TSTP Solution File: SET621+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET621+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 : n026.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 6.45s 1.68s
% Output : Proof 8.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET621+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:05:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.19/1.03 Prover 1: Preprocessing ...
% 2.19/1.03 Prover 4: Preprocessing ...
% 2.67/1.08 Prover 5: Preprocessing ...
% 2.67/1.08 Prover 0: Preprocessing ...
% 2.67/1.08 Prover 3: Preprocessing ...
% 2.67/1.08 Prover 2: Preprocessing ...
% 2.67/1.08 Prover 6: Preprocessing ...
% 4.53/1.42 Prover 1: Warning: ignoring some quantifiers
% 4.53/1.43 Prover 3: Warning: ignoring some quantifiers
% 4.53/1.46 Prover 3: Constructing countermodel ...
% 4.53/1.46 Prover 5: Proving ...
% 4.53/1.46 Prover 6: Proving ...
% 4.53/1.46 Prover 1: Constructing countermodel ...
% 4.53/1.47 Prover 4: Warning: ignoring some quantifiers
% 4.53/1.49 Prover 4: Constructing countermodel ...
% 4.53/1.51 Prover 2: Proving ...
% 4.53/1.52 Prover 0: Proving ...
% 6.45/1.68 Prover 3: proved (1031ms)
% 6.45/1.68
% 6.45/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.45/1.68
% 6.45/1.68 Prover 0: stopped
% 6.45/1.68 Prover 6: stopped
% 6.45/1.69 Prover 2: stopped
% 6.45/1.69 Prover 5: stopped
% 6.45/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.45/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.45/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.45/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.45/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.45/1.71 Prover 8: Preprocessing ...
% 6.45/1.72 Prover 7: Preprocessing ...
% 6.45/1.72 Prover 10: Preprocessing ...
% 6.93/1.73 Prover 11: Preprocessing ...
% 6.93/1.74 Prover 13: Preprocessing ...
% 7.22/1.79 Prover 1: Found proof (size 28)
% 7.22/1.79 Prover 1: proved (1153ms)
% 7.22/1.79 Prover 4: stopped
% 7.22/1.80 Prover 13: stopped
% 7.22/1.80 Prover 7: Warning: ignoring some quantifiers
% 7.22/1.80 Prover 8: Warning: ignoring some quantifiers
% 7.22/1.80 Prover 10: Warning: ignoring some quantifiers
% 7.22/1.81 Prover 7: Constructing countermodel ...
% 7.22/1.81 Prover 8: Constructing countermodel ...
% 7.22/1.81 Prover 8: stopped
% 7.22/1.81 Prover 7: stopped
% 7.22/1.82 Prover 10: Constructing countermodel ...
% 7.22/1.82 Prover 10: stopped
% 7.73/1.85 Prover 11: Warning: ignoring some quantifiers
% 7.73/1.85 Prover 11: Constructing countermodel ...
% 7.73/1.86 Prover 11: stopped
% 7.73/1.86
% 7.73/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.73/1.86
% 7.90/1.87 % SZS output start Proof for theBenchmark
% 7.90/1.87 Assumptions after simplification:
% 7.90/1.87 ---------------------------------
% 7.90/1.87
% 7.90/1.87 (commutativity_of_union)
% 7.90/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1)
% 7.90/1.90 | ~ $i(v0) | (union(v1, v0) = v2 & $i(v2)))
% 7.90/1.90
% 7.90/1.90 (difference_difference_union)
% 7.90/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 7.90/1.91 (difference(v0, v3) = v4) | ~ (union(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 7.90/1.91 | ~ $i(v0) | ? [v5: $i] : (difference(v5, v2) = v4 & difference(v0, v1) =
% 7.90/1.91 v5 & $i(v5) & $i(v4)))
% 7.90/1.91
% 7.90/1.91 (difference_distributes_over_union)
% 7.90/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 7.90/1.91 $i] : ( ~ (difference(v1, v2) = v4) | ~ (difference(v0, v2) = v3) | ~
% 7.90/1.91 (union(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] :
% 7.90/1.91 (difference(v6, v2) = v5 & union(v0, v1) = v6 & $i(v6) & $i(v5)))
% 7.90/1.91
% 7.90/1.91 (prove_th97)
% 7.90/1.91 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.90/1.91 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ( ~ (v9 = v4)
% 7.90/1.91 & difference(v3, v2) = v4 & difference(v1, v7) = v8 & difference(v0, v5) =
% 7.90/1.91 v6 & union(v6, v8) = v9 & union(v1, v2) = v5 & union(v0, v2) = v7 &
% 7.90/1.91 symmetric_difference(v0, v1) = v3 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 7.90/1.91 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.90/1.91
% 7.90/1.91 (symmetric_difference_defn)
% 7.90/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 7.90/1.92 (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3)
% 7.90/1.92 = v4) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) = v4 &
% 7.90/1.92 $i(v4)))
% 7.90/1.92
% 7.90/1.92 (function-axioms)
% 7.90/1.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.90/1.92 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 7.90/1.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.90/1.92 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 7.90/1.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.90/1.92 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 7.90/1.92 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 7.90/1.92 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.90/1.92 $i] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~
% 7.90/1.92 (symmetric_difference(v3, v2) = v0))
% 7.90/1.92
% 7.90/1.92 Further assumptions not needed in the proof:
% 7.90/1.92 --------------------------------------------
% 7.90/1.92 commutativity_of_symmetric_difference, difference_defn, equal_defn,
% 7.90/1.92 equal_member_defn, reflexivity_of_subset, subset_defn, union_defn
% 7.90/1.92
% 7.90/1.92 Those formulas are unsatisfiable:
% 7.90/1.92 ---------------------------------
% 7.90/1.92
% 7.90/1.92 Begin of proof
% 7.90/1.92 |
% 7.90/1.92 | ALPHA: (function-axioms) implies:
% 7.90/1.93 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.90/1.93 | (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3,
% 7.90/1.93 | v2) = v0))
% 7.90/1.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.90/1.93 | (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 7.90/1.93 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.90/1.93 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 7.90/1.93 |
% 7.90/1.93 | DELTA: instantiating (prove_th97) with fresh symbols all_14_0, all_14_1,
% 7.90/1.93 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6, all_14_7, all_14_8,
% 7.90/1.93 | all_14_9 gives:
% 8.21/1.93 | (4) ~ (all_14_0 = all_14_5) & difference(all_14_6, all_14_7) = all_14_5 &
% 8.21/1.93 | difference(all_14_8, all_14_2) = all_14_1 & difference(all_14_9,
% 8.21/1.93 | all_14_4) = all_14_3 & union(all_14_3, all_14_1) = all_14_0 &
% 8.21/1.93 | union(all_14_8, all_14_7) = all_14_4 & union(all_14_9, all_14_7) =
% 8.21/1.93 | all_14_2 & symmetric_difference(all_14_9, all_14_8) = all_14_6 &
% 8.21/1.93 | $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & $i(all_14_3) &
% 8.21/1.93 | $i(all_14_4) & $i(all_14_5) & $i(all_14_6) & $i(all_14_7) &
% 8.21/1.93 | $i(all_14_8) & $i(all_14_9)
% 8.21/1.93 |
% 8.21/1.93 | ALPHA: (4) implies:
% 8.21/1.94 | (5) ~ (all_14_0 = all_14_5)
% 8.21/1.94 | (6) $i(all_14_9)
% 8.21/1.94 | (7) $i(all_14_8)
% 8.21/1.94 | (8) $i(all_14_7)
% 8.21/1.94 | (9) $i(all_14_3)
% 8.21/1.94 | (10) $i(all_14_1)
% 8.21/1.94 | (11) symmetric_difference(all_14_9, all_14_8) = all_14_6
% 8.21/1.94 | (12) union(all_14_9, all_14_7) = all_14_2
% 8.21/1.94 | (13) union(all_14_8, all_14_7) = all_14_4
% 8.21/1.94 | (14) union(all_14_3, all_14_1) = all_14_0
% 8.21/1.94 | (15) difference(all_14_9, all_14_4) = all_14_3
% 8.21/1.94 | (16) difference(all_14_8, all_14_2) = all_14_1
% 8.21/1.94 | (17) difference(all_14_6, all_14_7) = all_14_5
% 8.21/1.94 |
% 8.21/1.94 | GROUND_INST: instantiating (commutativity_of_union) with all_14_3, all_14_1,
% 8.21/1.94 | all_14_0, simplifying with (9), (10), (14) gives:
% 8.21/1.94 | (18) union(all_14_1, all_14_3) = all_14_0 & $i(all_14_0)
% 8.21/1.94 |
% 8.21/1.94 | ALPHA: (18) implies:
% 8.21/1.94 | (19) union(all_14_1, all_14_3) = all_14_0
% 8.21/1.94 |
% 8.21/1.94 | GROUND_INST: instantiating (difference_difference_union) with all_14_9,
% 8.21/1.94 | all_14_8, all_14_7, all_14_4, all_14_3, simplifying with (6),
% 8.21/1.94 | (7), (8), (13), (15) gives:
% 8.21/1.94 | (20) ? [v0: $i] : (difference(v0, all_14_7) = all_14_3 &
% 8.21/1.94 | difference(all_14_9, all_14_8) = v0 & $i(v0) & $i(all_14_3))
% 8.21/1.94 |
% 8.21/1.94 | GROUND_INST: instantiating (difference_difference_union) with all_14_8,
% 8.21/1.94 | all_14_9, all_14_7, all_14_2, all_14_1, simplifying with (6),
% 8.21/1.94 | (7), (8), (12), (16) gives:
% 8.21/1.94 | (21) ? [v0: $i] : (difference(v0, all_14_7) = all_14_1 &
% 8.21/1.94 | difference(all_14_8, all_14_9) = v0 & $i(v0) & $i(all_14_1))
% 8.21/1.94 |
% 8.21/1.94 | DELTA: instantiating (20) with fresh symbol all_22_0 gives:
% 8.21/1.94 | (22) difference(all_22_0, all_14_7) = all_14_3 & difference(all_14_9,
% 8.21/1.94 | all_14_8) = all_22_0 & $i(all_22_0) & $i(all_14_3)
% 8.21/1.94 |
% 8.21/1.94 | ALPHA: (22) implies:
% 8.21/1.95 | (23) $i(all_22_0)
% 8.21/1.95 | (24) difference(all_14_9, all_14_8) = all_22_0
% 8.21/1.95 | (25) difference(all_22_0, all_14_7) = all_14_3
% 8.21/1.95 |
% 8.21/1.95 | DELTA: instantiating (21) with fresh symbol all_24_0 gives:
% 8.21/1.95 | (26) difference(all_24_0, all_14_7) = all_14_1 & difference(all_14_8,
% 8.21/1.95 | all_14_9) = all_24_0 & $i(all_24_0) & $i(all_14_1)
% 8.21/1.95 |
% 8.21/1.95 | ALPHA: (26) implies:
% 8.21/1.95 | (27) $i(all_24_0)
% 8.21/1.95 | (28) difference(all_14_8, all_14_9) = all_24_0
% 8.21/1.95 | (29) difference(all_24_0, all_14_7) = all_14_1
% 8.21/1.95 |
% 8.21/1.95 | GROUND_INST: instantiating (difference_distributes_over_union) with all_22_0,
% 8.21/1.95 | all_24_0, all_14_7, all_14_3, all_14_1, all_14_0, simplifying
% 8.21/1.95 | with (8), (14), (23), (25), (27), (29) gives:
% 8.21/1.95 | (30) ? [v0: $i] : (difference(v0, all_14_7) = all_14_0 & union(all_22_0,
% 8.21/1.95 | all_24_0) = v0 & $i(v0) & $i(all_14_0))
% 8.21/1.95 |
% 8.21/1.95 | GROUND_INST: instantiating (difference_distributes_over_union) with all_24_0,
% 8.21/1.95 | all_22_0, all_14_7, all_14_1, all_14_3, all_14_0, simplifying
% 8.21/1.95 | with (8), (19), (23), (25), (27), (29) gives:
% 8.21/1.95 | (31) ? [v0: $i] : (difference(v0, all_14_7) = all_14_0 & union(all_24_0,
% 8.21/1.95 | all_22_0) = v0 & $i(v0) & $i(all_14_0))
% 8.21/1.95 |
% 8.21/1.95 | DELTA: instantiating (31) with fresh symbol all_31_0 gives:
% 8.21/1.95 | (32) difference(all_31_0, all_14_7) = all_14_0 & union(all_24_0, all_22_0)
% 8.21/1.95 | = all_31_0 & $i(all_31_0) & $i(all_14_0)
% 8.21/1.95 |
% 8.21/1.95 | ALPHA: (32) implies:
% 8.21/1.95 | (33) union(all_24_0, all_22_0) = all_31_0
% 8.21/1.95 | (34) difference(all_31_0, all_14_7) = all_14_0
% 8.21/1.95 |
% 8.21/1.95 | DELTA: instantiating (30) with fresh symbol all_33_0 gives:
% 8.21/1.95 | (35) difference(all_33_0, all_14_7) = all_14_0 & union(all_22_0, all_24_0)
% 8.21/1.95 | = all_33_0 & $i(all_33_0) & $i(all_14_0)
% 8.21/1.95 |
% 8.21/1.95 | ALPHA: (35) implies:
% 8.21/1.95 | (36) union(all_22_0, all_24_0) = all_33_0
% 8.21/1.95 |
% 8.21/1.95 | GROUND_INST: instantiating (symmetric_difference_defn) with all_14_9,
% 8.21/1.95 | all_14_8, all_22_0, all_24_0, all_33_0, simplifying with (6),
% 8.21/1.95 | (7), (24), (28), (36) gives:
% 8.21/1.95 | (37) symmetric_difference(all_14_9, all_14_8) = all_33_0 & $i(all_33_0)
% 8.21/1.95 |
% 8.21/1.95 | ALPHA: (37) implies:
% 8.21/1.95 | (38) symmetric_difference(all_14_9, all_14_8) = all_33_0
% 8.21/1.95 |
% 8.21/1.95 | GROUND_INST: instantiating (commutativity_of_union) with all_22_0, all_24_0,
% 8.21/1.95 | all_33_0, simplifying with (23), (27), (36) gives:
% 8.21/1.95 | (39) union(all_24_0, all_22_0) = all_33_0 & $i(all_33_0)
% 8.21/1.95 |
% 8.21/1.95 | ALPHA: (39) implies:
% 8.21/1.95 | (40) union(all_24_0, all_22_0) = all_33_0
% 8.21/1.95 |
% 8.21/1.96 | GROUND_INST: instantiating (1) with all_14_6, all_33_0, all_14_8, all_14_9,
% 8.21/1.96 | simplifying with (11), (38) gives:
% 8.21/1.96 | (41) all_33_0 = all_14_6
% 8.21/1.96 |
% 8.21/1.96 | GROUND_INST: instantiating (2) with all_31_0, all_33_0, all_22_0, all_24_0,
% 8.21/1.96 | simplifying with (33), (40) gives:
% 8.21/1.96 | (42) all_33_0 = all_31_0
% 8.21/1.96 |
% 8.21/1.96 | COMBINE_EQS: (41), (42) imply:
% 8.21/1.96 | (43) all_31_0 = all_14_6
% 8.21/1.96 |
% 8.21/1.96 | REDUCE: (34), (43) imply:
% 8.21/1.96 | (44) difference(all_14_6, all_14_7) = all_14_0
% 8.21/1.96 |
% 8.21/1.96 | GROUND_INST: instantiating (3) with all_14_5, all_14_0, all_14_7, all_14_6,
% 8.21/1.96 | simplifying with (17), (44) gives:
% 8.21/1.96 | (45) all_14_0 = all_14_5
% 8.21/1.96 |
% 8.21/1.96 | REDUCE: (5), (45) imply:
% 8.21/1.96 | (46) $false
% 8.33/1.96 |
% 8.33/1.96 | CLOSE: (46) is inconsistent.
% 8.33/1.96 |
% 8.33/1.96 End of proof
% 8.33/1.96 % SZS output end Proof for theBenchmark
% 8.33/1.96
% 8.33/1.96 1338ms
%------------------------------------------------------------------------------