66 |
% 4.13/1.66 | Instantiating (42) with all_31_0_34, all_31_1_35, all_31_2_36 yields:
% 4.13/1.66 | (49) (all_31_0_34 = 0 & hates(all_31_2_36, all_31_1_35) = 0 & owner_of(odie) = all_31_1_35 & owner_of(garfield) = all_31_2_36) | ( ~ (all_31_2_36 = 0) & dog(odie) = all_31_2_36) | ( ~ (all_31_2_36 = 0) & cat(garfield) = all_31_2_36)
% 4.13/1.66 |
% 4.13/1.66 +-Applying beta-rule and splitting (48), into two cases.
% 4.13/1.66 |-Branch one:
% 4.13/1.66 | (50) (all_30_0_33 = jon & owner_of(odie) = jon) | ( ~ (all_30_0_33 = 0) & human(jon) = all_30_0_33)
% 4.13/1.66 |
% 4.13/1.66 +-Applying beta-rule and splitting (50), into two cases.
% 4.13/1.66 |-Branch one:
% 4.13/1.66 | (51) all_30_0_33 = jon & owner_of(odie) = jon
% 4.13/1.66 |
% 4.13/1.66 | Applying alpha-rule on (51) yields:
% 4.13/1.66 | (52) all_30_0_33 = jon
% 4.13/1.66 | (53) owner_of(odie) = jon
% 4.13/1.66 |
% 4.13/1.66 +-Applying beta-rule and splitting (49), into two cases.
% 4.13/1.66 |-Branch one:
% 4.13/1.66 | (54) (all_31_0_34 = 0 & hates(all_31_2_36, all_31_1_35) = 0 & owner_of(odie) = all_31_1_35 & owner_of(garfield) = all_31_2_36) | ( ~ (all_31_2_36 = 0) & dog(odie) = all_31_2_36)
% 4.13/1.66 |
% 4.13/1.66 +-Applying beta-rule and splitting (54), into two cases.
% 4.13/1.66 |-Branch one:
% 4.13/1.66 | (55) all_31_0_34 = 0 & hates(all_31_2_36, all_31_1_35) = 0 & owner_of(odie) = all_31_1_35 & owner_of(garfield) = all_31_2_36
% 4.13/1.66 |
% 4.13/1.66 | Applying alpha-rule on (55) yields:
% 4.13/1.66 | (56) all_31_0_34 = 0
% 4.13/1.66 | (57) hates(all_31_2_36, all_31_1_35) = 0
% 4.13/1.66 | (58) owner_of(odie) = all_31_1_35
% 4.13/1.66 | (59) owner_of(garfield) = all_31_2_36
% 4.13/1.66 |
% 4.13/1.66 +-Applying beta-rule and splitting (47), into two cases.
% 4.13/1.66 |-Branch one:
% 4.13/1.66 | (60) (all_27_0_31 = jon & owner_of(garfield) = jon) | ( ~ (all_27_0_31 = 0) & human(jon) = all_27_0_31)
% 4.13/1.67 |
% 4.13/1.67 +-Applying beta-rule and splitting (60), into two cases.
% 4.13/1.67 |-Branch one:
% 4.13/1.67 | (61) all_27_0_31 = jon & owner_of(garfield) = jon
% 4.13/1.67 |
% 4.13/1.67 | Applying alpha-rule on (61) yields:
% 4.13/1.67 | (62) all_27_0_31 = jon
% 4.13/1.67 | (63) owner_of(garfield) = jon
% 4.13/1.67 |
% 4.13/1.67 | Instantiating formula (18) with odie, jon, all_31_1_35 and discharging atoms owner_of(odie) = all_31_1_35, owner_of(odie) = jon, yields:
% 4.13/1.67 | (64) all_31_1_35 = jon
% 4.13/1.67 |
% 4.13/1.67 | Instantiating formula (18) with garfield, jon, all_31_2_36 and discharging atoms owner_of(garfield) = all_31_2_36, owner_of(garfield) = jon, yields:
% 4.13/1.67 | (65) all_31_2_36 = jon
% 4.13/1.67 |
% 4.13/1.67 | From (65)(64) and (57) follows:
% 4.13/1.67 | (66) hates(jon, jon) = 0
% 4.13/1.67 |
% 4.13/1.67 | Instantiating formula (6) with jon, jon, 0, all_0_10_10 and discharging atoms hates(jon, jon) = all_0_10_10, hates(jon, jon) = 0, yields:
% 4.13/1.67 | (67) all_0_10_10 = 0
% 4.13/1.67 |
% 4.13/1.67 | Equations (67) can reduce 2 to:
% 4.13/1.67 | (68) $false
% 4.13/1.67 |
% 4.13/1.67 |-The branch is then unsatisfiable
% 4.13/1.67 |-Branch two:
% 4.13/1.67 | (69) ~ (all_27_0_31 = 0) & human(jon) = all_27_0_31
% 4.13/1.67 |
% 4.13/1.67 | Applying alpha-rule on (69) yields:
% 4.13/1.67 | (70) ~ (all_27_0_31 = 0)
% 4.13/1.67 | (71) human(jon) = all_27_0_31
% 4.13/1.67 |
% 4.13/1.67 | Instantiating formula (32) with jon, all_27_0_31, 0 and discharging atoms human(jon) = all_27_0_31, human(jon) = 0, yields:
% 4.13/1.67 | (72) all_27_0_31 = 0
% 4.13/1.67 |
% 4.13/1.67 | Equations (72) can reduce 70 to:
% 4.13/1.67 | (68) $false
% 4.13/1.67 |
% 4.13/1.67 |-The branch is then unsatisfiable
% 4.13/1.67 |-Branch two:
% 4.13/1.67 | (74) ~ (all_27_0_31 = 0) & pet(garfield) = all_27_0_31
% 4.13/1.67 |
% 4.13/1.67 | Applying alpha-rule on (74) yields:
% 4.13/1.67 | (70) ~ (all_27_0_31 = 0)
% 4.13/1.67 | (76) pet(garfield) = all_27_0_31
% 4.13/1.67 |
% 4.13/1.67 | Instantiating formula (7) with garfield, 0, all_27_0_31 and discharging atoms pet(garfield) = all_27_0_31, pet(garfield) = 0, yields:
% 4.13/1.67 | (72) all_27_0_31 = 0
% 4.13/1.67 |
% 4.13/1.67 | Equations (72) can reduce 70 to:
% 4.13/1.67 | (68) $false
% 4.13/1.67 |
% 4.13/1.67 |-The branch is then unsatisfiable
% 4.13/1.67 |-Branch two:
% 4.13/1.67 | (79) ~ (all_31_2_36 = 0) & dog(odie) = all_31_2_36
% 4.13/1.67 |
% 4.13/1.67 | Applying alpha-rule on (79) yields:
% 4.13/1.67 | (80) ~ (all_31_2_36 = 0)
% 4.13/1.67 | (81) dog(odie) = all_31_2_36
% 4.13/1.67 |
% 4.13/1.67 | Instantiating formula (35) with odie, all_31_2_36, 0 and discharging atoms dog(odie) = all_31_2_36, dog(odie) = 0, yields:
% 4.13/1.67 | (82) all_31_2_36 = 0
% 4.13/1.67 |
% 4.13/1.67 | Equations (82) can reduce 80 to:
% 4.13/1.67 | (68) $false
% 4.13/1.67 |
% 4.13/1.67 |-The branch is then unsatisfiable
% 4.13/1.67 |-Branch two:
% 4.13/1.67 | (84) ~ (all_31_2_36 = 0) & cat(garfield) = all_31_2_36
% 4.13/1.67 |
% 4.13/1.67 | Applying alpha-rule on (84) yields:
% 4.13/1.67 | (80) ~ (all_31_2_36 = 0)
% 4.13/1.67 | (86) cat(garfield) = all_31_2_36
% 4.13/1.67 |
% 4.13/1.67 | Instantiating formula (19) with garfield, all_31_2_36, 0 and discharging atoms cat(garfield) = all_31_2_36, cat(garfield) = 0, yields:
% 4.13/1.67 | (82) all_31_2_36 = 0
% 4.13/1.67 |
% 4.13/1.67 | Equations (82) can reduce 80 to:
% 4.13/1.67 | (68) $false
% 4.13/1.67 |
% 4.13/1.67 |-The branch is then unsatisfiable
% 4.13/1.67 |-Branch two:
% 4.13/1.67 | (89) ~ (all_30_0_33 = 0) & human(jon) = all_30_0_33
% 4.13/1.67 |
% 4.13/1.67 | Applying alpha-rule on (89) yields:
% 4.13/1.67 | (90) ~ (all_30_0_33 = 0)
% 4.13/1.67 | (91) human(jon) = all_30_0_33
% 4.13/1.67 |
% 4.13/1.67 | Instantiating formula (32) with jon, all_30_0_33, 0 and discharging atoms human(jon) = all_30_0_33, human(jon) = 0, yields:
% 4.13/1.67 | (92) all_30_0_33 = 0
% 4.13/1.67 |
% 4.13/1.67 | Equations (92) can reduce 90 to:
% 4.13/1.67 | (68) $false
% 4.13/1.67 |
% 4.13/1.67 |-The branch is then unsatisfiable
% 4.13/1.67 |-Branch two:
% 4.13/1.67 | (94) ~ (all_30_0_33 = 0) & pet(odie) = all_30_0_33
% 4.13/1.67 |
% 4.13/1.67 | Applying alpha-rule on (94) yields:
% 4.13/1.67 | (90) ~ (all_30_0_33 = 0)
% 4.13/1.67 | (96) pet(odie) = all_30_0_33
% 4.13/1.67 |
% 4.13/1.67 | Instantiating formula (7) with odie, 0, all_30_0_33 and discharging atoms pet(odie) = all_30_0_33, pet(odie) = 0, yields:
% 4.13/1.67 | (92) all_30_0_33 = 0
% 4.13/1.67 |
% 4.13/1.67 | Equations (92) can reduce 90 to:
% 4.13/1.67 | (68) $false
% 4.13/1.67 |
% 4.13/1.67 |-The branch is then unsatisfiable
% 4.13/1.67 % SZS output end Proof for theBenchmark
% 4.13/1.68
% 4.13/1.68 1191ms
%------------------------------------------------------------------------------