TSTP Solution File: MSC012+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : Sun Jul 17 22:40:03 EDT 2022
% Result : Theorem 9.67s 2.93s
% Output : Proof 27.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Fri Jul 1 16:57:37 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.49/0.57 ____ _
% 0.49/0.57 ___ / __ \_____(_)___ ________ __________
% 0.49/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.57
% 0.49/0.57 A Theorem Prover for First-Order Logic
% 0.49/0.57 (ePrincess v.1.0)
% 0.49/0.57
% 0.49/0.57 (c) Philipp Rümmer, 2009-2015
% 0.49/0.57 (c) Peter Backeman, 2014-2015
% 0.49/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.57 Bug reports to peter@backeman.se
% 0.49/0.57
% 0.49/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.57
% 0.49/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.27/0.85 Prover 0: Preprocessing ...
% 1.27/0.90 Prover 0: Warning: ignoring some quantifiers
% 1.27/0.92 Prover 0: Constructing countermodel ...
% 1.62/1.02 Prover 0: gave up
% 1.62/1.02 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.62/1.03 Prover 1: Preprocessing ...
% 1.99/1.09 Prover 1: Warning: ignoring some quantifiers
% 1.99/1.09 Prover 1: Constructing countermodel ...
% 1.99/1.11 Prover 1: gave up
% 1.99/1.11 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.99/1.12 Prover 2: Preprocessing ...
% 2.25/1.16 Prover 2: Warning: ignoring some quantifiers
% 2.25/1.16 Prover 2: Constructing countermodel ...
% 2.60/1.30 Prover 2: gave up
% 2.60/1.30 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.60/1.31 Prover 3: Preprocessing ...
% 2.60/1.32 Prover 3: Warning: ignoring some quantifiers
% 2.60/1.32 Prover 3: Constructing countermodel ...
% 2.60/1.34 Prover 3: gave up
% 2.60/1.34 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.89/1.34 Prover 4: Preprocessing ...
% 2.98/1.38 Prover 4: Warning: ignoring some quantifiers
% 2.98/1.38 Prover 4: Constructing countermodel ...
% 5.39/1.95 Prover 4: gave up
% 5.39/1.95 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.39/1.95 Prover 5: Preprocessing ...
% 5.39/1.97 Prover 5: Warning: ignoring some quantifiers
% 5.39/1.97 Prover 5: Constructing countermodel ...
% 5.59/2.03 Prover 5: gave up
% 5.59/2.03 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.59/2.03 Prover 6: Preprocessing ...
% 5.85/2.05 Prover 6: Warning: ignoring some quantifiers
% 5.85/2.05 Prover 6: Constructing countermodel ...
% 5.94/2.08 Prover 6: gave up
% 5.94/2.09 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.94/2.09 Prover 7: Preprocessing ...
% 5.94/2.10 Prover 7: Proving ...
% 9.67/2.93 Prover 7: proved (844ms)
% 9.67/2.93
% 9.67/2.93 % SZS status Theorem for theBenchmark
% 9.67/2.93
% 9.67/2.93 Generating proof ... found it (size 59)
% 26.61/7.92
% 26.61/7.92 % SZS output start Proof for theBenchmark
% 26.61/7.92 Assumed formulas after preprocessing and simplification:
% 26.61/7.92 | (0) ~ goal & ! [v0] : ! [v1] : ! [v2] : ( ~ less(v1, v2) | ~ less(v0, v1) | less(v0, v2)) & ! [v0] : ! [v1] : ( ~ less(v0, v1) | ~ p(v1) | ~ p(v0)) & ! [v0] : (p(v0) | ? [v1] : (less(v0, v1) & p(v1))) & ! [v0] : ? [v1] : less(v0, v1)
% 26.61/7.92 | Applying alpha-rule on (0) yields:
% 26.61/7.92 | (1) ! [v0] : ! [v1] : ( ~ less(v0, v1) | ~ p(v1) | ~ p(v0))
% 26.61/7.92 | (2) ~ goal
% 26.61/7.92 | (3) ! [v0] : ? [v1] : less(v0, v1)
% 26.61/7.92 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ less(v1, v2) | ~ less(v0, v1) | less(v0, v2))
% 26.61/7.92 | (5) ! [v0] : (p(v0) | ? [v1] : (less(v0, v1) & p(v1)))
% 26.61/7.92 |
% 26.61/7.92 | Introducing new symbol ex_8_0_0 defined by:
% 26.61/7.92 | (6) ex_8_0_0 = arbitrary_constant
% 26.61/7.92 |
% 26.61/7.93 | Instantiating formula (5) with ex_8_0_0 yields:
% 26.61/7.93 | (7) p(ex_8_0_0) | ? [v0] : (less(ex_8_0_0, v0) & p(v0))
% 26.61/7.93 |
% 26.61/7.93 +-Applying beta-rule and splitting (7), into two cases.
% 26.61/7.93 |-Branch one:
% 26.61/7.93 | (8) p(ex_8_0_0)
% 26.61/7.93 |
% 26.61/7.93 | Introducing new symbol ex_17_0_2 defined by:
% 26.61/7.93 | (9) ex_17_0_2 = arbitrary_constant
% 26.61/7.93 |
% 26.61/7.93 | Instantiating formula (3) with ex_17_0_2 yields:
% 26.61/7.93 | (10) ? [v0] : less(ex_17_0_2, v0)
% 26.61/7.93 |
% 26.61/7.93 | Instantiating (10) with all_18_0_3 yields:
% 26.61/7.93 | (11) less(ex_17_0_2, all_18_0_3)
% 26.61/7.93 |
% 26.61/7.93 | Introducing new symbol ex_30_0_4 defined by:
% 26.61/7.93 | (12) ex_30_0_4 = all_18_0_3
% 26.61/7.93 |
% 26.61/7.93 | Instantiating formula (5) with ex_30_0_4 yields:
% 26.61/7.93 | (13) p(ex_30_0_4) | ? [v0] : (less(ex_30_0_4, v0) & p(v0))
% 26.61/7.93 |
% 26.61/7.93 +-Applying beta-rule and splitting (13), into two cases.
% 26.61/7.93 |-Branch one:
% 26.61/7.93 | (14) p(ex_30_0_4)
% 26.61/7.93 |
% 26.61/7.93 | Instantiating formula (1) with ex_30_0_4, ex_8_0_0 and discharging atoms p(ex_30_0_4), p(ex_8_0_0), yields:
% 26.61/7.93 | (15) ~ less(ex_8_0_0, ex_30_0_4)
% 26.61/7.93 |
% 26.61/7.93 | From (9) and (11) follows:
% 26.61/7.93 | (16) less(arbitrary_constant, all_18_0_3)
% 26.61/7.93 |
% 26.61/7.93 | From (6)(12) and (15) follows:
% 26.61/7.93 | (17) ~ less(arbitrary_constant, all_18_0_3)
% 27.00/7.93 |
% 27.00/7.93 | Using (16) and (17) yields:
% 27.00/7.93 | (18) $false
% 27.00/7.93 |
% 27.00/7.93 |-The branch is then unsatisfiable
% 27.00/7.93 |-Branch two:
% 27.00/7.93 | (19) ? [v0] : (less(ex_30_0_4, v0) & p(v0))
% 27.00/7.93 |
% 27.00/7.93 | Instantiating (19) with all_32_0_5 yields:
% 27.00/7.93 | (20) less(ex_30_0_4, all_32_0_5) & p(all_32_0_5)
% 27.00/7.93 |
% 27.00/7.93 | Applying alpha-rule on (20) yields:
% 27.00/7.93 | (21) less(ex_30_0_4, all_32_0_5)
% 27.00/7.93 | (22) p(all_32_0_5)
% 27.00/7.93 |
% 27.00/7.93 | Instantiating formula (1) with all_32_0_5, ex_8_0_0 and discharging atoms p(all_32_0_5), p(ex_8_0_0), yields:
% 27.00/7.93 | (23) ~ less(ex_8_0_0, all_32_0_5)
% 27.00/7.93 |
% 27.00/7.93 | Instantiating formula (4) with all_32_0_5, all_18_0_3, ex_17_0_2 and discharging atoms less(ex_17_0_2, all_18_0_3), yields:
% 27.00/7.93 | (24) ~ less(all_18_0_3, all_32_0_5) | less(ex_17_0_2, all_32_0_5)
% 27.00/7.93 |
% 27.00/7.93 +-Applying beta-rule and splitting (24), into two cases.
% 27.00/7.93 |-Branch one:
% 27.00/7.93 | (25) ~ less(all_18_0_3, all_32_0_5)
% 27.00/7.93 |
% 27.00/7.93 | From (12) and (21) follows:
% 27.00/7.93 | (26) less(all_18_0_3, all_32_0_5)
% 27.00/7.93 |
% 27.00/7.93 | Using (26) and (25) yields:
% 27.00/7.93 | (18) $false
% 27.00/7.93 |
% 27.00/7.93 |-The branch is then unsatisfiable
% 27.00/7.93 |-Branch two:
% 27.00/7.93 | (28) less(ex_17_0_2, all_32_0_5)
% 27.00/7.93 |
% 27.00/7.93 | From (9) and (28) follows:
% 27.00/7.93 | (29) less(arbitrary_constant, all_32_0_5)
% 27.00/7.93 |
% 27.00/7.94 | From (6) and (23) follows:
% 27.00/7.94 | (30) ~ less(arbitrary_constant, all_32_0_5)
% 27.00/7.94 |
% 27.00/7.94 | Using (29) and (30) yields:
% 27.00/7.94 | (18) $false
% 27.00/7.94 |
% 27.00/7.94 |-The branch is then unsatisfiable
% 27.00/7.94 |-Branch two:
% 27.00/7.94 | (32) ? [v0] : (less(ex_8_0_0, v0) & p(v0))
% 27.00/7.94 |
% 27.00/7.94 | Instantiating (32) with all_10_0_1 yields:
% 27.00/7.94 | (33) less(ex_8_0_0, all_10_0_1) & p(all_10_0_1)
% 27.00/7.94 |
% 27.00/7.94 | Applying alpha-rule on (33) yields:
% 27.00/7.94 | (34) less(ex_8_0_0, all_10_0_1)
% 27.00/7.94 | (35) p(all_10_0_1)
% 27.00/7.94 |
% 27.00/7.94 | Introducing new symbol ex_25_0_14 defined by:
% 27.00/7.94 | (36) ex_25_0_14 = all_10_0_1
% 27.00/7.94 |
% 27.00/7.94 | Instantiating formula (3) with ex_25_0_14 yields:
% 27.00/7.94 | (37) ? [v0] : less(ex_25_0_14, v0)
% 27.00/7.94 |
% 27.00/7.94 | Instantiating (37) with all_26_0_15 yields:
% 27.00/7.94 | (38) less(ex_25_0_14, all_26_0_15)
% 27.00/7.94 |
% 27.00/7.94 | Instantiating formula (4) with all_26_0_15, all_10_0_1, ex_8_0_0 and discharging atoms less(ex_8_0_0, all_10_0_1), yields:
% 27.00/7.94 | (39) ~ less(all_10_0_1, all_26_0_15) | less(ex_8_0_0, all_26_0_15)
% 27.00/7.94 |
% 27.00/7.94 +-Applying beta-rule and splitting (39), into two cases.
% 27.00/7.94 |-Branch one:
% 27.00/7.94 | (40) ~ less(all_10_0_1, all_26_0_15)
% 27.00/7.94 |
% 27.00/7.94 | From (36) and (38) follows:
% 27.00/7.94 | (41) less(all_10_0_1, all_26_0_15)
% 27.00/7.94 |
% 27.00/7.94 | Using (41) and (40) yields:
% 27.00/7.94 | (18) $false
% 27.00/7.94 |
% 27.00/7.94 |-The branch is then unsatisfiable
% 27.00/7.94 |-Branch two:
% 27.00/7.94 | (41) less(all_10_0_1, all_26_0_15)
% 27.00/7.94 | (44) less(ex_8_0_0, all_26_0_15)
% 27.00/7.94 |
% 27.00/7.94 | Introducing new symbol ex_52_0_16 defined by:
% 27.00/7.94 | (45) ex_52_0_16 = all_26_0_15
% 27.00/7.94 |
% 27.00/7.94 | Instantiating formula (5) with ex_52_0_16 yields:
% 27.00/7.94 | (46) p(ex_52_0_16) | ? [v0] : (less(ex_52_0_16, v0) & p(v0))
% 27.00/7.94 |
% 27.00/7.94 +-Applying beta-rule and splitting (46), into two cases.
% 27.00/7.94 |-Branch one:
% 27.00/7.94 | (47) p(ex_52_0_16)
% 27.00/7.94 |
% 27.00/7.94 | Instantiating formula (1) with ex_52_0_16, all_10_0_1 and discharging atoms p(ex_52_0_16), p(all_10_0_1), yields:
% 27.00/7.94 | (48) ~ less(all_10_0_1, ex_52_0_16)
% 27.00/7.94 |
% 27.00/7.94 | From (45) and (48) follows:
% 27.00/7.94 | (40) ~ less(all_10_0_1, all_26_0_15)
% 27.00/7.94 |
% 27.00/7.94 | Using (41) and (40) yields:
% 27.00/7.94 | (18) $false
% 27.00/7.94 |
% 27.00/7.94 |-The branch is then unsatisfiable
% 27.00/7.94 |-Branch two:
% 27.00/7.94 | (51) ? [v0] : (less(ex_52_0_16, v0) & p(v0))
% 27.00/7.94 |
% 27.00/7.94 | Instantiating (51) with all_54_0_17 yields:
% 27.00/7.94 | (52) less(ex_52_0_16, all_54_0_17) & p(all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 | Applying alpha-rule on (52) yields:
% 27.00/7.94 | (53) less(ex_52_0_16, all_54_0_17)
% 27.00/7.94 | (54) p(all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 | Instantiating formula (1) with all_54_0_17, all_10_0_1 and discharging atoms p(all_54_0_17), p(all_10_0_1), yields:
% 27.00/7.94 | (55) ~ less(all_10_0_1, all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 | Instantiating formula (4) with all_54_0_17, all_26_0_15, ex_25_0_14 and discharging atoms less(ex_25_0_14, all_26_0_15), yields:
% 27.00/7.94 | (56) ~ less(all_26_0_15, all_54_0_17) | less(ex_25_0_14, all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 | Instantiating formula (4) with all_54_0_17, all_26_0_15, ex_8_0_0 and discharging atoms less(ex_8_0_0, all_26_0_15), yields:
% 27.00/7.94 | (57) ~ less(all_26_0_15, all_54_0_17) | less(ex_8_0_0, all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 +-Applying beta-rule and splitting (57), into two cases.
% 27.00/7.94 |-Branch one:
% 27.00/7.94 | (58) ~ less(all_26_0_15, all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 | From (45) and (53) follows:
% 27.00/7.94 | (59) less(all_26_0_15, all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 | Using (59) and (58) yields:
% 27.00/7.94 | (18) $false
% 27.00/7.94 |
% 27.00/7.94 |-The branch is then unsatisfiable
% 27.00/7.94 |-Branch two:
% 27.00/7.94 | (59) less(all_26_0_15, all_54_0_17)
% 27.00/7.94 | (62) less(ex_8_0_0, all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 +-Applying beta-rule and splitting (56), into two cases.
% 27.00/7.94 |-Branch one:
% 27.00/7.94 | (58) ~ less(all_26_0_15, all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 | Using (59) and (58) yields:
% 27.00/7.94 | (18) $false
% 27.00/7.94 |
% 27.00/7.94 |-The branch is then unsatisfiable
% 27.00/7.94 |-Branch two:
% 27.00/7.94 | (65) less(ex_25_0_14, all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 | From (36) and (65) follows:
% 27.00/7.94 | (66) less(all_10_0_1, all_54_0_17)
% 27.00/7.94 |
% 27.00/7.94 | Using (66) and (55) yields:
% 27.00/7.94 | (18) $false
% 27.00/7.94 |
% 27.00/7.94 |-The branch is then unsatisfiable
% 27.00/7.94 % SZS output end Proof for theBenchmark
% 27.00/7.94
% 27.00/7.94 7363ms
%------------------------------------------------------------------------------