TSTP Solution File: PUZ047+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : PUZ047+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 18:08:53 EDT 2022
% Result : Theorem 3.55s 1.55s
% Output : Proof 6.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ047+1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun May 29 01:25:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.49/0.62 ____ _
% 0.49/0.62 ___ / __ \_____(_)___ ________ __________
% 0.49/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.62
% 0.49/0.62 A Theorem Prover for First-Order Logic
% 0.49/0.62 (ePrincess v.1.0)
% 0.49/0.62
% 0.49/0.62 (c) Philipp Rümmer, 2009-2015
% 0.49/0.62 (c) Peter Backeman, 2014-2015
% 0.49/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.62 Bug reports to peter@backeman.se
% 0.49/0.62
% 0.49/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.62
% 0.49/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.96 Prover 0: Preprocessing ...
% 1.90/1.12 Prover 0: Constructing countermodel ...
% 3.55/1.55 Prover 0: proved (872ms)
% 3.55/1.55
% 3.55/1.55 No countermodel exists, formula is valid
% 3.55/1.55 % SZS status Theorem for theBenchmark
% 3.55/1.55
% 3.55/1.55 Generating proof ... found it (size 24)
% 5.81/2.08
% 5.81/2.08 % SZS output start Proof for theBenchmark
% 5.81/2.08 Assumed formulas after preprocessing and simplification:
% 5.81/2.08 | (0) p(south, south, south, south, start) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (take_cabbage(v2) = v1) | ~ (take_cabbage(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (take_goat(v2) = v1) | ~ (take_goat(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (take_wolf(v2) = v1) | ~ (take_wolf(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (go_alone(v2) = v1) | ~ (go_alone(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ p(north, v0, north, v1, v2) | ? [v3] : (take_goat(v2) = v3 & p(south, v0, south, v1, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ p(south, v0, south, v1, v2) | ? [v3] : (take_goat(v2) = v3 & p(north, v0, north, v1, v3))) & ! [v0] : ~ p(north, north, north, north, v0) & ! [v0] : ( ~ p(north, north, north, south, v0) | ? [v1] : (take_wolf(v0) = v1 & p(south, south, north, south, v1))) & ! [v0] : ( ~ p(north, north, south, north, v0) | ? [v1] : (take_cabbage(v0) = v1 & p(south, north, south, south, v1))) & ! [v0] : ( ~ p(north, north, south, north, v0) | ? [v1] : (take_wolf(v0) = v1 & p(south, south, south, north, v1))) & ! [v0] : ( ~ p(north, north, south, north, v0) | ? [v1] : (go_alone(v0) = v1 & p(south, north, south, north, v1))) & ! [v0] : ( ~ p(north, south, north, north, v0) | ? [v1] : (take_cabbage(v0) = v1 & p(south, south, north, south, v1))) & ! [v0] : ( ~ p(north, south, north, south, v0) | ? [v1] : (go_alone(v0) = v1 & p(south, south, north, south, v1))) & ! [v0] : ( ~ p(south, north, south, north, v0) | ? [v1] : (go_alone(v0) = v1 & p(north, north, south, north, v1))) & ! [v0] : ( ~ p(south, north, south, south, v0) | ? [v1] : (take_cabbage(v0) = v1 & p(north, north, south, north, v1))) & ! [v0] : ( ~ p(south, south, north, south, v0) | ? [v1] : (take_cabbage(v0) = v1 & p(north, south, north, north, v1))) & ! [v0] : ( ~ p(south, south, north, south, v0) | ? [v1] : (take_wolf(v0) = v1 & p(north, north, north, south, v1))) & ! [v0] : ( ~ p(south, south, north, south, v0) | ? [v1] : (go_alone(v0) = v1 & p(north, south, north, south, v1))) & ! [v0] : ( ~ p(south, south, south, north, v0) | ? [v1] : (take_wolf(v0) = v1 & p(north, north, south, north, v1)))
% 6.03/2.12 | Applying alpha-rule on (0) yields:
% 6.03/2.12 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (go_alone(v2) = v1) | ~ (go_alone(v2) = v0))
% 6.03/2.12 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ p(south, v0, south, v1, v2) | ? [v3] : (take_goat(v2) = v3 & p(north, v0, north, v1, v3)))
% 6.03/2.12 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ p(north, v0, north, v1, v2) | ? [v3] : (take_goat(v2) = v3 & p(south, v0, south, v1, v3)))
% 6.03/2.12 | (4) ! [v0] : ~ p(north, north, north, north, v0)
% 6.03/2.12 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (take_goat(v2) = v1) | ~ (take_goat(v2) = v0))
% 6.03/2.12 | (6) ! [v0] : ( ~ p(south, north, south, south, v0) | ? [v1] : (take_cabbage(v0) = v1 & p(north, north, south, north, v1)))
% 6.03/2.12 | (7) ! [v0] : ( ~ p(north, north, south, north, v0) | ? [v1] : (take_cabbage(v0) = v1 & p(south, north, south, south, v1)))
% 6.03/2.12 | (8) p(south, south, south, south, start)
% 6.03/2.12 | (9) ! [v0] : ( ~ p(south, north, south, north, v0) | ? [v1] : (go_alone(v0) = v1 & p(north, north, south, north, v1)))
% 6.03/2.12 | (10) ! [v0] : ( ~ p(north, north, south, north, v0) | ? [v1] : (go_alone(v0) = v1 & p(south, north, south, north, v1)))
% 6.03/2.12 | (11) ! [v0] : ( ~ p(south, south, north, south, v0) | ? [v1] : (take_cabbage(v0) = v1 & p(north, south, north, north, v1)))
% 6.03/2.13 | (12) ! [v0] : ( ~ p(north, south, north, north, v0) | ? [v1] : (take_cabbage(v0) = v1 & p(south, south, north, south, v1)))
% 6.03/2.13 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (take_cabbage(v2) = v1) | ~ (take_cabbage(v2) = v0))
% 6.03/2.13 | (14) ! [v0] : ( ~ p(south, south, south, north, v0) | ? [v1] : (take_wolf(v0) = v1 & p(north, north, south, north, v1)))
% 6.03/2.13 | (15) ! [v0] : ( ~ p(north, north, south, north, v0) | ? [v1] : (take_wolf(v0) = v1 & p(south, south, south, north, v1)))
% 6.03/2.13 | (16) ! [v0] : ( ~ p(south, south, north, south, v0) | ? [v1] : (take_wolf(v0) = v1 & p(north, north, north, south, v1)))
% 6.03/2.13 | (17) ! [v0] : ( ~ p(north, north, north, south, v0) | ? [v1] : (take_wolf(v0) = v1 & p(south, south, north, south, v1)))
% 6.03/2.13 | (18) ! [v0] : ( ~ p(south, south, north, south, v0) | ? [v1] : (go_alone(v0) = v1 & p(north, south, north, south, v1)))
% 6.03/2.13 | (19) ! [v0] : ( ~ p(north, south, north, south, v0) | ? [v1] : (go_alone(v0) = v1 & p(south, south, north, south, v1)))
% 6.03/2.13 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (take_wolf(v2) = v1) | ~ (take_wolf(v2) = v0))
% 6.03/2.13 |
% 6.03/2.13 | Instantiating formula (2) with start, south, south and discharging atoms p(south, south, south, south, start), yields:
% 6.03/2.13 | (21) ? [v0] : (take_goat(start) = v0 & p(north, south, north, south, v0))
% 6.03/2.13 |
% 6.03/2.13 | Instantiating (21) with all_7_0_0 yields:
% 6.03/2.13 | (22) take_goat(start) = all_7_0_0 & p(north, south, north, south, all_7_0_0)
% 6.03/2.13 |
% 6.03/2.13 | Applying alpha-rule on (22) yields:
% 6.03/2.13 | (23) take_goat(start) = all_7_0_0
% 6.03/2.13 | (24) p(north, south, north, south, all_7_0_0)
% 6.03/2.13 |
% 6.03/2.13 | Instantiating formula (19) with all_7_0_0 and discharging atoms p(north, south, north, south, all_7_0_0), yields:
% 6.03/2.13 | (25) ? [v0] : (go_alone(all_7_0_0) = v0 & p(south, south, north, south, v0))
% 6.03/2.13 |
% 6.03/2.13 | Instantiating (25) with all_16_0_2 yields:
% 6.03/2.13 | (26) go_alone(all_7_0_0) = all_16_0_2 & p(south, south, north, south, all_16_0_2)
% 6.03/2.13 |
% 6.03/2.13 | Applying alpha-rule on (26) yields:
% 6.03/2.13 | (27) go_alone(all_7_0_0) = all_16_0_2
% 6.03/2.13 | (28) p(south, south, north, south, all_16_0_2)
% 6.03/2.13 |
% 6.03/2.13 | Instantiating formula (11) with all_16_0_2 and discharging atoms p(south, south, north, south, all_16_0_2), yields:
% 6.03/2.13 | (29) ? [v0] : (take_cabbage(all_16_0_2) = v0 & p(north, south, north, north, v0))
% 6.03/2.13 |
% 6.03/2.13 | Instantiating (29) with all_27_0_5 yields:
% 6.03/2.13 | (30) take_cabbage(all_16_0_2) = all_27_0_5 & p(north, south, north, north, all_27_0_5)
% 6.03/2.13 |
% 6.03/2.13 | Applying alpha-rule on (30) yields:
% 6.03/2.13 | (31) take_cabbage(all_16_0_2) = all_27_0_5
% 6.03/2.13 | (32) p(north, south, north, north, all_27_0_5)
% 6.03/2.13 |
% 6.03/2.13 | Instantiating formula (3) with all_27_0_5, north, south and discharging atoms p(north, south, north, north, all_27_0_5), yields:
% 6.03/2.13 | (33) ? [v0] : (take_goat(all_27_0_5) = v0 & p(south, south, south, north, v0))
% 6.03/2.13 |
% 6.03/2.13 | Instantiating (33) with all_44_0_11 yields:
% 6.03/2.13 | (34) take_goat(all_27_0_5) = all_44_0_11 & p(south, south, south, north, all_44_0_11)
% 6.03/2.13 |
% 6.03/2.13 | Applying alpha-rule on (34) yields:
% 6.03/2.13 | (35) take_goat(all_27_0_5) = all_44_0_11
% 6.03/2.13 | (36) p(south, south, south, north, all_44_0_11)
% 6.03/2.13 |
% 6.03/2.13 | Instantiating formula (14) with all_44_0_11 and discharging atoms p(south, south, south, north, all_44_0_11), yields:
% 6.03/2.13 | (37) ? [v0] : (take_wolf(all_44_0_11) = v0 & p(north, north, south, north, v0))
% 6.03/2.13 |
% 6.03/2.13 | Instantiating (37) with all_73_0_23 yields:
% 6.03/2.13 | (38) take_wolf(all_44_0_11) = all_73_0_23 & p(north, north, south, north, all_73_0_23)
% 6.03/2.13 |
% 6.03/2.13 | Applying alpha-rule on (38) yields:
% 6.03/2.13 | (39) take_wolf(all_44_0_11) = all_73_0_23
% 6.03/2.13 | (40) p(north, north, south, north, all_73_0_23)
% 6.03/2.13 |
% 6.03/2.13 | Instantiating formula (10) with all_73_0_23 and discharging atoms p(north, north, south, north, all_73_0_23), yields:
% 6.03/2.13 | (41) ? [v0] : (go_alone(all_73_0_23) = v0 & p(south, north, south, north, v0))
% 6.03/2.14 |
% 6.03/2.14 | Instantiating (41) with all_118_0_43 yields:
% 6.03/2.14 | (42) go_alone(all_73_0_23) = all_118_0_43 & p(south, north, south, north, all_118_0_43)
% 6.03/2.14 |
% 6.03/2.14 | Applying alpha-rule on (42) yields:
% 6.03/2.14 | (43) go_alone(all_73_0_23) = all_118_0_43
% 6.03/2.14 | (44) p(south, north, south, north, all_118_0_43)
% 6.03/2.14 |
% 6.03/2.14 | Instantiating formula (2) with all_118_0_43, north, north and discharging atoms p(south, north, south, north, all_118_0_43), yields:
% 6.03/2.14 | (45) ? [v0] : (take_goat(all_118_0_43) = v0 & p(north, north, north, north, v0))
% 6.03/2.14 |
% 6.03/2.14 | Instantiating (45) with all_237_0_100 yields:
% 6.03/2.14 | (46) take_goat(all_118_0_43) = all_237_0_100 & p(north, north, north, north, all_237_0_100)
% 6.03/2.14 |
% 6.03/2.14 | Applying alpha-rule on (46) yields:
% 6.03/2.14 | (47) take_goat(all_118_0_43) = all_237_0_100
% 6.03/2.14 | (48) p(north, north, north, north, all_237_0_100)
% 6.03/2.14 |
% 6.03/2.14 | Instantiating formula (4) with all_237_0_100 and discharging atoms p(north, north, north, north, all_237_0_100), yields:
% 6.03/2.14 | (49) $false
% 6.03/2.14 |
% 6.03/2.14 |-The branch is then unsatisfiable
% 6.03/2.14 % SZS output end Proof for theBenchmark
% 6.03/2.14
% 6.03/2.14 1504ms
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