TSTP Solution File: SET620+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET620+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 : n015.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 15:25:40 EDT 2023
% Result : Theorem 7.69s 1.77s
% Output : Proof 10.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET620+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 : n015.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 15:54:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.27/1.00 Prover 4: Preprocessing ...
% 2.27/1.00 Prover 1: Preprocessing ...
% 2.27/1.04 Prover 5: Preprocessing ...
% 2.27/1.04 Prover 3: Preprocessing ...
% 2.27/1.04 Prover 6: Preprocessing ...
% 2.27/1.04 Prover 0: Preprocessing ...
% 2.27/1.04 Prover 2: Preprocessing ...
% 4.83/1.46 Prover 3: Warning: ignoring some quantifiers
% 4.83/1.46 Prover 5: Proving ...
% 4.83/1.47 Prover 1: Warning: ignoring some quantifiers
% 4.83/1.48 Prover 4: Warning: ignoring some quantifiers
% 4.83/1.48 Prover 6: Proving ...
% 4.83/1.49 Prover 3: Constructing countermodel ...
% 4.83/1.49 Prover 1: Constructing countermodel ...
% 4.83/1.51 Prover 4: Constructing countermodel ...
% 5.16/1.51 Prover 0: Proving ...
% 5.16/1.53 Prover 2: Proving ...
% 6.75/1.67 Prover 1: gave up
% 6.75/1.67 Prover 3: gave up
% 6.75/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.75/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.75/1.70 Prover 8: Preprocessing ...
% 7.26/1.73 Prover 7: Preprocessing ...
% 7.69/1.77 Prover 0: proved (1140ms)
% 7.69/1.77
% 7.69/1.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.69/1.77
% 7.69/1.78 Prover 6: stopped
% 7.69/1.78 Prover 5: stopped
% 7.69/1.78 Prover 2: stopped
% 7.69/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.69/1.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.69/1.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.69/1.80 Prover 8: Warning: ignoring some quantifiers
% 7.69/1.80 Prover 7: Warning: ignoring some quantifiers
% 7.69/1.80 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.69/1.81 Prover 8: Constructing countermodel ...
% 7.69/1.82 Prover 10: Preprocessing ...
% 7.69/1.82 Prover 11: Preprocessing ...
% 7.69/1.82 Prover 7: Constructing countermodel ...
% 7.69/1.83 Prover 13: Preprocessing ...
% 7.69/1.83 Prover 16: Preprocessing ...
% 8.32/1.88 Prover 10: Warning: ignoring some quantifiers
% 8.54/1.89 Prover 10: Constructing countermodel ...
% 8.85/1.93 Prover 13: Warning: ignoring some quantifiers
% 8.92/1.95 Prover 16: Warning: ignoring some quantifiers
% 8.92/1.97 Prover 16: Constructing countermodel ...
% 8.92/1.97 Prover 10: gave up
% 8.92/1.97 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 8.92/1.97 Prover 13: Constructing countermodel ...
% 8.92/1.98 Prover 8: gave up
% 8.92/1.99 Prover 19: Preprocessing ...
% 8.92/2.03 Prover 4: Found proof (size 69)
% 8.92/2.03 Prover 4: proved (1389ms)
% 8.92/2.03 Prover 7: stopped
% 8.92/2.03 Prover 13: stopped
% 8.92/2.04 Prover 16: stopped
% 8.92/2.06 Prover 11: Warning: ignoring some quantifiers
% 8.92/2.07 Prover 11: Constructing countermodel ...
% 8.92/2.08 Prover 11: stopped
% 8.92/2.10 Prover 19: Warning: ignoring some quantifiers
% 8.92/2.11 Prover 19: Constructing countermodel ...
% 9.56/2.11 Prover 19: stopped
% 9.56/2.11
% 9.56/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.56/2.11
% 9.56/2.14 % SZS output start Proof for theBenchmark
% 9.56/2.14 Assumptions after simplification:
% 9.56/2.14 ---------------------------------
% 9.56/2.14
% 9.56/2.14 (commutativity_of_intersection)
% 10.25/2.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~
% 10.25/2.17 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] :
% 10.25/2.17 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~
% 10.25/2.17 $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 10.25/2.17
% 10.25/2.17 (commutativity_of_symmetric_difference)
% 10.25/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, v0) =
% 10.25/2.18 v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) = v2 &
% 10.25/2.18 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.25/2.18 (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 10.25/2.18 (symmetric_difference(v1, v0) = v2 & $i(v2)))
% 10.25/2.18
% 10.25/2.18 (commutativity_of_union)
% 10.25/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ $i(v1)
% 10.25/2.18 | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] :
% 10.25/2.18 ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (union(v1, v0)
% 10.25/2.18 = v2 & $i(v2)))
% 10.25/2.18
% 10.25/2.18 (difference_distributes_over_union)
% 10.25/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.25/2.18 $i] : ( ~ (difference(v1, v2) = v4) | ~ (difference(v0, v2) = v3) | ~
% 10.25/2.18 (union(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] :
% 10.25/2.18 (difference(v6, v2) = v5 & union(v0, v1) = v6 & $i(v6) & $i(v5))) & ! [v0:
% 10.25/2.18 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 10.25/2.18 (difference(v3, v2) = v4) | ~ (union(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 10.25/2.19 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (difference(v1, v2) = v6 &
% 10.25/2.19 difference(v0, v2) = v5 & union(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 10.25/2.19
% 10.25/2.19 (difference_into_intersection)
% 10.25/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~
% 10.25/2.19 $i(v1) | ~ $i(v0) | ? [v3: $i] : (difference(v0, v2) = v3 & difference(v0,
% 10.25/2.19 v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.25/2.19 (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 10.25/2.19 (intersection(v0, v1) = v3 & difference(v0, v3) = v2 & $i(v3) & $i(v2)))
% 10.25/2.19
% 10.25/2.19 (prove_th96)
% 10.25/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.25/2.19 $i] : ( ~ (v5 = v2) & intersection(v0, v1) = v4 & symmetric_difference(v0,
% 10.25/2.19 v1) = v2 & difference(v3, v4) = v5 & union(v0, v1) = v3 & $i(v5) & $i(v4)
% 10.25/2.19 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.25/2.19
% 10.25/2.19 (symmetric_difference_defn)
% 10.25/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) =
% 10.25/2.20 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (difference(v1,
% 10.25/2.20 v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2 & $i(v4) &
% 10.25/2.20 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.25/2.20 (difference(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 10.25/2.20 $i] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 &
% 10.25/2.20 union(v4, v2) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : !
% 10.25/2.20 [v2: $i] : ( ~ (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 10.25/2.20 : ? [v4: $i] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4
% 10.25/2.20 & union(v2, v4) = v3 & $i(v4) & $i(v3)))
% 10.25/2.20
% 10.25/2.20 (function-axioms)
% 10.25/2.20 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.25/2.20 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 10.25/2.20 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.25/2.20 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 10.25/2.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.25/2.20 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: $i]
% 10.25/2.20 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.25/2.20 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) =
% 10.25/2.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 10.25/2.20 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] :
% 10.25/2.20 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) |
% 10.25/2.20 ~ (union(v3, v2) = v0))
% 10.25/2.20
% 10.25/2.20 Further assumptions not needed in the proof:
% 10.25/2.20 --------------------------------------------
% 10.25/2.20 difference_defn, equal_defn, equal_member_defn, intersection_defn,
% 10.25/2.20 reflexivity_of_subset, subset_defn, union_defn
% 10.25/2.20
% 10.25/2.20 Those formulas are unsatisfiable:
% 10.25/2.20 ---------------------------------
% 10.25/2.20
% 10.25/2.20 Begin of proof
% 10.25/2.21 |
% 10.25/2.21 | ALPHA: (symmetric_difference_defn) implies:
% 10.25/2.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v0, v1) = v2)
% 10.25/2.21 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 10.25/2.21 | (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 &
% 10.25/2.21 | union(v2, v4) = v3 & $i(v4) & $i(v3)))
% 10.25/2.21 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v1, v0) = v2)
% 10.25/2.21 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 10.25/2.21 | (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 &
% 10.25/2.21 | union(v4, v2) = v3 & $i(v4) & $i(v3)))
% 10.25/2.21 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0,
% 10.25/2.21 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 10.25/2.21 | (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) =
% 10.25/2.21 | v2 & $i(v4) & $i(v3) & $i(v2)))
% 10.25/2.21 |
% 10.25/2.21 | ALPHA: (difference_into_intersection) implies:
% 10.25/2.21 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) =
% 10.25/2.21 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (difference(v0, v2) =
% 10.25/2.21 | v3 & difference(v0, v1) = v3 & $i(v3)))
% 10.25/2.21 |
% 10.25/2.21 | ALPHA: (difference_distributes_over_union) implies:
% 10.25/2.22 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 10.25/2.22 | ~ (difference(v3, v2) = v4) | ~ (union(v0, v1) = v3) | ~ $i(v2) |
% 10.25/2.22 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (difference(v1,
% 10.25/2.22 | v2) = v6 & difference(v0, v2) = v5 & union(v5, v6) = v4 & $i(v6)
% 10.25/2.22 | & $i(v5) & $i(v4)))
% 10.25/2.22 |
% 10.25/2.22 | ALPHA: (commutativity_of_union) implies:
% 10.25/2.22 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~
% 10.25/2.22 | $i(v1) | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2)))
% 10.25/2.22 |
% 10.25/2.22 | ALPHA: (commutativity_of_intersection) implies:
% 10.25/2.22 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) =
% 10.25/2.22 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2)))
% 10.25/2.22 |
% 10.25/2.22 | ALPHA: (commutativity_of_symmetric_difference) implies:
% 10.25/2.22 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1,
% 10.25/2.22 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1)
% 10.25/2.22 | = v2 & $i(v2)))
% 10.25/2.22 |
% 10.25/2.22 | ALPHA: (function-axioms) implies:
% 10.25/2.22 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.25/2.22 | (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 10.25/2.22 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.25/2.22 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 10.25/2.22 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.25/2.22 | (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3,
% 10.25/2.22 | v2) = v0))
% 10.25/2.22 |
% 10.25/2.22 | DELTA: instantiating (prove_th96) with fresh symbols all_16_0, all_16_1,
% 10.25/2.22 | all_16_2, all_16_3, all_16_4, all_16_5 gives:
% 10.25/2.22 | (12) ~ (all_16_0 = all_16_3) & intersection(all_16_5, all_16_4) = all_16_1
% 10.25/2.22 | & symmetric_difference(all_16_5, all_16_4) = all_16_3 &
% 10.25/2.22 | difference(all_16_2, all_16_1) = all_16_0 & union(all_16_5, all_16_4)
% 10.25/2.22 | = all_16_2 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & $i(all_16_3)
% 10.25/2.22 | & $i(all_16_4) & $i(all_16_5)
% 10.25/2.22 |
% 10.25/2.22 | ALPHA: (12) implies:
% 10.25/2.23 | (13) ~ (all_16_0 = all_16_3)
% 10.25/2.23 | (14) $i(all_16_5)
% 10.25/2.23 | (15) $i(all_16_4)
% 10.25/2.23 | (16) $i(all_16_1)
% 10.25/2.23 | (17) union(all_16_5, all_16_4) = all_16_2
% 10.25/2.23 | (18) difference(all_16_2, all_16_1) = all_16_0
% 10.25/2.23 | (19) symmetric_difference(all_16_5, all_16_4) = all_16_3
% 10.25/2.23 | (20) intersection(all_16_5, all_16_4) = all_16_1
% 10.25/2.23 |
% 10.25/2.23 | GROUND_INST: instantiating (6) with all_16_4, all_16_5, all_16_2, simplifying
% 10.25/2.23 | with (14), (15), (17) gives:
% 10.25/2.23 | (21) union(all_16_4, all_16_5) = all_16_2 & $i(all_16_2)
% 10.25/2.23 |
% 10.25/2.23 | ALPHA: (21) implies:
% 10.25/2.23 | (22) union(all_16_4, all_16_5) = all_16_2
% 10.25/2.23 |
% 10.25/2.23 | GROUND_INST: instantiating (5) with all_16_5, all_16_4, all_16_1, all_16_2,
% 10.25/2.23 | all_16_0, simplifying with (14), (15), (16), (17), (18) gives:
% 10.25/2.23 | (23) ? [v0: $i] : ? [v1: $i] : (difference(all_16_4, all_16_1) = v1 &
% 10.25/2.23 | difference(all_16_5, all_16_1) = v0 & union(v0, v1) = all_16_0 &
% 10.25/2.23 | $i(v1) & $i(v0) & $i(all_16_0))
% 10.25/2.23 |
% 10.25/2.23 | GROUND_INST: instantiating (8) with all_16_4, all_16_5, all_16_3, simplifying
% 10.25/2.23 | with (14), (15), (19) gives:
% 10.25/2.23 | (24) symmetric_difference(all_16_4, all_16_5) = all_16_3 & $i(all_16_3)
% 10.25/2.23 |
% 10.25/2.23 | ALPHA: (24) implies:
% 10.25/2.23 | (25) symmetric_difference(all_16_4, all_16_5) = all_16_3
% 10.25/2.23 |
% 10.25/2.23 | GROUND_INST: instantiating (3) with all_16_5, all_16_4, all_16_3, simplifying
% 10.25/2.23 | with (14), (15), (19) gives:
% 10.25/2.23 | (26) ? [v0: $i] : ? [v1: $i] : (difference(all_16_4, all_16_5) = v1 &
% 10.25/2.23 | difference(all_16_5, all_16_4) = v0 & union(v0, v1) = all_16_3 &
% 10.25/2.23 | $i(v1) & $i(v0) & $i(all_16_3))
% 10.25/2.23 |
% 10.25/2.23 | GROUND_INST: instantiating (7) with all_16_4, all_16_5, all_16_1, simplifying
% 10.25/2.23 | with (14), (15), (20) gives:
% 10.25/2.23 | (27) intersection(all_16_4, all_16_5) = all_16_1 & $i(all_16_1)
% 10.25/2.23 |
% 10.25/2.23 | ALPHA: (27) implies:
% 10.25/2.23 | (28) intersection(all_16_4, all_16_5) = all_16_1
% 10.25/2.23 |
% 10.25/2.23 | GROUND_INST: instantiating (4) with all_16_5, all_16_4, all_16_1, simplifying
% 10.25/2.23 | with (14), (15), (20) gives:
% 10.25/2.23 | (29) ? [v0: $i] : (difference(all_16_5, all_16_1) = v0 &
% 10.25/2.23 | difference(all_16_5, all_16_4) = v0 & $i(v0))
% 10.25/2.23 |
% 10.25/2.23 | DELTA: instantiating (29) with fresh symbol all_24_0 gives:
% 10.25/2.23 | (30) difference(all_16_5, all_16_1) = all_24_0 & difference(all_16_5,
% 10.25/2.23 | all_16_4) = all_24_0 & $i(all_24_0)
% 10.25/2.23 |
% 10.25/2.23 | ALPHA: (30) implies:
% 10.25/2.24 | (31) difference(all_16_5, all_16_4) = all_24_0
% 10.25/2.24 | (32) difference(all_16_5, all_16_1) = all_24_0
% 10.25/2.24 |
% 10.25/2.24 | DELTA: instantiating (26) with fresh symbols all_32_0, all_32_1 gives:
% 10.25/2.24 | (33) difference(all_16_4, all_16_5) = all_32_0 & difference(all_16_5,
% 10.25/2.24 | all_16_4) = all_32_1 & union(all_32_1, all_32_0) = all_16_3 &
% 10.25/2.24 | $i(all_32_0) & $i(all_32_1) & $i(all_16_3)
% 10.25/2.24 |
% 10.25/2.24 | ALPHA: (33) implies:
% 10.25/2.24 | (34) $i(all_32_1)
% 10.25/2.24 | (35) difference(all_16_5, all_16_4) = all_32_1
% 10.25/2.24 | (36) difference(all_16_4, all_16_5) = all_32_0
% 10.25/2.24 |
% 10.25/2.24 | DELTA: instantiating (23) with fresh symbols all_34_0, all_34_1 gives:
% 10.25/2.24 | (37) difference(all_16_4, all_16_1) = all_34_0 & difference(all_16_5,
% 10.25/2.24 | all_16_1) = all_34_1 & union(all_34_1, all_34_0) = all_16_0 &
% 10.25/2.24 | $i(all_34_0) & $i(all_34_1) & $i(all_16_0)
% 10.25/2.24 |
% 10.25/2.24 | ALPHA: (37) implies:
% 10.25/2.24 | (38) $i(all_34_0)
% 10.25/2.24 | (39) union(all_34_1, all_34_0) = all_16_0
% 10.25/2.24 | (40) difference(all_16_5, all_16_1) = all_34_1
% 10.25/2.24 | (41) difference(all_16_4, all_16_1) = all_34_0
% 10.25/2.24 |
% 10.25/2.24 | GROUND_INST: instantiating (10) with all_24_0, all_32_1, all_16_4, all_16_5,
% 10.25/2.24 | simplifying with (31), (35) gives:
% 10.25/2.24 | (42) all_32_1 = all_24_0
% 10.25/2.24 |
% 10.25/2.24 | GROUND_INST: instantiating (10) with all_24_0, all_34_1, all_16_1, all_16_5,
% 10.25/2.24 | simplifying with (32), (40) gives:
% 10.25/2.24 | (43) all_34_1 = all_24_0
% 10.25/2.24 |
% 10.25/2.24 | REDUCE: (39), (43) imply:
% 10.25/2.24 | (44) union(all_24_0, all_34_0) = all_16_0
% 10.25/2.24 |
% 10.25/2.24 | REDUCE: (34), (42) imply:
% 10.25/2.24 | (45) $i(all_24_0)
% 10.25/2.24 |
% 10.25/2.24 | GROUND_INST: instantiating (5) with all_16_4, all_16_5, all_16_1, all_16_2,
% 10.25/2.24 | all_16_0, simplifying with (14), (15), (16), (18), (22) gives:
% 10.25/2.24 | (46) ? [v0: $i] : ? [v1: $i] : (difference(all_16_4, all_16_1) = v0 &
% 10.25/2.24 | difference(all_16_5, all_16_1) = v1 & union(v0, v1) = all_16_0 &
% 10.25/2.24 | $i(v1) & $i(v0) & $i(all_16_0))
% 10.25/2.24 |
% 10.25/2.24 | GROUND_INST: instantiating (6) with all_34_0, all_24_0, all_16_0, simplifying
% 10.25/2.24 | with (38), (44), (45) gives:
% 10.25/2.24 | (47) union(all_34_0, all_24_0) = all_16_0 & $i(all_16_0)
% 10.25/2.24 |
% 10.25/2.24 | ALPHA: (47) implies:
% 10.25/2.24 | (48) union(all_34_0, all_24_0) = all_16_0
% 10.25/2.24 |
% 10.25/2.24 | GROUND_INST: instantiating (2) with all_16_4, all_16_5, all_24_0, simplifying
% 10.25/2.24 | with (14), (15), (31) gives:
% 10.25/2.24 | (49) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_16_4, all_16_5)
% 10.25/2.24 | = v0 & difference(all_16_4, all_16_5) = v1 & union(v1, all_24_0) =
% 10.25/2.24 | v0 & $i(v1) & $i(v0))
% 10.25/2.24 |
% 10.25/2.24 | GROUND_INST: instantiating (1) with all_16_4, all_16_5, all_32_0, simplifying
% 10.25/2.25 | with (14), (15), (36) gives:
% 10.25/2.25 | (50) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_16_4, all_16_5)
% 10.25/2.25 | = v0 & difference(all_16_5, all_16_4) = v1 & union(all_32_0, v1) =
% 10.25/2.25 | v0 & $i(v1) & $i(v0))
% 10.25/2.25 |
% 10.25/2.25 | GROUND_INST: instantiating (3) with all_16_4, all_16_5, all_16_3, simplifying
% 10.25/2.25 | with (14), (15), (25) gives:
% 10.25/2.25 | (51) ? [v0: $i] : ? [v1: $i] : (difference(all_16_4, all_16_5) = v0 &
% 10.25/2.25 | difference(all_16_5, all_16_4) = v1 & union(v0, v1) = all_16_3 &
% 10.25/2.25 | $i(v1) & $i(v0) & $i(all_16_3))
% 10.25/2.25 |
% 10.25/2.25 | GROUND_INST: instantiating (4) with all_16_4, all_16_5, all_16_1, simplifying
% 10.25/2.25 | with (14), (15), (28) gives:
% 10.25/2.25 | (52) ? [v0: $i] : (difference(all_16_4, all_16_1) = v0 &
% 10.25/2.25 | difference(all_16_4, all_16_5) = v0 & $i(v0))
% 10.25/2.25 |
% 10.25/2.25 | DELTA: instantiating (52) with fresh symbol all_46_0 gives:
% 10.25/2.25 | (53) difference(all_16_4, all_16_1) = all_46_0 & difference(all_16_4,
% 10.25/2.25 | all_16_5) = all_46_0 & $i(all_46_0)
% 10.25/2.25 |
% 10.25/2.25 | ALPHA: (53) implies:
% 10.25/2.25 | (54) difference(all_16_4, all_16_5) = all_46_0
% 10.25/2.25 | (55) difference(all_16_4, all_16_1) = all_46_0
% 10.25/2.25 |
% 10.25/2.25 | DELTA: instantiating (50) with fresh symbols all_60_0, all_60_1 gives:
% 10.25/2.25 | (56) symmetric_difference(all_16_4, all_16_5) = all_60_1 &
% 10.25/2.25 | difference(all_16_5, all_16_4) = all_60_0 & union(all_32_0, all_60_0)
% 10.25/2.25 | = all_60_1 & $i(all_60_0) & $i(all_60_1)
% 10.25/2.25 |
% 10.25/2.25 | ALPHA: (56) implies:
% 10.25/2.25 | (57) union(all_32_0, all_60_0) = all_60_1
% 10.25/2.25 | (58) difference(all_16_5, all_16_4) = all_60_0
% 10.25/2.25 | (59) symmetric_difference(all_16_4, all_16_5) = all_60_1
% 10.25/2.25 |
% 10.25/2.25 | DELTA: instantiating (49) with fresh symbols all_68_0, all_68_1 gives:
% 10.25/2.25 | (60) symmetric_difference(all_16_4, all_16_5) = all_68_1 &
% 10.25/2.25 | difference(all_16_4, all_16_5) = all_68_0 & union(all_68_0, all_24_0)
% 10.25/2.25 | = all_68_1 & $i(all_68_0) & $i(all_68_1)
% 10.25/2.25 |
% 10.25/2.25 | ALPHA: (60) implies:
% 10.25/2.25 | (61) difference(all_16_4, all_16_5) = all_68_0
% 10.25/2.25 | (62) symmetric_difference(all_16_4, all_16_5) = all_68_1
% 10.25/2.25 |
% 10.25/2.25 | DELTA: instantiating (51) with fresh symbols all_78_0, all_78_1 gives:
% 10.25/2.25 | (63) difference(all_16_4, all_16_5) = all_78_1 & difference(all_16_5,
% 10.25/2.25 | all_16_4) = all_78_0 & union(all_78_1, all_78_0) = all_16_3 &
% 10.25/2.25 | $i(all_78_0) & $i(all_78_1) & $i(all_16_3)
% 10.25/2.25 |
% 10.25/2.25 | ALPHA: (63) implies:
% 10.25/2.25 | (64) difference(all_16_5, all_16_4) = all_78_0
% 10.25/2.25 | (65) difference(all_16_4, all_16_5) = all_78_1
% 10.25/2.25 |
% 10.25/2.25 | DELTA: instantiating (46) with fresh symbols all_80_0, all_80_1 gives:
% 10.25/2.25 | (66) difference(all_16_4, all_16_1) = all_80_1 & difference(all_16_5,
% 10.25/2.25 | all_16_1) = all_80_0 & union(all_80_1, all_80_0) = all_16_0 &
% 10.25/2.25 | $i(all_80_0) & $i(all_80_1) & $i(all_16_0)
% 10.25/2.25 |
% 10.25/2.25 | ALPHA: (66) implies:
% 10.25/2.25 | (67) difference(all_16_4, all_16_1) = all_80_1
% 10.25/2.25 |
% 10.25/2.26 | GROUND_INST: instantiating (10) with all_24_0, all_78_0, all_16_4, all_16_5,
% 10.25/2.26 | simplifying with (31), (64) gives:
% 10.25/2.26 | (68) all_78_0 = all_24_0
% 10.25/2.26 |
% 10.25/2.26 | GROUND_INST: instantiating (10) with all_60_0, all_78_0, all_16_4, all_16_5,
% 10.25/2.26 | simplifying with (58), (64) gives:
% 10.25/2.26 | (69) all_78_0 = all_60_0
% 10.25/2.26 |
% 10.25/2.26 | GROUND_INST: instantiating (10) with all_32_0, all_68_0, all_16_5, all_16_4,
% 10.25/2.26 | simplifying with (36), (61) gives:
% 10.25/2.26 | (70) all_68_0 = all_32_0
% 10.25/2.26 |
% 10.25/2.26 | GROUND_INST: instantiating (10) with all_68_0, all_78_1, all_16_5, all_16_4,
% 10.25/2.26 | simplifying with (61), (65) gives:
% 10.25/2.26 | (71) all_78_1 = all_68_0
% 10.25/2.26 |
% 10.25/2.26 | GROUND_INST: instantiating (10) with all_46_0, all_78_1, all_16_5, all_16_4,
% 10.25/2.26 | simplifying with (54), (65) gives:
% 10.25/2.26 | (72) all_78_1 = all_46_0
% 10.25/2.26 |
% 10.25/2.26 | GROUND_INST: instantiating (10) with all_34_0, all_80_1, all_16_1, all_16_4,
% 10.25/2.26 | simplifying with (41), (67) gives:
% 10.25/2.26 | (73) all_80_1 = all_34_0
% 10.25/2.26 |
% 10.25/2.26 | GROUND_INST: instantiating (10) with all_46_0, all_80_1, all_16_1, all_16_4,
% 10.25/2.26 | simplifying with (55), (67) gives:
% 10.25/2.26 | (74) all_80_1 = all_46_0
% 10.25/2.26 |
% 10.25/2.26 | GROUND_INST: instantiating (11) with all_16_3, all_68_1, all_16_5, all_16_4,
% 10.25/2.26 | simplifying with (25), (62) gives:
% 10.25/2.26 | (75) all_68_1 = all_16_3
% 10.25/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (11) with all_60_1, all_68_1, all_16_5, all_16_4,
% 10.72/2.26 | simplifying with (59), (62) gives:
% 10.72/2.26 | (76) all_68_1 = all_60_1
% 10.72/2.26 |
% 10.72/2.26 | COMBINE_EQS: (73), (74) imply:
% 10.72/2.26 | (77) all_46_0 = all_34_0
% 10.72/2.26 |
% 10.72/2.26 | SIMP: (77) implies:
% 10.72/2.26 | (78) all_46_0 = all_34_0
% 10.72/2.26 |
% 10.72/2.26 | COMBINE_EQS: (68), (69) imply:
% 10.72/2.26 | (79) all_60_0 = all_24_0
% 10.72/2.26 |
% 10.72/2.26 | COMBINE_EQS: (71), (72) imply:
% 10.72/2.26 | (80) all_68_0 = all_46_0
% 10.72/2.26 |
% 10.72/2.26 | SIMP: (80) implies:
% 10.72/2.26 | (81) all_68_0 = all_46_0
% 10.72/2.26 |
% 10.72/2.26 | COMBINE_EQS: (70), (81) imply:
% 10.72/2.26 | (82) all_46_0 = all_32_0
% 10.72/2.26 |
% 10.72/2.26 | SIMP: (82) implies:
% 10.72/2.26 | (83) all_46_0 = all_32_0
% 10.72/2.26 |
% 10.72/2.26 | COMBINE_EQS: (75), (76) imply:
% 10.72/2.26 | (84) all_60_1 = all_16_3
% 10.72/2.26 |
% 10.72/2.26 | COMBINE_EQS: (78), (83) imply:
% 10.72/2.26 | (85) all_34_0 = all_32_0
% 10.72/2.26 |
% 10.72/2.26 | REDUCE: (48), (85) imply:
% 10.72/2.26 | (86) union(all_32_0, all_24_0) = all_16_0
% 10.72/2.26 |
% 10.72/2.26 | REDUCE: (57), (79), (84) imply:
% 10.72/2.26 | (87) union(all_32_0, all_24_0) = all_16_3
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (9) with all_16_3, all_16_0, all_24_0, all_32_0,
% 10.72/2.26 | simplifying with (86), (87) gives:
% 10.72/2.26 | (88) all_16_0 = all_16_3
% 10.72/2.26 |
% 10.72/2.26 | REDUCE: (13), (88) imply:
% 10.72/2.26 | (89) $false
% 10.72/2.27 |
% 10.72/2.27 | CLOSE: (89) is inconsistent.
% 10.72/2.27 |
% 10.72/2.27 End of proof
% 10.72/2.27 % SZS output end Proof for theBenchmark
% 10.72/2.27
% 10.72/2.27 1652ms
%------------------------------------------------------------------------------