TSTP Solution File: SET622+3 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET622+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.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 : 300s
% DateTime : Thu Aug 31 15:25:41 EDT 2023
% Result : Theorem 6.57s 1.59s
% Output : Proof 8.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET622+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 09:52:08 EDT 2023
% 0.21/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.30/0.99 Prover 4: Preprocessing ...
% 2.30/0.99 Prover 1: Preprocessing ...
% 2.30/1.04 Prover 3: Preprocessing ...
% 2.30/1.04 Prover 2: Preprocessing ...
% 2.30/1.04 Prover 5: Preprocessing ...
% 2.30/1.04 Prover 6: Preprocessing ...
% 2.82/1.05 Prover 0: Preprocessing ...
% 4.93/1.36 Prover 3: Warning: ignoring some quantifiers
% 4.93/1.37 Prover 5: Proving ...
% 4.93/1.37 Prover 3: Constructing countermodel ...
% 4.93/1.38 Prover 6: Proving ...
% 4.93/1.38 Prover 1: Warning: ignoring some quantifiers
% 4.93/1.40 Prover 1: Constructing countermodel ...
% 4.93/1.42 Prover 0: Proving ...
% 5.54/1.43 Prover 4: Warning: ignoring some quantifiers
% 5.54/1.45 Prover 2: Proving ...
% 5.72/1.47 Prover 4: Constructing countermodel ...
% 6.57/1.59 Prover 3: proved (958ms)
% 6.57/1.59
% 6.57/1.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.57/1.59
% 6.57/1.59 Prover 0: stopped
% 6.57/1.59 Prover 6: stopped
% 6.57/1.59 Prover 2: stopped
% 6.57/1.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.57/1.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.57/1.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.57/1.60 Prover 5: stopped
% 6.57/1.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.57/1.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.57/1.63 Prover 13: Preprocessing ...
% 6.57/1.64 Prover 8: Preprocessing ...
% 7.14/1.64 Prover 11: Preprocessing ...
% 7.14/1.65 Prover 1: Found proof (size 22)
% 7.14/1.65 Prover 1: proved (1020ms)
% 7.14/1.65 Prover 10: Preprocessing ...
% 7.14/1.65 Prover 7: Preprocessing ...
% 7.14/1.66 Prover 4: stopped
% 7.35/1.67 Prover 11: stopped
% 7.35/1.67 Prover 10: stopped
% 7.35/1.68 Prover 7: stopped
% 7.35/1.68 Prover 13: stopped
% 7.35/1.72 Prover 8: Warning: ignoring some quantifiers
% 7.63/1.73 Prover 8: Constructing countermodel ...
% 7.63/1.74 Prover 8: stopped
% 7.63/1.74
% 7.63/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.63/1.74
% 7.63/1.74 % SZS output start Proof for theBenchmark
% 7.63/1.75 Assumptions after simplification:
% 7.63/1.75 ---------------------------------
% 7.63/1.75
% 7.63/1.75 (associativity_of_intersection)
% 7.74/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 7.74/1.78 (intersection(v3, v2) = v4) | ~ (intersection(v0, v1) = v3) | ~ $i(v2) |
% 7.74/1.78 ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (intersection(v1, v2) = v5 &
% 7.74/1.78 intersection(v0, v5) = v4 & $i(v5) & $i(v4)))
% 7.74/1.78
% 7.74/1.78 (commutativity_of_intersection)
% 7.74/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~
% 7.74/1.78 $i(v1) | ~ $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 7.74/1.78
% 7.74/1.78 (commutativity_of_symmetric_difference)
% 7.74/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) =
% 7.74/1.78 v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v1, v0) = v2 &
% 7.74/1.78 $i(v2)))
% 7.74/1.78
% 7.74/1.78 (commutativity_of_union)
% 7.74/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1)
% 7.74/1.78 | ~ $i(v0) | (union(v1, v0) = v2 & $i(v2)))
% 7.74/1.78
% 7.74/1.78 (difference_difference_union2)
% 7.74/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 7.74/1.78 $i] : ( ~ (union(v3, v4) = v5) | ~ (difference(v0, v1) = v3) | ~
% 7.74/1.78 (intersection(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 7.74/1.78 $i] : (difference(v1, v2) = v6 & difference(v0, v6) = v5 & $i(v6) &
% 7.74/1.78 $i(v5)))
% 7.74/1.78
% 7.74/1.78 (prove_th98)
% 7.74/1.79 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.74/1.79 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ( ~ (v9 = v4)
% 7.74/1.79 & symmetric_difference(v1, v2) = v3 & union(v6, v8) = v9 & union(v1, v2) =
% 7.74/1.79 v5 & difference(v0, v5) = v6 & difference(v0, v3) = v4 & intersection(v7,
% 7.74/1.79 v2) = v8 & intersection(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 7.74/1.79 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.74/1.79
% 7.74/1.79 (symmetric_difference_and_difference)
% 7.74/1.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 7.74/1.79 (union(v0, v1) = v2) | ~ (difference(v2, v3) = v4) | ~ (intersection(v0,
% 7.74/1.79 v1) = v3) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) = v4 &
% 7.74/1.79 $i(v4)))
% 7.74/1.79
% 7.74/1.79 (function-axioms)
% 7.74/1.80 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.74/1.80 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 7.74/1.80 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.74/1.80 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 7.74/1.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.74/1.80 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) =
% 7.74/1.80 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 7.74/1.80 ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 7.74/1.80 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) |
% 7.74/1.80 ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 7.74/1.80 [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3,
% 7.74/1.80 v2) = v0))
% 7.74/1.80
% 7.74/1.80 Further assumptions not needed in the proof:
% 7.74/1.80 --------------------------------------------
% 7.74/1.80 difference_defn, equal_defn, equal_member_defn, intersection_defn,
% 7.74/1.80 reflexivity_of_subset, subset_defn, symmetric_difference_defn, union_defn
% 7.74/1.80
% 7.74/1.80 Those formulas are unsatisfiable:
% 7.74/1.80 ---------------------------------
% 7.74/1.80
% 7.74/1.80 Begin of proof
% 7.74/1.80 |
% 7.74/1.80 | ALPHA: (function-axioms) implies:
% 7.74/1.80 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.74/1.80 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 7.74/1.80 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.74/1.80 | (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3,
% 7.74/1.80 | v2) = v0))
% 7.74/1.80 |
% 7.74/1.80 | DELTA: instantiating (prove_th98) with fresh symbols all_17_0, all_17_1,
% 7.74/1.80 | all_17_2, all_17_3, all_17_4, all_17_5, all_17_6, all_17_7, all_17_8,
% 7.74/1.80 | all_17_9 gives:
% 7.74/1.81 | (3) ~ (all_17_0 = all_17_5) & symmetric_difference(all_17_8, all_17_7) =
% 7.74/1.81 | all_17_6 & union(all_17_3, all_17_1) = all_17_0 & union(all_17_8,
% 7.74/1.81 | all_17_7) = all_17_4 & difference(all_17_9, all_17_4) = all_17_3 &
% 7.74/1.81 | difference(all_17_9, all_17_6) = all_17_5 & intersection(all_17_2,
% 7.74/1.81 | all_17_7) = all_17_1 & intersection(all_17_9, all_17_8) = all_17_2 &
% 7.74/1.81 | $i(all_17_0) & $i(all_17_1) & $i(all_17_2) & $i(all_17_3) &
% 7.74/1.81 | $i(all_17_4) & $i(all_17_5) & $i(all_17_6) & $i(all_17_7) &
% 7.74/1.81 | $i(all_17_8) & $i(all_17_9)
% 7.74/1.81 |
% 7.74/1.81 | ALPHA: (3) implies:
% 7.74/1.81 | (4) ~ (all_17_0 = all_17_5)
% 7.74/1.81 | (5) $i(all_17_9)
% 7.74/1.81 | (6) $i(all_17_8)
% 7.74/1.81 | (7) $i(all_17_7)
% 7.74/1.81 | (8) intersection(all_17_9, all_17_8) = all_17_2
% 7.74/1.81 | (9) intersection(all_17_2, all_17_7) = all_17_1
% 7.74/1.81 | (10) difference(all_17_9, all_17_6) = all_17_5
% 7.74/1.81 | (11) difference(all_17_9, all_17_4) = all_17_3
% 7.74/1.81 | (12) union(all_17_8, all_17_7) = all_17_4
% 7.74/1.81 | (13) union(all_17_3, all_17_1) = all_17_0
% 7.74/1.81 | (14) symmetric_difference(all_17_8, all_17_7) = all_17_6
% 7.74/1.81 |
% 7.74/1.81 | GROUND_INST: instantiating (associativity_of_intersection) with all_17_9,
% 7.74/1.81 | all_17_8, all_17_7, all_17_2, all_17_1, simplifying with (5),
% 7.74/1.81 | (6), (7), (8), (9) gives:
% 7.74/1.81 | (15) ? [v0: $i] : (intersection(all_17_8, all_17_7) = v0 &
% 7.74/1.81 | intersection(all_17_9, v0) = all_17_1 & $i(v0) & $i(all_17_1))
% 7.74/1.81 |
% 7.74/1.81 | GROUND_INST: instantiating (commutativity_of_union) with all_17_8, all_17_7,
% 7.74/1.81 | all_17_4, simplifying with (6), (7), (12) gives:
% 7.74/1.81 | (16) union(all_17_7, all_17_8) = all_17_4 & $i(all_17_4)
% 7.74/1.81 |
% 7.74/1.81 | ALPHA: (16) implies:
% 7.74/1.81 | (17) $i(all_17_4)
% 7.74/1.81 | (18) union(all_17_7, all_17_8) = all_17_4
% 7.74/1.81 |
% 7.74/1.81 | GROUND_INST: instantiating (commutativity_of_symmetric_difference) with
% 7.74/1.81 | all_17_8, all_17_7, all_17_6, simplifying with (6), (7), (14)
% 7.74/1.81 | gives:
% 7.74/1.81 | (19) symmetric_difference(all_17_7, all_17_8) = all_17_6 & $i(all_17_6)
% 7.74/1.81 |
% 7.74/1.81 | ALPHA: (19) implies:
% 7.74/1.81 | (20) symmetric_difference(all_17_7, all_17_8) = all_17_6
% 7.74/1.81 |
% 7.74/1.81 | DELTA: instantiating (15) with fresh symbol all_25_0 gives:
% 7.74/1.81 | (21) intersection(all_17_8, all_17_7) = all_25_0 & intersection(all_17_9,
% 7.74/1.81 | all_25_0) = all_17_1 & $i(all_25_0) & $i(all_17_1)
% 7.74/1.81 |
% 7.74/1.81 | ALPHA: (21) implies:
% 7.74/1.81 | (22) $i(all_25_0)
% 7.74/1.82 | (23) intersection(all_17_9, all_25_0) = all_17_1
% 7.74/1.82 | (24) intersection(all_17_8, all_17_7) = all_25_0
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (difference_difference_union2) with all_17_9,
% 7.74/1.82 | all_17_4, all_25_0, all_17_3, all_17_1, all_17_0, simplifying
% 7.74/1.82 | with (5), (11), (13), (17), (22), (23) gives:
% 7.74/1.82 | (25) ? [v0: $i] : (difference(all_17_4, all_25_0) = v0 &
% 7.74/1.82 | difference(all_17_9, v0) = all_17_0 & $i(v0) & $i(all_17_0))
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (commutativity_of_intersection) with all_17_8,
% 7.74/1.82 | all_17_7, all_25_0, simplifying with (6), (7), (24) gives:
% 7.74/1.82 | (26) intersection(all_17_7, all_17_8) = all_25_0 & $i(all_25_0)
% 7.74/1.82 |
% 7.74/1.82 | ALPHA: (26) implies:
% 7.74/1.82 | (27) intersection(all_17_7, all_17_8) = all_25_0
% 7.74/1.82 |
% 7.74/1.82 | DELTA: instantiating (25) with fresh symbol all_33_0 gives:
% 7.74/1.82 | (28) difference(all_17_4, all_25_0) = all_33_0 & difference(all_17_9,
% 7.74/1.82 | all_33_0) = all_17_0 & $i(all_33_0) & $i(all_17_0)
% 7.74/1.82 |
% 7.74/1.82 | ALPHA: (28) implies:
% 7.74/1.82 | (29) difference(all_17_9, all_33_0) = all_17_0
% 7.74/1.82 | (30) difference(all_17_4, all_25_0) = all_33_0
% 7.74/1.82 |
% 7.74/1.82 | GROUND_INST: instantiating (symmetric_difference_and_difference) with
% 7.74/1.82 | all_17_7, all_17_8, all_17_4, all_25_0, all_33_0, simplifying
% 7.74/1.82 | with (6), (7), (18), (27), (30) gives:
% 8.09/1.82 | (31) symmetric_difference(all_17_7, all_17_8) = all_33_0 & $i(all_33_0)
% 8.09/1.82 |
% 8.09/1.82 | ALPHA: (31) implies:
% 8.09/1.82 | (32) symmetric_difference(all_17_7, all_17_8) = all_33_0
% 8.09/1.82 |
% 8.09/1.82 | GROUND_INST: instantiating (2) with all_17_6, all_33_0, all_17_8, all_17_7,
% 8.09/1.82 | simplifying with (20), (32) gives:
% 8.09/1.82 | (33) all_33_0 = all_17_6
% 8.09/1.82 |
% 8.09/1.82 | REDUCE: (29), (33) imply:
% 8.09/1.82 | (34) difference(all_17_9, all_17_6) = all_17_0
% 8.09/1.82 |
% 8.09/1.82 | GROUND_INST: instantiating (1) with all_17_5, all_17_0, all_17_6, all_17_9,
% 8.09/1.82 | simplifying with (10), (34) gives:
% 8.09/1.82 | (35) all_17_0 = all_17_5
% 8.09/1.82 |
% 8.09/1.82 | REDUCE: (4), (35) imply:
% 8.09/1.82 | (36) $false
% 8.09/1.82 |
% 8.09/1.82 | CLOSE: (36) is inconsistent.
% 8.09/1.82 |
% 8.09/1.82 End of proof
% 8.09/1.82 % SZS output end Proof for theBenchmark
% 8.09/1.82
% 8.09/1.82 1213ms
%------------------------------------------------------------------------------